METAPHOR AND COGNITION
STUDIES IN COGNITIVE SYSTEMS VOLUME 13
EDITOR
James H. Fetzer, University of Minnesota, Duluth ADVISORY EDITORIAL BOARD
Fred Dretske, Stanford University Ellery Eells, University of Wisconsin, Madison Alick Elithom, Royal Free Hospital, London Jerry Fodor, Rutgers University Alvin Goldman, University of Arizona Jaakko Hintikka, Boston University Frank Keil, Cornell University William Rapaport, State University of New York at Buffalo Barry Richards, Imperial College, London Stephen Stich, Rutgers University Lucia Vaina, B osto n University Terry Winograd, Stanford University
The titles published in this series are listed at the end of this volume.
METAPHOR AND COGNITION An lnteractionist Approach
by BIPIN INDURKHY A
Computer Science Department. Boston University, Boston, MA. U.S.A.
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'' KLUWER ACADEMIC PUBLISHERS DORDRECHT I BOSTON I LONDON
Library of Congress Cataloging-in-Publication Data InoJrkhy!.
B1p1n .
Metapho�
1959cogn1t1on
anc
an
Jnterac:1on1st
approach
1
B1p1n
'ncunhva. � .
c• .
Incluoes ISBN
1.
--
IStud1es
0-7923-1687-8
Symbcl1sm
alk .
Analogy--Psvchciog;cal
5.
Cogn1t1on.
I.
T1tle.
cogn•t•ve systems
references
3.
BC'l58.l53
1n
o>�11ogr3ph1ca1
2.
;
v .
131
1ndexes.
paperl
�etaphor--Psycho1oglca1
aspects.
II.
and
4.
S•m•larlty
aspects.
Ser1es.
1992
153--oc20
92-7189
ISBN 0-7923-1687-8
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 Nij hoff, 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-ji"ee paper On the Cover: Other World by M.C. Escher. © 194 7 M.C. Escher I Cordon Art - Baam- Holland Collection Haags Gemeentemuseum, The Hague All Rights Reserved
© 1992 Kluwer Academic Publishers 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 photocopyi.ng, recording or by any information storage and retrieval system, without written permission from the copyright owner. Printed in the Netherlands
l'mL tke
memory of my grandmother and to Xela
SERIES PREFACE This series will include monographs and collections of studies devoted to the investigation and exploration of knowledge, information, and data-processing systems of all kinds, no matter whether human, (other) animal, or machine. Its scope is intended to span the full range of interests from classical problems in the philosophy of mind and philosophical psychology through issues in cognitive psychology and sociobiology (concerning the mental powers of other species) to ideas related to artificial intelligence and com puter science. While primary emphasis will be placed upon theoretical, conceptual, and epistemological aspects of these problems and domains, empirical, experimental, and methodological studies will also appear from time to time. The nature of metaphor and the nature of cognition are both illuminated in this stimulating study by Bipin Indurkhya. Beginning with a distinction between conventional metaphors, similarity-based metaphors, and similarity creating metaphors, he elaborates the idea that similarity-creating metaphors, which affect an interaction between the source of the metaphor and its target, fulfill a fundamental role in human cognition. In addition to the development of his own account, lndurkhya thoughtfully examines alternative theories and evaluates
their strengths and weaknesses.
By placing the problems of
metaphor within the framework of cognition, this work makes an exception ally valuable contribution to understanding the nature of the mind.
J. H. F.
vii
Contents Acknowledgments
XV
Pro logue
The Pro b l e m
I 1
11
Characterizing Metaphor
13
1.1 1 .2
Introduction . . . . . . . Some Examples of Metaphors
13 14
1 .3
Characteristics of Linguistic. Metap hors
17
1 .4
Degrees of Metaphoric Conten t : T h e Conventional vs. the Metaphorical Metaphors i n Non- Linguistic Domains Metaphors, S i m i les, A nalogies and Models 1 . 6 . 1 Metaphors and S i m iles . . 1 . 6 . 2 Metaphors a n d Analogies . 1 . 6 . 3 Metaphors and Models Conclusions . . . . . .
1 .5 1 .6
1.7 2
1
.
.
.
.
Enter Similarity-Creating Metaphors
19 21 26 26 28 34 36 39
2.1 2.2 2.3
Introduction . . . . . . . . . Some Examples of S i m i larity- Creat i ng Metaphors Psy chological S t u dies of t he Creation of S i m i larity .
40
2.4
Creation of S i m i larity i n Metaphor- Related P henomena
48
.
.
.
.
.
39
45
X
2.5
2.6 3
48 49 54 56
2.5. 1
S i m i lari ties Before and A fter the Metaphor .
57
2.5.2
S i m i l arities A fter but Not Before the Met aphor
59
2 . 5 .3 S i m i larities Before but not A fter the Metaphor . Conclusions: The Problem of Sim i larity- Creati ng Metap hors
63 63
Approaches to Similarity-Creating Metaphors
65
3.1 3 .2 3 .3
Introdu ction Max B lack . P au l Ricoeur
65 68 74
3 .4
Carl H ausman
75
3.5
W heel wright - M ac Cormac
76
3.6
3.8
The Lakoffian A pproach . . M y Earlier Approach . . . . K i t t ay's Perspecti val Theory
3.9
Conclusions . . . . . .
78 84 86 90
Cognition as Interaction
93
4. 1 4. 2
93 94
3.7
4
2 .4 . 1 S i m i le . 2 . 4 . 2 A nalogy 2.4 . 3 Models . S i m ilari ties and Creati ve P roblem Solving
Introduct ion . . . . . . Empirical S upport for the Interaction View of Cogni tion 4 . 2. 1 4.2.2 4 . 2. 3 4 .2.4
4.3 4. 4 4.5
4.6
Concepts are M ore than Aggregates of Sense D ata .
Concepts can O rganize the World D i fferently . . . . Concepts Cannot O rgani ze the Worl d Arbitrarily . 'Uni ver �als' and the Physiological Basis of Cognition 4.2.5 Summary . . . . . . . . . . . . From Kant to Goodman: Worldmaking P i aget's Constructivism . . . . . . . . Lakoff-Johnson: The Bodily Basis of Cognition . Conclusions . . . . . . . . . . . . . . . . . . . .
95 1 00 1 04 1 05 111 111 116
1 24 1 27
xi
A Theory
II 5
129
An Interactionist Approach to Cognition: Informal Overview
5. 1
Introduct ion .
5.2
A n Example .
5.3 5.4 5.5 5.6 5.7
6
131
1 35 Concept Networks . 151 Environments and Sensorimotor Data Sets 1 58 Cogni t i ve Relations and Coherency 161 A ccommodat ion and Projection 1 64 Cogni t i ve Models . . . . . . 1 69 5 . 7 . 1 G roupings on the Env i ronment 1 70 5 . 7 . 2 A ccom modation and Projection : A nother Perspect i ve . 1 74 5.7.3 5.7.4
5.8 5.9
131
Representation and Description . . . . . .
Layered Cogni t i ve System and M ulti p l e "Worlds"
1 76 1 78 1 79
S u mm ary . . . . . . . . . . . . . . . . . .
187
Some O ther M i scellaneous Notions . . .
.
An Interactionist Approach to Cognition: Formal Concepts
6. 1
Introduction . . . . . .
6.2 6.3
Classes and G roupings Relations and Induced G roupi ngs 6 . 3 . 1 P reli m i nary Defin i tions . 6.3.2 6.3.3
6.4
Functions and Operators 6.4.1
6.4.2
6.5
D i functional Relations . Relations Within a C l ass Functions Operators
189
1 89 191 1 94 1 94 1 96 201 202 203 204
A lgebras and Structures 6 . 5 . 1 A lgebras . . . . . 6 . 5. 2 D escriptions and S t ructures
20.5 205 209
6.5.3
214
Closu res and Generating Classes .
xii
6.5.4 6.5.5
C losu re Over Operators Computabi l i ty of O perators
6.6
Subalgebras a n d F i n i t e Generat i v i ty
216 2 16 2 17
6.7
G roupings on A l gebras: A lgebras o f Classes
220
6.8
Rel at ions Between A l gebras: Correspondences 6 . 8. 1 P roducts o f Algebras and Correspondences 6 . 8 . 2 G roupi ngs Induced b y Correspondences 6 . 8 . 3 Difunctional Correspondences
223 224 227 229
.
6.9
Cogn i t i ve Models . . . . . . . . . . . 6 . 9 . 1 Basic Defi n i tion . . . . . . . 6. 9 . 2 Local Coherency and Coherency . 6. 9 . 3 Some Characteristics of Cogni t i ve Models 6 . 10 Cogni t i ve Models Over an Environment .
235 236
6.11 P roj ecti ve and A ccommodating Models 6.12 F i n i te Representab i l i ty and Coherency
239 24 1
An Interaction Theory of Metaphor
245
7. 1 7.2 7.3 7.4
I n t roduction . . . . . . M etaphor as P rojection . omenclat u re Associ ated with Metaphor Modes of Metaphor . . . . . . . . . . . . 7. 4 . 1 S i m i l ari ty-Based ( Comparat i ve) Metaphors .
245 246 253 256 256
7.4.2
271
7.5
Summary .
.
7
III 8
.
Si m i l ari ty-Creating (Proj ective) Metaphors .
The Implications
Some Metaphor-Related Issues
8.1 8.2
232 232 234
279 283 285
Introduction . . . . . . . . . . T h e Thesis ' A ll K nowledge is M etaphorical'
286
8.2. 1 8.2.2
287 289
Version 1: All Knowledge i s Projecti ve Version 2 : A l l Thought i s Comparati ve
285
xiii
8.2.3 8.2.4 8.3
8.4 9
Version 3 : A ll Conventional Mean ings A rise By Way of M et aphor . . . . . . . . . L akoff- Mac Cormac Debate
Metaphor and Correctness . . . . . 8 . 3 . 1 Correctness, Trut h and Coherency . 8.3 . 2 U nderstanding v s . Correctness . . . 8 . 3 . 3 Conventional a n d M etaphorical Correct ness A p tness ( Q u ality ) of Metaphor . . . . . . .
On Predictive Analogy and Induction
9.1 9.2
I ntroduction . . . . . . . . . . . . Predictive A nalogy and Metaphor
9.3
The Search for Logical Justi fication o f P red i ct i ve A nalogy 9.3. 1 9.3.2
9.4
9.5 9.6 9.7
P redictive A nalogy as an Inductive Process . . . . . P redictive A nalogy a s a First O rder Generali zation
9 . 3 . 3 P redictive A nalogy as a Second O rder General ization The Search for Empi rical J ustification of P red i c t i ve Analogy
290 292 30 1 301 305 306 309 315 . 315
318 322 323 325 327
329 9 .4 . 1 Evidence from C l assroom Experiments . . . . . . . . 329 9 . 4 . 2 Evidence from Real-World Problem-Solving Activit i es . 332 The ' D ar k Side' of P redictive A nalogy 334 339 P redi c t i ve A nalogy and Cogn i tion . . . The Problem of Induction . . 343
9.8
The S am p l i ng Princip le, Randomness, and the Generalized Grue Paradox . . . . . . . . 9.9 The ' D ark Side' of Induction . 9 . 1 0 Induction in Cogni t io n . . . .
344 350 352
Computational Approaches to Metaphor and Analogy
357
10 On
10.1
Introduction
.
. . . . . . . . . . . . .
357
1 0 .2 Comp u t at i onal Approaches to Linguistic Metaphors 1 0 . 3 Com p ut ational A pproaches to Predi c t i ve A nalogy
. . . . . . .
360 365
1 0 . 4 A Computat iona] Model of Creati ve Analogies: Douglas H ofstadter . . . . .. . . . . . . .
376
xiv
1 0 .4 . 1 A n Aside: Context- Sens i t ivity of Descriptions i n Evan s ' . . . . . . . . . . . . . . . . . . . . . 378 Approach 10 . 4 . 2 Resumption: Hofstadter and M i t chell ' s Copycat . 384 1 0. 5 P rojecti ve ( S i m ilarity- C reati n g ) Metaphor in Artificial Intelligence . . . . . . . . . . . . 392 10 . 5 . 1 Projection as ' Top- Dow n ' G rouping 392 . 395 1 0 . 5 . 2 Novel vs. Conventional P rojection . .
.
.
.
.
.
1 0 . 5 . 3 The C reation of S i m ilarity . . . . . 10. 6 Model ing Met aphor as Change of Representat i on 10 . 7 Conclusions . . . . . . . . . . . . . . . . . . . . .
. 400 .. 401 . 408
B ib l iograp hy
411
N ame Index
433
Subject Index
439
Acknowledgments I wou l d l i ke to express my thanks and appreciat ion to the following people who h ave contribu ted to this manuscript in various ways: •
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To Remko Scha for providing encouragement, i deas , and much con structi ve criticism t h rough the ent i re project . To M ark Joh n son for providing an encouragi ng feedback on a long essay t h at I wrote as an abridged version of t he book i n 1 988. To Erica Melis for providing many usefu l comments on the abridged version of the book an d on earlier drafts of some chapters. To Sylvia Candelari a de Ram for a t horough readi n g of early drafts of Chapters 1 , 5, 6 and 7 . Her numerous comments , especially on Chapter 6 , were i nstrumental in add i n g to the clarity of the fi nal draft . To George Lakoff for providing an encouragi ng feedback on an earlier draft of Chapter 7 and for providi ng val uable com ments . To Melan ie M itchell for pai nstakingly goi ng through a very rough ver sion of the enti re manuscri p t . Her detai led comments were an invalu able aid in revising the manuscript . To M argo G uerti n and Scott O ' H ara for read i ng through coun tless drafts and catchi ng m any syntactic and semantic errors . To M ary A t k i n s , Regina Bl aney and Beryl Nel on for read ing parts of the fi n al draft and offering comments . To Doug Hofstadter and Melanie Mitchell for ments on parts of the final manuscri p t .
providing extensive
com
To Spyridon B raoudakis a n d Dan Solis for carefully going over the entire fi n al draft and mak i ng n umerous comments. To Marie- Dom i n i q ue G ineste and an anonymous Academic P ublishers for wri t i ng very positive and
reviewer for Kluwer en c o u rag i n g revi ews
of the m a n u s c r i p t, an d for mak i ng comments on var i ous parls of i llhaL were q u i te helpfu l d u r i n g rev i si on s.
XV
xvi •
•
To S i mon Ross for doing a wonderfu l j ob as the edi tor i n get t i n g t h e manuscript reviewed prompt ly, a n d i n offeri n g much useful advice i n get t i ng the copyright permissions a n d i n the p reparation of the camera ready copy. To the N at ional Scien ce Foundation for grant No. I R I - 9 1 05806, w h i ch supported in part the p reparation of t h e manuscrip t .
I would also l i ke t o express m y grat i t ude to various i nd i v iduals and i nstitu t ions for allowing me to i nclude some copyrighted m aterial in t h i s book: •
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Oth e r World by M . C . Escher ( on the cover) : @ 1 947 M . C . Escher / Cordon Art - Baarn - Holland, Collection l-Iaags Gemeentemuseum , The H ague. Reproduced w i t h the k i n d permission o f Cordon Art a n d H aags Gemeentemuseum. Fog by Carl Sandburg ( page 2): From C H I C A G O POEMS by Carl Sandburg, @19 1 6 by H ol t , Rinehart and Winston , I n c . and renewed 1 944 by Carl Sandburg, repri nted w i t h the permi ssion of H arcourt Brace Jovanovich, Inc. Pa rk bei Lu(zern) (Pm·k n ea r L u(cerne)) ( 1 93 8 ) by Paul K lee ( plate 1 ) : Paul Klee- S t i ft ung/Kunstmuseum Bern , @ 1 9 9 1 by VAG A , New York ; reproduced w i t h t h e k i n d permission o f Kunstmuseum Bern . Th e MmTiage of Giovan n i (?), Arnolfin i and Giovan n a Cen a m i (?), ( 1 434) by J an Van Eyck ( plate 2 ) : The National G al lery, London, reproduced w i t h the k i n d permission of the National Gallery.
Quotat ions from A l fred H i tchcock ( pages 24 and 44 ) : @ 1 96 7 by Fran cois Tru ffaut , revised @ 1 984 by Francois Truffaut , reprinted i n the U.S. and C anada w i t h the permission of S imon & Schuster, and elsewhere w i t h the k i n d permission of Seeker and Warburg . While Hawthorn i n the West of Irela n d b y Eavan Boland (page 41): @1989 by Eavan Boland, original ly published in The New Yorker, reprinted w i t h t he kind permission of Eavan Bolan d and The New Yorker .
Se'ascape by Stephen Spender (page 42) : from C O L LECTED POEMS 1 928-1 985 by Stephen Spender, @ 1 946 by S t e p h e n
Excerpt from
Spender, repri nted i n the British Commonwealt h (excluding Canada) with the k i n d permi ssion of Faber and Faber Limited, and elsewhere with the permission of Random House, Inc.
XVII
•
Composition with Blu e and Yellow, (1935) by P iet Mon drian ( plate
3): Hirshhorn Museum and Sculpt u re Garden , Smithsonian Instit u
tion, G i ft of Joseph H. H i rshhorn Foun d at i o n , 1 972, ( photograph by Lee Stalsworth ) ; reproduced w i t h t he k i n d permission of H i rsh horn M useum and Sculptur e Garden . •
•
•
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Quotation from Piet Mondri an ( p age 43 ): @1986 by Harry Holtzman, reproduced w i t h the k i n d perm ission of Mr. Holtzman and G .K. Hall & Co. L e Cauter (Tea T ime), ( 1 9 1 1 ) by Jean Metzi nger ( p l ate 4 ) : P h iladel phia M u seum of Art : The Louise and Wal ter A rensberg Collection , reprod u ced w i t h the k i n d permission of P h i l adel p h i a M useum of A r t .
Figures from P. A . Kolers ' Aspects of Motion Pe 1·ception ( page 99 ) : @ 1 972 by Pergamon P ress , repri nted w i t h the k i n d perm i ssion of Perg amon P ress. Figu re from A . R. L ur i a's Cognitive Developm ent ( page 103): @ 1 976 by the P resident and Fel lows of H arvard Col l ege, repri nted with the kind permission of H arvard Un ivers i ty P ress . Q uotations and figures from T . G . Evans' " A Program for the Solution of a Class of Geometric- A n alogy I n telligence-Test Questions" ( Section 10.4.1): @ 1 968 by MIT P ress, reproduced here with the kind permis sion of M I T P ress.
Prologue This book i s about metaphor and cogni t ion , an d about the relations h i p between the two. W h i le t here remain s much dispute about w hat metaphor is, how it works, and what role i t plays in cognition , t here seems to be general agreement that metaphor i nvolves two objects or s i tuations and some kind of t ransference from one object or situation to the other. One object i s referred to a s t he topic, t he tenor, the primary subjec t , or t he t arget domai n , and t h e other object as t h e vehi cle, t he secon dary subjec t , o r t h e source domai n . For instan ce, in "The chairperson of the meeting plowed t h rough the agenda," the target is the meeti ng, the source is the act of plowing, and the transference exists i n being able to describe the meeting meaningfu l l y by using the seman t i cally distant term of ' p lowi ng'. I t i s also gen erally accepted that metaphors are not l i m i ted to individual words, or even p hrases, but a whole poem or a novel can be metaphorical as well . A nyone who h as read Dylan Thomas ' Th e fo1·ce that th m ugh the g1·een fuse drives th e flower, Mel v i l le's Moby Dick, or Hem i ngway's Th e Old Ma n a n d the Sea would know that these works become much more interesti ng and i nsightfu l when given an i nterpretation other than the l iteral one. H ere, while the source i s explicitly given , the target is not specified at all ; it is up to t he i ndivi dual reader to find her own t arget and carry out her own i nterpretation . The point i s that one needs a target domain and a meani ngful i n terpretation i n order for the work to become metaphorical . For i nstance, I once read an i nterpretation of Frank Baum 's Th e Wizm·d of Oz, a popular fantasy book t hat described i t as a sati re of the A merican pol i t i cal situation existi n g at the t ur n of the centu ry, when the book was first published.1 To get the satirical effect, however, the characters of the book need to be given an appropriate i n terpretation i n t hat context-t hat the Wicked Witch of th e East be identified with t h e fi n an c i al i nst i t u t i ons of the N or t h east e rn U.S., t h e T i n Woodman be identified wi th the industrial workers, t he Emerald City be identified w i t h Washington D . C., the cap i t al of the U.S., and so o n . Classification of metaphors themselves i s somewhat controversial. B u t for our purpose, we need only make a d i s t i n c t i o n between conve n t i on al m e t a phors, similarity-based met ap hors, and si milarity-creating metaphors. Con ventional met aphors are t hose met aphors t h at are so much a part of everyday speech that t hey seem hardly metaphorical . The 'plow ' me t apho r mentioned above is a case i n poi n t . Conventional metaphors are e v i den ce to the fact 11 remember reading it in the Sunday edition of the Buffalo News sometime in December 1987
2
Metaphor and Cognition
that metaphoric t ransference is not someth i ng confined to poetry and lit erat ure, but is very m u ch a part of our everyd ay speech . T hey h ave been studied extensively by George Lakoff and his colleagues [Lakoff & Joh nson 1 980; Lakoff & Turner 1989]. In thi s study, however, convent ional metap hors play only a minimal role. My main concern is not so much w i t h why our everyday concepts are structured i n one way rather t h an another, but w i t h how n e w concepts a n d mean ings emerge. S i m i l ari ty-based metaphors invite the reader to make a comparison be tween the source and the target , as the t ransference of meaning is based on some existing s i m i larity between them. For instance, in "The sky i s cry ing" the reader i s d rawn into comparin g the rain falling down from the sky w i t h t h e tears falling down from the eyes o f a person . T hese metaphors h ave been captured in what is commonly known as the compari son theory of metaphor [Henle 1 958]. In a similarity-creat i ng metaphor, however, t here are no similarities be tween the source and the target when the metaphor is first encountered . Yet , after the metaphor is assi m i lated , ( i f i t i s assimilated at all , ) t here are sim i l arities between the two. T hus, the metaphor c rea t es t he s i m ilarit i es between the source and the target . To appreciate the force of a s i m ilarity creating metaphor, t ry the following experi ment . For each of t he fol lowing pai rs of words, t ry to enumerate the simi lari t ies between the referen t s of the two words: snake-eel, dog-computer, snowsto1·m -autom ob ile, cat-fog, fog clock. For i n stance, for the snake- eel pair, you might say t h at t hey are both long, slithery, etc. I f you cannot find any similarities , j ust say so. G i ve yourself, say about five m inutes, for each pai r . Now consi der Carl San d b u rg's beaut i fu l poem Fog: The fog comes on l i t t le cat feet . It sits looki ng over harbor and c i ty on silent h au n ches and then moves on .
After readi ng the poem , the fog at once appears similar to the cat! T hey both creep up on you ever so silently. Moreover, I would be very surprised i f t his s i m i larity was inclu ded i n your initial comparison o f fog and cat, u nless you peeked ahead, or you were al ready fami liar with t he poem, and the words fog-cal remi n ded you of i t . Thus, i t wou l d be appropriate to acknowledge that
Prologue
3
t he metaphor created the s i m i larit ies . I f you need more convincing to accept the phenomenon of creation of similarity, I present m any more examples i n C h apter 2 , since similari ty-creati n g metaphors are m y pri mary concern i n t hi s book . The existence of s im ilarity-creating metaphors has not been u n i versally acknowledged . The reason i s that i n a s i m i l ari ty-creati n g metaphor, t here are always s i m i lari ties after t h e metaphor is p resented and u nderstood. So if a person is presented w i t h a metaphor, and then asked to explai n her under stan d i ng of i t , she would i n variably gi ve a similarity-based accoun t . But t h is fails to address the questi on o f whet her the simi larit i es were t here before the metaphor or not . ( O ne notable exception i s the i nteresting study of Cam ac and G lucksbu rg [ 1 984] , w h i ch is d iscussed i n C h apter 2 . ) Consequently, i t might n o t b e surprising t hat almost all t h e research on metaphor i n cogni t i ve science has been in the p u rsu i t of similarity-based metaphors. E m p i ri cal studies and theories h ave sought to articulate exactly w hat k i n ds of si milari t i es u nderlie metaphors [ Gentner, Falkenhai ner, & S korstad 198 7 ; Gentner & S tuart 1 983; M algady & Johnson 1 980; O rtony 1 979] . Following these leads , the compu t at i on al models h ave focused either on b o w t h e s i m i l arities might be comp uted , gi ven a source and a target ( Weiner 1 984 , 1 985; Fass 1989); or on how the similar i ties might be used i f t hey are expl icitly given (Carbonell 1 982; Marti n 1 988) . S i mi larity-creati n g metaphors have been left out i n t he cold . I nteres t i ngly, however, a n approach to metaphor i n t he phi losoph ical trad i tion-an approach t h at is widely known as the intera ction th eory-- w as created expressly to account for similarity-creating metaphors. Originat i ng i n I.A. Richards' Philosophy of Rhetoric, the i nteraction t heory owes its present for m l ar g ely to the works of such scholars i:1S Max Bl ack [1962; 1979], Carl H ausman [ 1 983 ; 1984; 1989], and Paul Ricoeur [1977]. Hars h l y cri ticizing the c o mp ari s on theory of metaphor for its i n ab i lity to address t h e creation of s imil a r i t y interaction theory p ro p oses that every m et ap h or involves an i nter action between i ts source and its target, a process in w h i ch the t arget (and possib ly the source) i s reorganized, and new s i m i l arit ies between the source and the target emerge. This account, w h i c h is exam i ned i n Chapter 3, is, however, quite vague, and even paradoxical at times. ,
For i nstance, it neither pins down what exactly thi s mysterious 'interac tion' i s , nor specifies exactly how the new similarities e me r ge There is a crucial problem here: the creation of similari ty i s obviously not an arbitrary p ro cess I f it were, then anyt h i ng would be mean i n gfu l and there would be n o way to maintain a disti n ction between wh a t is genui nely metaphorical .
.
4
Met aphor an d Cognition
and w h at i s certai nly nonsensical . B u t t hen what constrains t h is creation process? I t cannot be the similarities between the source and the target , for this would t u rn the i n teraction theory into nothing b u t a variant of the com parison theory, and all the crit i cism that the interactionists d irected against t he comparison theory can be d i rected at t hemselves . So t he question i s s t i l l unanswered: w here do t he created s i m ilarities come from ? A few scholars have tried to elaborate the i nteraction t heory and t ackle some of t hese i ssues head on, but again , by and large, either t hese elabo rations are quite vague t hemselves , relying on metaphors and analogies to communicate the key concepts involved i n their explanations, or t hey t urn the i nteraction theory into a variant of comparison theory. H ausman [1983], for instan ce, postulated ' u n iqueness ' and 'extra- l i nguistic' con d itions to ex plai n how metaphors can create new mean ings and similarit i es , but t hese conditions t hemselves are not spelled out w i t h much clarity. Verbrugge [ 1 980] proposed t hat a metaphor works by ' transform i ng' the target i nto the source, t hereby mak i n g it s i m i l ar to the source, but then i t i s not specified exactly what this t ransformation p rocess is, and what constrains i t so t h at arb i trary transformations are ruled out . Tourangeau and Sternberg [1982] proposed a 'domains-interaction' view , w h i ch is p urported to be a ' more specific for mulat ion of the i nteraction view , ' but w h i ch , i n essence, turns out to be t he comparison view i n d i sguise, because i t assumes an u n derlying analogy to be the basis of every metaphor. A notable except ion is provided by K i t t ay's [ 1 987] perspec t ival theory, which comes quite close to prov i d i ng a reasonable explanation of the creation of similarity. B u t , for the most part , we see t h at the i nteraction t heories have s t i l l retai ned t heir fuzzy character, which m ay wel l be the s ingle most i mportant reason cogni t i ve science researchers h ave shied away from them [ Waggoner 1990]. There i s also a minor i nconsistency i n the interaction view t hat is some times overlooked. At one place in his classic essay 'Metaphor,' Black re m arked, "If to call a man a wolf is to put h i m in a s pe c ial l ight , we must not forget t h at the metaphor m akes t h e w ol f seem more human t han he oth erwi se wou l d . " This clearly implies a symmetry i n the interaction between the source and the t arget However, at o t h er places in his d is c uss i on t here is a clearly implied as y m m e tr y For e x am p l e in his later essay 'More about Metaphor,' in a deeply insightfu l sect ion t i t led 'Thi nkin g in Metaphors ' Black cons iders how different concepts can organize the figure of the S tar of David differently. I n organizing the figure of Star of D av i d as t h ree parallelograms wi t h t heir axes one hundred and twenty degrees apart , the process does not, at the same t i m e organize our concept of parallelograms as a part of t he figure of the Star of Dav i d-t hat i s , t he parallelogram does not app e ar to be .
.
,
,
Prologue
5
Star-of- D av i d-li ke after the i nteraction. W h i le a few i nteractionists, such as Verbrugge an d 1\it t ay, see the i n teraction view a s essentially asymmetr i cal , others , Hausman for i nstance, have emphasized the symmetry aspect of the i n teract ion . H ausman [1989, p . 67] went as far as to argue that one need not disti ngu ish between the source and target of a metaphor. A result of this con fusion bas been that many scholars now accept the symmetry property to be a key aspect of the i nteraction t heory [Waggoner 1990], an d some, such as Lakoff and Turner [1989, pp. 131-133], use arguments agai nst the sym metry property as a way to d iscred i t the whole i nteraction theory. B lack 's i n s i ght fu l observations i n ' T h i n k i ng i n M etaphors ' seem t o have been grossly overlooked . Then t here i s the problem of explai n i ng the role of metaphor i n cogni t i o n . I t h as been recognized for quite some t i me now t hat metaphor i s not j ust a phenomenon of language, but pervades all aspects of cogn i t i o n . It h as been claimed that metaphors play a key role i n learn i ng and education [ Holstein 1970; Petrie 1979; Sticht 1979], and t hey are an i nval uable ai d to p roblem solvi n g [Schon 1963]. In the early stages of form ulat i ng a scient i fi c t heory, met ap hors are often i n d ispensable [ Gruber 1978; Hesse 1980; M i l ler 1978; Roth bart 1984, p p . 611-612]. Religious schol ars have emphasi zed time and again t h at religious symbols ( scriptures, rituals, etc . ) derive thei r sig n i fi cance due to t hei r metaphorical n at u re, and should not be taken l i terally [ B rown 1983; Soskice 1985; T i l l i ch 1961; Wheel wright 1954]. For i n stance, the Christ i an ritual of tak i ng communion i s meani ngful only i f one u nder stands it metaphoricall y. Hone does not bel ieve in the transsubstant i ation doctrine, then neither i s the bread li terally the body of the Christ , nor i s the w i ne l iterally H i s blood, a n d a metaphorical i n terpretation i s requi red to render the ritual meani ngful . Even if one adopts the transsubstan t i ation doct r ine, a metaphorical i nterpretation i s st i l l requ i red to att ach significance to what would l iterally be a can n i b alisti c act. The wel l- k nown mythologis t J oseph Campbell [1949; 1986; 1988] argued t h roughout h i s prol i fi c career t h a t m y t h s are met aphorical ways of capturing the very essence of the expe rience of l iving, and, with an appropri ate metaphorical i n terpretation , various ancient myths are still as relevant as they m i ght have once been. Besides literature, met aphors pervade various other art forms. The ab stractionism p revalent i n contemporary arts parti c u l arly requ i res a metaphor i cal i nterpret at i on for a work to be meani ngfu l . W i l lem De Kooni ng's Exca vations, Barnett Newman 's Achilles, and J ackson Pollock 's Cathedral are all examples of pai n t ings that req uire metaphorical i nterpretations to be u nder stood. Joh n Cage's compos i t ion 4'3311 which is essentia.ll y 4 m i n u tes and 3 3
6
Met aphor and Cogni tion
seconds of silence, is another case in poi n t . ( See Cage's ' Lectu re on Not h ing, ' i n Cage [ 1 96 1 ) , p p . 1 08-1 27 . See also Rowel l [ 1 983] for the role of metaphors in music, including an i nterpretation of 4 ' 33" [p. 220] . ) Fox [ 1 982) , in i n t ro ducing the works of six modern sculptors, Vito A cconci , S i ah A rmaj an i , A l i ce Aycock , Lauren Ewing, Robert Morris , and Dennis Oppenheim , h as further emphasized the reli ance of contemporary art on metaphor to commun i cate i t s meaning. Whi t tock [ 1 990] has analyzed several different types of metaphors i n feature fi lms, m any of w h i ch were consciously i nt roduced by the directors . For i nstance, the classic shower scene from A l fred H i tchcock 's Psycho i s seen as an act of spirit ual cleansing: Marion C rane ( J anet Leigh ) , hav ing decided to go back and return the money she absconded w i t h , is not j ust washing away her body, but i s also ridding herself of the gui l t [Wood 1 989, p . 1 46] . This identification enhances t he shock of her subsequent murder a great deal [ W h i ttock 1 990, p. 53] . Fi nal ly, ant h ropologists have poi nted out t hat many of our own social, cultural and moral val ues result from the metaphors t h at are p revalent in our society and cult u re [Kempton 1 987; Lakoff & Kovecses 1 98 7 ; Q u i n n 1 987; Reddy 1 979; Schon 1 9 7 9 ; Turner 1 9 74] . For i nstance, Q u i n n 's study found t h at t here are different metaphors u n derlying t he modern A merican concept of marri age: 'a manufactu red product , ' 'an ongoing journey, ' 'an i n vestment , ' a n d s o o n . She also fou n d t h at a n i n d i v idual's perception o f whether h i s o r h e r marr i age i s a success or a fai l ure, whether t here i s some problem facing the marriage, and i f so, how i t might be corrected , etc. are all determined by the u nderlying metaphor. G i ven t h i s overwhelm i n g evidence for the variety of roles metaphors play i n cogni t i o n , one would expect a t heory of metaphor to shed some light on what it i s about metaphor that m akes i t pervade so many d i fferent fac e t s of cogn i t i on . In fac t , the evidence is so strong as to suggest that a t heory of metaphor should perhaps be set within a fr am e work of cogni t ion . That i s , t h ere should be a general account of cogni t i o n , and metaphor should be presented as one of the mechanisms u sed in cogn i tion. J n exploring t h i s hypothes i s , w e fi n d that there exi s ts a problem i n cogni t i on that is remarkably parallel to the problem posed by similarity-creati n g metaphors . T hi s problem has to do w i t h a v i ew of cogni t i on according to w h i ch the world view of a cogni t i ve agent does not reflect some pre-exis t i ng structures i n the external world , but is created by the cogni t i ve agent . Yet , t h i s creation is not arb i trary, but i s constrained b y t h e external world . Per haps not surprisi ngly, this view is referred to as th e interaction view of cog nition, sin c e it sees cogn ition as a process of i nteracti o n between a cognitive
Prologue
7
agent and its envi ronment . W h i le a version of the i nteraction view of cognition is i m plicit i n K ant 's celebrated Critique of PU1·e Reason, it i s on ly in this cent u ry that it has been art i c u l ated as such , i n the monumental works of Ernst Cassi rer [ 1 955] , Nelson Goodman [ 1 9 78] , and Jean P i aget [ 1 936; 1 945; 1 967; 1 970] . I n the past few decades , many scholars from various d i sci p l i nes as d i verse as phi los ophy, psychology, neurophysiology, l inguist ics , and anth ropology, have pro vided persuasi ve evidence and arguments i n su pport of the i nteraction view of cognition. Yet , l i ke the i nteraction t heories of metaphor, most accounts of the i nter action view of cognition remai n somewhat vague. W h i le t hey offer helpful analogies and met aphors, they do not exp l i c i tly address some of the key problems. For i n stance, what exactly is the nat u re of i nteraction? Exactly how does the external worl d constrain t he world view of the cogn i t i ve agent? Not i ce that t here seems to be a paradox here, for to tal k expl icitly of the i nteraction , the external world needs to be given an ontology ; and to talk of t he external worl d constrai ning t he worl d view of the cognitive agent , t here is the i mp l i cit assumpt ion that the external world has a struct u re that i s i ndependent of the cogni t i ve agent . H owever, bot h these feat u res are i n con sistent with the central thesis of the i nteraction view of cognition, wh ich is to deny a m in d- i n dependent ontology and struct u re to the external world . It i s the vagueness on s u ch i ssues that i s pri mari ly responsible for some m i s u nderstandings of the i nteraction view of cogn ition , especially by its crit i cs . For i n stance, the i nteractionists often talk of ' coheren cy' as a way to specify t h at the cogni t i ve agent 's worl d view must ' fit ' the external world. However, for lack o f a precise characterization of coh eren cy, i t is someti mes confused w i t h the i nt ernal cons istency of cogni t i ve structures ( M ac Cormac 1 985, pp. 2 1 1 -2 1 5] . G i ven that i nteractionism i n cog n i tion and i n teractionism i n metaphor are both concerned with the i ssue of creat i v i ty, and that there are some obvious s i m ilari ties between the key problems fac i n g each of these views, one would expect that it should be poss i ble to add ress t hem in a u n i fied framework . M oreover, i f it turns out that metaphors i n volve an i nteraction not u n l i ke the i nteraction of cognition , then this might explain exact ly what role metaphor plays i n cognition , and why metaphor is an asset to so many cogni t i ve act i v ities.
I ndeed , the study p resented i n this book i s u ndertaken i n this very spir i t . chief objecti ve i s to present a u n ified framework for t h e i n t er ac t io n view of metaphor and the i nteraction view of cogn i t i o n . I lay out this framework My
8
Metaphor an d Cogni tion
i n detai l-even i ncluding a mat hematical version i n t he trad i t io n of formal seman t ics-so as to dispel much of the fuzziness that has surrounded the ear l ier versions of each of the i nteraction views. I also attempt to resolve the apparent paradoxes and i n consistencies of each view mentioned above. As far as metaphors are concerned , my focus i n t h i s study, perhaps obvi ously, i s on s i m i l ar i ty-creat i ng metaphors. However, the account of metaphor presented here also i ncludes a t reatment of s i m i l ar ity-based metaphors , sin ce these too have a role to play i n cogni tion-albeit a d i fferent role t h an the one p layed by s i m i l arity-creati n g metaphors-and a u n ified t heory of metaphor ought to i n clude both types of metaphor. Moreover , in this way, the reader w i l l be better able to appreciate t he di fferent cogni t i ve force of each type of metaphor. This book i s organi zed in t h ree parts. Part One of the book i n t roduces, in greater detai l , the problems of metaphor and cogni t io n . In Chapter One, I characterize my use N the term metaphor, and arti c ulate the range of p henomena t h at I cover u n der i t . I t i s i m portant to do so, for t here are significant variations i n the l i terature as to w hat exactly is considered a metaphor, and how i t is related to s i m i le, analogy, models , etc. I n Chapter Two, s i m i lari ty-creat ing metaphors are i nt roduced . I t starts out w i t h some examples of s i m i l arity-creat ing metaphors, and t hen reviews a few research efforts that have been made to em pirically demonstrate the creation of sim i l ari ty. I t i s also argued t h at i n phenomena. often considered to be closely related to metaphor-namely s i m i l e , model s , and analogy-t here exist coun terparts of s i m i l arity-creati n g metaphors. It t hen h ighlights the role played by s i m i larity- creat i ng metaphors ( as opposed to s i m i l ari ty-based metaphors ) i n cogni t i o n . The chapter concludes w i t h a d iscussion of t he p roblems posed by s i m i l arity - creating metaphors . C h a pt e r Th ree disc usses various attempts that have b ee n made to address of s i m i larity-creati n g metaphors . A s one might expect, t h i s c ha p t e r i s essent i ally an overview of various i nteraction t heories o f me t aphor , tak i ng note of their i nsights as wel l as their shortco m ings. C h ap ter Four i n t ro duces the i nteraction view of cogni t ion, and points out some of its problems that parallel the problems of s i m i l arity-creati ng metaphors . It also exam i nes t hree d ifferent versions of i n teractionisms, giving speci al attention to the views of Nelson G oodman and Jean P i aget , and analyzes how far the problems of the i nteraction view are resol ved i n each version . In P a r t Two of t he book, I lay out my framework for metaphor and cogni t i o n . I n Chapter F i ve, I present m y i nteraction view o f cogn i t i o n i n formally, including a detai led , t hough somewhat arti fi c i al , example to i llustrate all the t h e p ro b l e m s
9
Prologue
key concepts of the theory. Chapter S i x contai ns a formal i zat ion, using some elementary concepts from Un i versal Algebra, of the framework i n t roduced i n Chapter F i ve. W h i le t h i s chapter can b e safely ski pped w i t hout affecting the readab i l i ty of the rest of the book, i t may be of i nterest to formal sem ant i cists and anyone else i nterested in formal models of cogn i t i o n . As far as the math ematical background required to read this chapter is concerned , only some very basic mathematical fl uency-fam i liarity w i t h sets , fu nctions, relations, etc.-is req u i red , as I h ave kept the discussion slow-paced and provided many examples. Following that, in Chapter Seven , I present a t h eory of metaphor w i t h i n t h i s framework of cognition . My account t reats both s i m i l arity- based metaphors and s i m i l arity-creat i ng metaphors, and I argue t hat d i fferent cog n i t i ve mechanisms are cal led into play for each class of metaphors. I n Part Three of t he book , I present some i m p l i cat ions of t h i s framework of metaphor and cogni t ion . Chapter Eight exami n es some issues related to metaphor i ncluding t he l iteral-metaphorical d ichotomy, t he thesis t h at all knowledge i s metaphorical , and metaphori cal truth and aptness. In Chapter Nine, I exam i ne the problems of predictive an alogy-also known as an alogical reasoning-and i n d uction . I argue that both these processes are best seen as cogni t i ve processes that are useful at t i mes, and yet , m u ch l i ke our visual system, create their own i l l usions that can be detri mental to cogni tion at other t i mes . It is erroneous to see t hem as processes t hat are somehow j ustified, even in a p robabilistic sense, by the structure of reali ty. Chapter Ten t akes a look at computat i onal approaches to metaphor and analogy. Here, after poin t i ng out the fail u re of most of the exi s t i n g computation al models of metaphors and analogy to address the creat i v i ty issue, I go on to argue t h at t here exist artificial i ntelligence systems t h at are capable of gen erat i ng creat i ve metaphors and analog i es. O b v i o usly, my v i ews i n t h i s book p resent a convergence of many points t h at h ave b een made i n d i fferen t contexts by various scholars of metaphor and c ogn i t i o n and i s a d i st i l l at i on of t he res u l t i n g framework. W h i l e l h ave provided expli c i t references t h roughout the book , I wou l d l i ke to acknowl edge here in a general way my i ntellectual debt to Max B l ack, Ernst Cassirer, Nelson Goodman , Paul R i coeur , and most of all to J ean P i aget , whose nu merous w ri t i ngs have been a . source of constant i m petus to me in carrying out t h i s research . A reader acquainted with any of their works should not be surprised to find fam i l i ar t hemes reverberat ing beneath the views presented ,
here.
Part I
The P roblem
Chapter 1 Characteriz ing Met ap hor
1.1
I nt r o duct ion
Before we begin t h i s study, i t i s necessary to characterize the term ' metaphor' i t self, for in the l iterature it is used w i t h a w i de variety of mean i ngs. In the n arrowest sense, metaphor refers to a specific way of using the words and p hrases of a language, and i n a broad sense i t i s app lied to the process of concep tualization i t self, lead i ng to the aphorism " All t hought i s metaphori cal. " Then t here are the phenomena of s i m i le, analogy, and models , t h at are considered to be closely related to metaphor, but there are wide variations i n how t hese relations are percei ved . Researchers d o not always state explicitly t he range of phenomena covered by their use of the term metaphor, leaving this t as k to the reader. This practi ce has someti mes generated needless con t roversy about t h e n at u re of metaphor d u e to m i sunderstood positions, as we w i l l see in C h ap t e r 8. To avoid this u n n ecessary confu s i o n , this c h apter i s devoted to art i c u lat i n g the exact sense in which I am using the term metaphor in this book . My objecti ve here i s not so m u c h t o come u p w i t h a pre c ise definition of m e t ap h or , but rather to give you some i dea about the range of phenomena I am coveri n g i n my use of the ter m . I start by consi dering some e x amples of l i nguistic metaphors i n Section 2 i n order to i solate their i dentifying charac teristics. T hese characteristics are summed up in Section 3. In Section 4, I point out t h at the metaphoric content of a statement ( or a piece of te x t ) is a matter of degree . There i s a conti nuum from convention al metaphors, which are so m u ch a part of t h e everyday speech that t hey hardly seem metaphor i cal , t o novel m e t aphors t h at are v i b rant and creati ve at once. It is the novel-metaphor end of the continuum t hat is most i nteresting for this st udy , 13
14
Part I: The Problem
because my mai n objecti ve is to explore how new concepts and meani ngs emerge through metaphors, and how similarities are created . I n Section 5 , I present examples of metaphors i n t he non-linguistic do mai ns of pain ti ngs, films and rel igion , and extend my characterization of metaphor to i n clude them also. I also show here t h at non-l i nguistic meta phors share many of the characteristics of li nguistic metaphors. Then , i n Section 6 , I br·iefly exam i ne t h e relationsh i p o f metaphors to s i m i les, analo gies , and models . Agai n , t he objective here is not so much to establish one correct way to relate t hese t h i ngs to metaphors, but rather, given the focus of this study, to show to what extent si m i les, analogies and models embody the cogni t i ve mechanism t h at renders novel metaphors meani ngfu l . I t i s im portant to clar i fy this because I use examples of what are considered s i m i les, analogies and models to illustrate and analyze the c reation of similarity and other characteristics of metaphors in Chapters 2 and 7. F i n ally, Section 7 summarizes the main points of this chapter. 1 .2
S o me Examples of Met aphors
Consider a s im ple metaphor, "The sky i s crying." W hat makes i t a metaphor, as opposed to, say, "John is cryi ng," w h i ch is considered literal? First of all , not i ce that each of the statements is a description of some object or event ( real or i m agined ) . Let us call this real or i m agined object (or event ) the tm-gel . Now i n "John is cryi ng," the description can be applied to the target ( John ) using conventional meani ngs of t he words. ( B y the term ' conven tional meani ngs' I refer to the meani ngs t h at can be obtained by looki ng up the words in some standard dictionary. ) However, in "The sky i s crying," t he word 'cry' cannot be applied to the t arget ( sk y ) in a meani ngfu l way w h i le using its conventional meani ng . S t i l l , most people would u nderstand it to mean t hat it i s rai n i ng. T h i s understan d i ng i s derived from interpret ing t he word 'cry' un conventionally in applying it to the target . The basis of this i n terpretation is an u n derlyi ng similarity between teardrops falling down the cheeks of a cryi ng person , and rain d rops fal l i n g fro m t h e sky. O nce this i nterpretation has been arri ved at , it can be extended ( more or less, ) depend i ng o n one's i m aginative potential and w i l l i ngness t o d o so. For i n stance, i n u n derstan d i ng "The sky i s cryi ng," one m i gh t associate a certai n mood o f u n i versal sadness with this utterance, based on i t s s i m ilarity w i t h the emot ion usually associ ated w i t h cry i n g . Thus, t h e i nterpretation does not j ust involve t he concept 'cry ' in its meani ng, but also bri ngs into play other concepts associated with ' cry, ' such
Chapter
1:
Characterizing Metaphor
15
as ' teardrop s , ' 'sadness , ' and so on . Let us call the part of the descri ption that i s given an unconventional i nterpretation, as well as al l the related concepts i t call s into p l ay the s o u rc e . Consider now another example, "The defense counsel created a smoke screen of w i t nesses . " Here the target i s a certai n action that the defense counsel took . As w i t h the last example, the descri ption cannot be applied to the t arget by using the conventional meani ngs of t he words . I n particular, the term ' smoke screen' cannot be conventionally applied to the target . Ac cording to Webster's dictionary, 'smoke screen ' means 'a screen of smoke to h i n der enemy observation of a m i l itary force, area, or act ivity. ' To make the description meaningfu l , 'smoke screen' and its related concepts ( the source) h ave to be gi ven an unconventional interpretation . The basis of the un conventional i nterpretat ion is the s i m i l arity between the effect the witnesses called by the defense counsel are h aving, and the effect the smoke screen h as d u ring a m i l itary maneuver. In both the above examples of metaphor, the target was explicitly men tioned i n t he description. However, this might not always be the case. For i n st ance, consider "The old rock is becoming britt l e with age." The de scription m ight h ave been of a rock , in which case it woul d be interpreted conventionally. However, one coul d have also said i t of an old professor. In t h i s case, it is the context alone that specifies the target , and all the concepts used in the description ( an d their related concept s ) become the source of the metaphor, and have to be given u n conventional i nterpretations. I n fact , even w hen t he t arget seems to be explicitly mentioned in the descri ption, the context can change it. For example, i n discussing "The sky i s cry i ng," we tacitly assumed that i t is about the sky, w h i ch became the t ar ge t . B u t t h e s a m e s t a t e m e n t cou l d a.l so h ave b e e n i n te n d ed to d es c r i b e a p e r s on w i t h big p a le b l ue eyes who is crying. T h e fa c e of the c r y i ng person now b e comes the t arget , a n d the sky and its rel a.ted co n ce p t s become the source. Thus, context p l ays a dom i n ant role i n i dent i fy i n g t h e t arget , w h i ch , i n turn, affects ( gi ve n a description ) what is c o n s i d e red l o be the so u rce o f a metaphor. Let us now c o ns i d er " T h e c h a i rp e rson of the m eet i n g plowed t h rough the agenda." The target here is how the chai rperson conducted a certai n meeting. If we t ake t he conventional m ea ni n g of ' p lo w ' to be, 'to move i n a way resembling that of a p low cutting into or going thro ug h the s o i l , ' then i t ca n n o t b e applied to t h e t a r g e t as i t i s ; a n u n co n vent i o n a l i n terpretation i s called for. S u ch a n i nterpretation c a n be arrived a t based on t he u nderlying s i m i l a r i t i e s between the actions of a farmer i n plowing and the actions of the
16
Part I: The Problem
chairperson . The farmer keeps a st raight course w i t h her plow , u p rooting dead roots , weeds , small stones, and whatever happens to come i n her way. The chai rperson sticks to the agenda and summarily brushes aside pointless objections and d i scussions. H owever, the dictionary meani ng of ' plow ' also i n c ludes 'to p roceed steadi ly and laboriously, ' and w i t h t h i s meaning the description can be convention ally app lied to the target , and would no longer be considered metaphorical . ( I n fac t , one reviewer of t h i s manuscri pt obj ected to my using the above .statement as an example of metaphor. She noted in her review that she, having grown up i n a city, learned this meani ng of ' plow' first . To her, the above descri ption of a meet ing was not metaphorical at all . ) Thus, we see that w hi ch i nterpretations are cons idered conventional and w h i ch ones are consi dered u nconventional , whether someth i ng is considered metaphor or not , i s quite subject i ve. I n all of the examples seen so far, t here was basically one way of i nterpret ing the source in the target unconventionally, t hough this bas i c i nterpretation could be extended i n d i fferent ways subjecti vely ( as in attributing sadness to the sky ) . However, this i s not always the case. O n ce I heard a cal l - i n show on t he radio w here the host asked the l isteners to call in with a description of their love l i fe in terms of food. H ere the target was fixed . The source was also fixed in t he sense t hat the love l i fe had to be described using food concepts only. B u t people cal ling i n w i t h their descriptions reflected different ways of applying food to their love l i ves . For i nstance, one caller described her love l i fe as an onion ( i t smells and m akes you cry ) . A nother caller described h i s love life a s a fresh fru i t ( it i s s eason al ) . I n fac t , even i f w e t ake o n e p a r t i c ular description, say ' love life as a fresh fr u i t , ' different people wou l d interpret it d i fferent ly. ( It i s good and healthy, it i s sweet and j uicy, and so o n . ) Thus, we see that the unconventional i nterpretations that make metaphors m e aningfu l are not u n ique, but are subjecti ve. T h e s u b j ec t i v i ty of m e t aphors i s even more p ro n o u n ced i n the cases w here no target is supplied, either expli citly by the statement or implici t ly by the contex t . T hi s is oft e n t he case with metaphors of poetry and , as we w i l l see later, o f art s . For instance, consi der Melville's Moby Dick. There i s n o target mentioned or h inted t here. O f course, t he story is q u i t e meaningful as i t i s-as a conventional d e s c ri p t i o n of an imagined event . But ·it i s cer t ainly possible to interpret it metaphorically in many d i fferent ways i n many different domain s . N o w consider "Sincerity p lowed t h rough depravity," a n d ass u me t hat t he context does not help you at all i n identifying a target . What could the de-
Chapt er
1:
Characterizing Metaphor
17
scription b e about ? What coul d i t possi bly mean? You m ight consi der i t to be a statement about emotions, but t hen ' p low' with its conventional meaning cannot be applied to t h i s target . I f you cannot come u p w i t h any i nterpre t ation of t h i s statement , then it woul d h ave to be discarded as anomalous or mean ingless . H owever, w i t h a little b i t of i m agi n ation , even the above statement can be m ade mean ingfu l . Imagine some government department where corruption permeated everything until an honest and sin cere ad m i n istrator took over. Her h i gh standards of moral i ntegri ty and her concern for the employees of the department touched the hearts of m any of them , and soon the corrup tion was weeded out . The above description wou l d be q u i te mean ingfu l and appropriate i n this contex t . Well , my scenario m i g h t n o t be so convi ncing. You c a n t r y to make o n e of you r own ; I am sure it wou l d not be very hard . Or you can look up the i n ter esting studies of Pollio & B u rn s [ 1 977] and Poll i o & S m i t h [ 1 979] . The point here is simply that the distinction between meani ngfu l n ess and anomaly is not so easily draw n . Yet , i n any gi ven contex t , there are statements that are clearly anomalous, for to any one individual , even one who is q u i te i m agi na t i ve, not all statements are meaningfu l . Therefore, not every u n conventional j uxtaposit ion of words and phrases consti tutes a metaphor. Consider now "These highways are snakes" and " Sn akes are highways." These two examples i l l ustrate the asym metry of metaphors. The fi rst de scrip tion is about highways. The u nconventional i n terpretation of 'snakes' one m akes here i s t h at t hese h ighways are long and windy. The second de scription , w hi ch is abou t s n akes , appears anomalous at first . Wit h s om e effo rt , we can perhaps i m ag i n e a l o n g snake, with ant s r u n n i ng up and down along t h e l e n g t h of i t s body, and ren der t h e sentence mean i ngfu l . Com pari ng t he two i nterpretat i o n s , however , we see t hat they are q u i te d i ffe r e n t . Thus, we see t h at a metaphor i s n o t a symmet ric com parison b e t w ee n the source and the t arget , and reversing the source and the target m i g h t change the meaning of the metaphor drastically; i t m ight even turn the metaphor i nto an a n o m a ly . ( See Connor & Kogan [ 1 980] ; Malgady & J ohnson [ 1 980] ; and Verbrugge [ 1 980] for empirical studies of asymmetry in metaphors . ) 1 .3
C haract erist ics of L i nguist i c Met ap hors
We can now summarize the main characteristics of metaphors, at least i n the l i nguistic set t i ng, t h at were gleaned from the d iscussion of the examples i n
18
Part I: The Problem
the last section . 1 . A metaphor is a description of an object or even t , real or i magined , using concepts t h at cannot be applied to the object or event i n a con ventional way. The object or the event being described i s called the t ar get , and the concepts that cannot be applied conventionally are called the source. The source does not j ust include the concepts mentioned i n the description that cannot be applied conventionally to the t arget , but other related concepts as well . 2 . The source o f a metaphor is always supplied by t he description ( t he text ) . The target m ay be explicitly hi nted at by the description, may be determi ned by the context , or may not be provi ded at all . Whenever the target is p rovided , context plays a more dominant role i n determi n i ng i t than the descri ption .
3 . The metaphor i s made meani ngful by interpreting the source u n con ventionally i n t he target . The unconventional i nterpretation can be ar ri ved at on the basis of some underlying simi larity between the source concepts and the target. If no i nterpretation can be fou n d , then the description is considered anomalous . This suggests that the simi lari ties between the source a n d the target might be one of the identi fying characteristics of metaphor. However, as I demonstrate i n the next chapter, certain metaphors c1·eate the similarities between the source and the target. Taking the p henomenon of creation of similarity for granted at the momen t , let us say that t h ere are al ways similarities b e t ween t h e so u r c e and the ta rge t afte r t h e m e ta p h or i s und er s t ood , if i t i s understood at a l l . 4.
statement i s c o n s i dered m e t a p h o r i cal or not i s q u i te sub reasons for i t . O n e i s t h at what one t akes as th e c o n ve n t i on a l mean i n g of a word or a phrase is s u b j e c t i ve . So, what is a con ve n t i o n al descri ption for one might be a metaphor for another. Secondly, varying degrees of imagination are requi red to m ake sense of w hat seems l i ke an anomaly, and since d i ffe re n t persons h ave d i fferent i m aginat i ve potentials, w hat is an anomaly for some might be a deeply i nsightful metaphor for an ot h er. W h et h e r
jective.
a
T h e r e a r e t wo
5 . What a m e t aphor m ea n s i s i t self q u i t e s u b j ect i ve , t hough different m et a ph o r s leave more or less room for subj e c t i v i t y of m ea n i n g . When ever the target of a metaphor i s not specified , the reader can choose
Chapter
1:
19
Ch aracterizing Metaphor
her own t arget ( as i n i nterpreti ng Melville's Moby Dick metaphorical ly ) . W hen t he target i s specified b y t h e context , o r mentioned explicitly i n the description ( t he text ) , different readers can give unconventional in terpretation to the source in different ways ( as i n ' love l i fe as a fresh frui t ' metaphor) . Even w hen t here i s a rather u nambiguous i nterpre tation of the source in applying it to the target unconventionally ( as i n "The sky is crying," ) t here are other connotations ( such as t he aura of sadness in the above example) t h at might be present , w h i ch heighten the emoti ve force of the metaphor differently for different readers. 6. Metaphors are asymmetric. That is, w hen t he source and the t arget of a metaphor are reversed , the meani ng can change dramatically, and the description may even cease to be a metaphor. 1 .4
D egrees of Metaphoric C o nt e nt : T he C o nvent ional vs . t he Met ap horical
The examples discussed above clearly suggest t h at the metaphoric content of a description in a given context is not someth i ng t h at i s all t here or is completely absent , but i s a matter of degree. For i nstan ce, "John i s crying" i s clearly non-metaphorical or li teral ; "The sky is cryi ng" and ' l ove l i fe as a fresh fru i t ' are clearly metaphorical ; but "The chairperson of the meeting plowed t h rough the agenda" is not so clear cut. Some scholars, such as M ac Cormac , woul d rather call it l i teral but use the term dea d metaphor' rec ogn i z i n g t h at i t was metaphorical once, before the m e an i n g of 'plow' that i s transferred by the metaphor became so frequently used t h at it became a part of t h e c o n v e n t i onal meaning, and was incorporated i n t h e di ctionary-to d i s t i n gu i s h it from examples l i ke "John i s crying." Others, such as Lakoff, c onc e d e t h at t h e t e r m ' p l o w ' is used w i t h i t s c on v en t i o n al meaning, but argue, nonetheless, that t h i s example sti l l evokes the i m age of metaphorical t ransference i n the m inds of at least some readers, and , consequently, prefer to call it a ' convent i onal metaphor. ' As the issues of w hat is a m et a p h or w hat is a conventional m e t apho r w h at is a dead metaphor, a n d w h at is l i te r al are qui te controversial [Lak o ff 1 986; Lakoff 1 987a; M ac Cormac 1 9 8 5 , Chap . 3] a c o n t roversy that i s analyzed in Chapter 8-I wou l d l i ke to clar i fy my own posi tio n here, especially si nce I h ave cha rac te r i z e d metaphors i n cont rast w i t h t h e c onven t ion a l Clearly, t here i s a continuum w i t h respect to the degree of metaphoric content . On one end are the novel metaphors such as ' love life as a fresh '
,
,
.
Part I: The Problem
20
fru i t . ' Then come the metaphors that are widely used in a l anguage and c u l t ur e but s t i l l retain thei r i nterpretive nature, such as "Their marriage is on a rocky road . " At t he other end of the continuum are t hose metaphors that have become so much a part of the conventional language ( as reflected i n the dictionary mean i n g ) t h at to many people there i s no element of i nterpretation or t ransference. "The chai rperson p lowed t h rough the meeti ng agenda" is a case i n poi n t . The only reason to call such examples ' metaphors' i s to d raw attention to t h e fact t h at they were novel metaphors once. I refer to t h i s cont i nuum a s the m etaph o ric-co n t e n t conti n u u m , a n d i dentify i t s t w o ends as n o vel-metaph o 1·ical and co nventional respectively. Contrasting with this conti n u u m , t here i s , of course, the l iteral that i n c l u des examples such as "John is crying." Obviously, one wou ld l i ke to exclude l iteral statements from being called metaphori cal ; and one wou ld l i ke to i n c l ude the novel- metaphorical end ( ' l ove l i fe as a fresh fru i t ' ) and t he m iddle of the metaphoric-content continuum ( ' marriage as a rocky road ' ) under the term ' metaphor . ' So the only bone of contention i s the conventional end of the metaphoric-content continuum ( ' conducting the meeting as plow i n g . ' ) I n emphasizing t h at a metaphorical i nterpretation has to be unconventional , I seem to be excluding this end of the continuum from being i n cluded i n the metaphorical . W h i l e many people woul d h ave no problem w i t h this usage, Lakoffian scholars m ight objec t , si nce they have been using examples from the con vent i onal end of the metaphoric-content continuum to argue that metaphors pervade our everyday speech , actions, and behavior. I do not dispute t h i s remarkable feat accomp l ished b y Lakoff a n d his colleagues . In fac t , i t only provi des add i tional mot ivati on for t h i s st udy t h at undertakes to address how new concepts an d mean i ngs emerge t h rough metaphor s , and how s i m i l arit ies a re created . If many of what we now regard as convention al m e an i n gs con ceptual organi zations, and perceptions of s i m i larities between two situations started out as novel metaphors , then t h i s i s all the more reason to find ou t how novel metaphors work , and how t hey create new meani n gs and new s i m i larities . B u t t hen for t h i s object i ve, i t seems reasonable to t ake conventional metaphors, whi ch already form a part of day-to-day, accepted concept ual or gan ization as given , and focus on u n conventional and novel metaphors that break the convent i on al barriers, an d yet co m m un i c a t e meaningfu lly, and of ten i ns i gh t fu lly Of course, one could also focus on convention al metaphors by ro l l i n g t im e back, and analyzing how "The chairperson of the meeti ng plowed t h rough the agenda" wou l d be rendered meaningful if 'to proceed steadily and Ia,
.
Chapter
1:
21
Characterizing Metaphor
boriously' were not a part o f the conventional meaning o f ' p l ow . ' S u ch an approach woul d be unavoidable if t here were a dearth of novel and u n con ventional metaphors. But given t he abundant supply of fresh and vibrant metaphors t h at stretch language in new and u nconventional ways, this ap proach i s u n necessary. A consequence of my characterizing the metaphorical in contrast with the conventional is that a conventional-metaphorical dichotomy i s automatically created. S i n ce some scholars have argued , q u i te vehemently at times, that all knowledge is metaphorical , the position I am taking m ight be seen as opposing t h i s view . I t ake u p this issue in C hapter 8, w here I argue that my views are, in fac t , qui te consistent w ith t h i s " A l l k nowledge is metaphorical" t hesis , and the apparent conflict comes from the different ways i n which t he term ' metaphor' is used . 1.5
Met ap hors i n Non- L ingui s t i c D o mains
Let us now move beyond the metaphors of l anguage, and see i f a similar phen omenon can be found i n non-l i nguistic domai n s such as painti ngs, films, and rel igion . Before doing so, we need to generali ze the concept of ' text . ' What are t h e k i nds o f t h ings w e might possibly consider as metaphorical? A religious ritual, a painting, and a certai n j u xtaposition of i m ages i n a fi l m are all examples of t h ings that have the potent ial of b e i n g metaphorical . A general term that subsumes them all is perhaps a complex symbol or a struc�ured s e t of symbols.
The next th ing i s to extend the dichotomy between the conventional an d Here agai n , there seems to b e l i t t le problem , s i n ce most s y m bols h ave conven t i o n al i n t e r p re t at i o n s ass o ci at e d with them . I n order for somet h i n g t o a c t a s a s y m b o l , i t h a.s t o represent s om e t h i ng e l s e , a n d t h at somet h i ng e l s e becomes t h e i n terpretation the metaphori cal so t h a t it appl ies to symbols.
of the symbol. Moreover, most symbols work within a larger social or cultural setting, so that t h e i r i nterpret a t i on s are fixed by convention . T hu s we can look for metap hors among non-conventional i nterpretations of symbol s . ,
for i n s t an c e . Clearly, a pai nting o f a park t h at shows p o n d , lovers stroll i ng arm- i n - arm , l i t t l e children feed ing t h e ducks, and so on, shows all t h ese t h i ngs t h ro u g h con ven t i o n a l m e a n i ngs . A picture of a t ree conventionally re fer s t o a t r ee j ust l i ke the word ' tree' in Engli s h refers to a t ree. H owever, in Paul K l ee ' s Park near L (1tceme) [ P l ate 1 ] we see a more abstract symbol ism. Here, i t seems more approp r i a t e Consider p ai n t i n g s ,
t rees ,
r ol l i n g
gree n s , a
,
P LATE 1 : Paul K lee, Park bei L u (zern) (Park n ear L u (cern e)) , 1 938, Paul K lee- S ti ft u ng/ K u nstmuseum Bern, @ 1 99 1 , by VAG A , New Yor k .
PLATE
2:
J an Van
Eyck, The Marriage of Giovanni (?), A rnolfini and
Gio vanna Cenami (?), 1434, The National Gallery, London .
22
Part I: The Problem
to say t hat the figu res refer to t rees and people metaphorically. A nother exam ple of metaphorical i nterpretation in a painting i s Jan Van Eyck 's Th e J\lfa rriage of Giova n n i (?), A rnolfini a n d Giova n n a Cen a m i (?), [Plate 2] . H ere, the image of a si ngle candle i n the chandelier ( wh i ch conventionally refers to a candle, of course) i s supposed to allude to the presence of the Holy Spirit, the shoes on the floor and the brush i n the background are meant to symbol i ze the sanctity of the momen t , the dog represents loyalty, the apple in the window s i l l i s supposed to convey the relationship between sexual i ty and the Fal l of M an , and the bed i s symbol i c of the consummation of the marriage vows [Whitford 1 987, pp. 64-65] . ( Some of t hese i n terpretations might have been conven tional during a certain period . ) Consider the symbol ism of religion . I n the Christian ritual of taking communion, the referen ce to the bread and the wine, respecti vely, as the body and the blood of the Christ is very much a part of the accepted Catholic convention . H owever, when you drink wine and eat bread with your supper, t hese acts are not consi dered symboli c i n any way, for they do not refer to a nyth i ng outside of themselves in t h at context ; t hey do not function as symbols. What m akes the same actions taken at the communion symbol i c i s their reference to the blood and the body o f the C h rist . So to regard i t as metaphorical wou ld be l i ke saying that w hen the word ' t ree' refers to t rees, sin ce the reference i s not l i terally t o t he word ' t ree, ' the interpretation i s metaphorical . Thus, from my p o i n t o f v i e w , the communion r i t u a l , i f i t i s considered metaphori cal a t a l l , l i es a t the convent i on al e n d o f t h e m e t ap h o ri c c o n t e n t con t i n u u m . O n the other han d , Joseph Cam pbel l 's i nterpretat ion of com m u n ion as a way of b e c o m i n g one wit h H i m ( "The C h r i s t is i n me!" )-an interpretation w h i c h i s consistent w it h the message of t h e Thomas gospel-i s c e r t ai n l y quite u n co n ve nt i on a l [ C a m p b e l l 1 98 8 , p . 57] . A not h e r excel lent example of i n t e rpr et i n g r e l i g i o u s symbols m e t aphor i c a l l y is Campbe l l ' s in t e r p re t a t i o n of C h r i s t ' s death and resu rrect ion, w herein death is seen as co n sciou sne s s leaving the body and r e s u r r e c t i o n is seen as consciousness j o i n i ng w i t h the u n i versal consciousness of w h i ch all l i fe i s a m an i fe s t at ion [Campbell 1 988, p p . 56-57] . In fact , both t hese i nterpretations by Campbell , with which many C hristian s mig ht fe e l q u i te u n comfortable, echo the them e of B u d d h i s m . Nevertheless, i f one i s w i l l i ng to sus p e n d t h e conventional ways of i nterpreti n g t h e B i ble i n the Christian t r a d i t i on , Ca m p b e l l ' s m e an i n g comes across with absol u t e c l ar i t y ; t h e m e an i n g i s i n d isp u t a b l y metaphorical. Consider symbolism i n films now. Alfred H i t chcock 's Rear Window opens u p w i t h the p er s p i r i n g face of .J ames S tewar t . The camera t hen m o ves on to
Ch apter
1:
Chara.cterizing Metaphor
23
reveal his leg in a cas t , t hen to a nearby table t h at has a broken camera and a stack of m agaz ines on i t , t hen to the wal l , where t here are pict u res of racing cars toppled on the t rack . The j uxtaposi tion of images clearly suggests that i t i s a h o t summer day, a n d t hat Ji mmy Stewart is a professional photographer, who b roke his leg taking pictures of a car race. Now get t i ng all this i n for m ation from the montage u ndoubtably requires a.n element of i nterpretation, b u t all the necessary i nterpretations are quite conventional . O n t he other h an d , Charlie Chapl i n 's cut from a flock of sheep to a crowd descending i nto an u n dergroun d stat ion i n A1odern Tim es evokes a metaphorical comparison . [Whittock 1 990, p . 5 1 .] The use of the shower scene i n H i tchcock's Psych o to indi cate spiri tual cleansing that was mentioned i n the prologue is another exam ple of metaphorical i n terpretation . It lies at the middle of the metaphori c-content cont i nuum-l i ke the ' m arriage is a j ourney ' metaphor. It is rem in iscent of ritual bat h i ng ( as in H i nduism ) , d i pp i ng i n H oly Water ( as in the Chris t i an t radi tion of baptism ) , and washing the h ands, feet and mouth before visiting a holy shrine ( as in Buddhism ) . In each of these cases, the act of was h i ng the body symbolizes a clean s i ng of the spirit and washing away of si n s . In fac t , t h i s symbolism has also been used in other fi l m s . In Richard Benj am i n ' s Mermaids, Charlotte F l ax ( W i nona Ryder ) , a teenager who has strong religious feelings , kisses her boyfriend i n a fi t of passion . I m m e d i a t e ly afterwards, she is ove r w h e l m e d by fee l i ngs of g u i l t , and we see her t ak i n g a s h ow e r w h i l e h av i n g thoughts ( h e a r d aloud i n t h e backgrou n d ) of guilt and repentan c e .
A no t h e r
e x a m p le of m e t ap h o r i c a l use of s ym bo l s w i t h a s i m i l a r de g ree co n t e n t i s i n D av i d Lean ' s Doctor Zh ivago , w h e n Yu ri ( Omar
of metaphoric
Sharif) and Lara ( J ulie Christie) " fir s t touch, accidental ly, on a t ro l l ey, Lean t heir mystic union w i t h a. s park fr o m t h e t r oll e y ' s ove rhead w i res . " [A n d e r egg 1 984, p 1 29.]
s igna l s
T here are also m any examples o f symbolism i n film t h at l i e a t t h e novel m et a p h or i c a l end of the meta p h o r i c - c o n t e n t c o n t i n u um . W h i ttock d i s cu sses a p a rt i c u l a r striking example fr o m M i chel angelo A nt o n i o n i ' s /I Deserto Rosso ( Th e Red Desert) : " G i uliana ( Monica V i t t i ) i s seen against a wall that has large blot ch e s of p ai n t spattered u p on i t . [The S h o t t o w hi ch I am referring is i l lustrated on p. 273 of Stanley J . Solomon, Th e Clas sic Cin e m a : Essays i n Criticism ( New Yor k : H arcourt B race J o va n o v i ch , 1 973 ) . ] Because of her posi tion , she is both l i n ked and j uxtaposed to t hese blotches. Although thei r presence has
24
Part I: The Proble1 a l i teral exp la n ation-colors are bei ng tried out before the room is repai n ted-t he striking nature of their i rrational shapes, set agai nst the trim figure of the woman , suggests the p resence of an emotional disturbance in G i u l i ana t hat belies her outer calm ness . " [ W h i t tock 1 990, p . 59]
l n fac t , i n all of the few color films A ntonioni made, the colors h ave been u se< economically, but quite deli berately and often metaphoricall y to enhance tlu cinemat i c i mpact [ Ri fk i n 1 982, Chap. 5] . A nother i nteresting metaphorical use of the screen image i s provided i n A l fred H i tchcock 's Th e Birds. In H i t chcock 's o w n words :
"At the begi n n i n g of the fi l m w e show Rod Taylor i n the b i r d shop. H e catches the canary that h as escaped from its cage, and after p u t t i ng it back , he says to Tippi Hedren, ' I ' m p u t t i ng you back i n your gil ded cage, Melanie Daniel s . ' I added that sentence during the shoot i ng because I fel t i t added to her characterization as a wealthy, s h al low playgi r l . A n d l ater on, when the g u l l s attack the v i ll age, Melanie Daniels takes refuge i n a glass telephone booth and I show her as a bird i n a cage. This time i t i s n ' t a gilded cage, but a cage of m i sery, and i t 's also the begin n i ng of her ordeal by fire, so to speak . I t ' s a reversal of the age-old confl i ct between men and b i rds. Here t he human beings are in the cages and the birds are on the outside. " [ Truffaut 1 984, p . 288 . ] David Lean 's classic cut from a n extinguished match to a desert sunrise i n Latm·en ce of A mbia is another case i n poi n t . The c u t serves a s a n anchor for several metaphorical i n te r p re t a t i on s . T h e bold ness w i t h which Lawrence ( Peter O ' Too le ) ext i nguishes a l i t match by s q u eezi ng t he flame between h i s fingers b e c o m es a powerful met aphor for his l a t e r defiance o f t h e unforgiving s u n in the deserl . A lso, t he desert s u n rise b e c om e s a v i b rant metaphor fo r the begi n n i n g o f a career for Lawrence t hat woul d soon reach the s i zz li n g i ntensity of the midday desert sun . ( See also Anderegg [ 1 984] , p . 1 1 1 . ) Thus, we see t hat metaphors a re not l imited t o l anguage, but pervade fo r m s of symbol i s m . It is i nteresting to note here that non - l i n g u i s t i c m e t ap h o r s s hare m any of the characteristics o f l i nguistic met ap hors t h at were pointed out in Section 4. Non- l i nguistic metaphors also work by describing or representing some object o r event in a way t hat requ ires t he symbols used in the d e sc r i pt i o n ( o r re p r e s e n t at i o n ) to be interpreted in an u n co n v e n ti o n al w ay. So, the source-target d ichotomy c a n be app lied to n o n - l i ng u i s t i c meta phors as well . The t arget is the o b j e c t or event being descri bed , and t he m any
Chapter
1:
Characterizing Metaphor
25
source is the set of symbols used in the description t h at cannot be conven tionally i nterpreted ( as well as related symbols that are cal led into play ) . For i nstance, i n Antonion i ' s metaphor mentioned above, the emotional state of G i u liana is the target , and the blotches of paint on the wal l are the source. T hen , w h i le the source i s always explicitly provi ded by the symbols used i n t he representation , t he target might o r might not b e explicitly gi ven . For in stance, i n the Van Eyck pai n t i ng, the target i s expl icitly indi cated by the title and the way the woman an d t h e man are dressed . In A ntonion i ' s metaphor, t he t arget is h i nted at very subtly. In Lean 's cut from the exti nguished match to the desert sunrise, the target is not provided at al l . I n almost all the examples presented here, the u n conventional i nterpreta t ion of the source symbols is based on an underlyi n g s i m i l arity between the mean ings of t he source symbols and t he t arget object or event . For i nstance, in t he K lee pai n ti ng, various shapes resemble ( abst ractl y ) t rees and profiles of the human body; i t is t his s i m i l arity that makes the pai nting meani ngfu l . I n Chap l i n ' s metaphor i n Modern Tim es, i t i s t h e s i m i l arity between t h e flock of sheep and the crowd that renders the j uxtaposi tion of the i mages mean i ngfu l . ( Of course, there are also many i nstances of non-li nguistic metaphors t h at c1·eate the s i m i l ar i ties between the source an d the target , but t hey are discussed in t he next chapter . ) Then , o f course, non-l i nguistic metaphors can also b e understood differ ently by different people, or not u nderstood at al l . For i nstance, th ree ti mes in Luis B uiiuel 's Th e Discreet Cha1·m of the Bourgeoisie, we see a sequence w here the six main characters of t h e fi l m are wal king along a road which runs t h rough a barren landscape. This sequence i s i nterpreted by fi l m critic G w y n ne Edward s : " [T]he s h o t c reates a sense o f the ch aracters ' suspension in space and t i m e , of thei r uni versality, and also of their bewi lderment and isolat i o n . " [ Edwards 1 9 8 2 , p. 263 . ] V i rg i n i a H i ggi n bo t h am wri tes about the same seq uen c e : " T h e l e i t mo t i f of t h e c h a r ac t e r s head i n g d o w n the high way seems to stress the i mportan ce of m o t i o n in the l i ve s of the elite. For B uiiuel, their perpetual acti vity i s often m i n d le s s and without di rection . " [ H i ggin bot h am 1 9 7 9 , p . 1 72 . ] C r i t i c John Si mon , on the other h a n d , consi ders the sequence quit e trite, if not mean i ngless : " [T]he t h ree or fou r recu rren ces of t h e shot wi t h i n crem ent a l variations tel l us n o more than t h a t our b o u rgeo i se sextet is trudging down the r oad of l i fe with a d i ffe re n t expression on each face. " [Simon 1 9 78, p. 366 . ] Finally, t her e are t w o character i s t i cs o f l i ngu i s t i c metaphors that are much more pronounced in non- l i n g u i s t i c m e t ap h o rs . O ne is t hat non- l i nguistic m e t a p h o r s are more o b v i o usly asymmetric than the l i nguistic ones. This
26
Part I: The Problem
is because the rel ation between a symbol and i t s referent i s , in general , a u n i d i rectional one. ( How coul d the emotional state of G i u l i ana be a symbol for the blotches of pai nts on the screen ? ) The other i s t h at m any more non l i nguisti c metaphors seem optional , l i ke the metaphorical i nterpretations of Moby Dick and T h e Wiza rd of Oz, t han l i nguistic metaphors. I n all the examples presented here, w i t h the exception of the K lee pain t ing, the complex symbol ( w hether i t be a screen image, a painting, or a piece of religious tex t ) i s meani ngful conventionally. O n e can certainly look a t t h e Van Eyck , read the ew Testamen t , and watch Th e Birds, and understand and enj oy each acti v i ty w i t hout i nterpreting anything metaphorically. 1 .6
M e t ap hors , S i miles , A nalogies and Mo dels
Metaphors are often considered close cousins of, i f not iden t i cal w i t h , sim iles, analogies , and models . However, t here i s no consensus among various researchers as to what t hese relat ionships are, and a review of t he l iterature reveals only a maze of con fl i ct i ng views and opinions. For the purpose of this study, I woul d l i ke to articulate my own posit ion on t hese relationships, si nce I use exam p les t hat might be considered si m iles, analogies, or models by some of you . A s some of t hese examples are crucial to my arguments, i t is i mportant t h at I c l arify a t the outset how and why I see these phenomena as relevant to the study of metaphors . 1 .6.1
•
M e t ap hors and S imiles
Consi der simi les fi rst . S i m i les a re characterized as statements of the form " X is l i ke Y , " as i n " T h ese h i g h ways are like snakes . " However, as O r t o n y ( 1 9 7 9 ] has pointed out , the presence of the word ' l i ke' i s not sufficient by itself to form a s i m i le, s i n ce t here also exist statements of li teral similarity such as "Encycloped i as are l i ke diction aries . " To see how a s i m i l e (or a statement o f l iteral similarity) relates to meta phors , we must figure out t he target of t he description expressed by the s i m i le. There are t wo possi b i l i t ies here. Most often , t he s i m i le " X is l i ke Y" is intended to be a statement about X. That i s , "Th ese highways are l i ke snakes" is supposed to be about t hese highways. In this case, we can see what happens when the s i m i le is applied to t he t arget . The only part of the description t h at m ight be problemat ic is ' l i ke snakes . ' However, the word
Ch ap t er
1:
Ch aracterizing Metaphor
27
' l i ke ' conventionally means 'simi lar to' ( and not ' iden t ical w i th . ' ) So, the statement i s conventionally say i ng t h at t hese h ighways are s i m i lar to snakes i n certain respects , and , t herefore, no unconventional i nterpretation is cal led for . The same can be said of the statements of l i teral s i m i l ari ty. The second possi ble target for "X is l i ke Y" is the li keness between X and Y . That i s , the statement "These h ighways are l i ke s nakes" m ight be i ntended to describe t he l i keness between t hese highways and snakes. In this case, the description i s i nterpreted conventional ly even more so than i n t he previous case. Thus, as long as X and Y are s i m i l ar i n certai n respects , " X is l i ke Y" does not call for an u n convent i onal i n terpretation , and disqualifies as metaphor (given my characterization of metaphor. ) This conclusion , however, rests o n t he conventional mean i n g o f the word ' l i ke' and a p u rely l inguistic analysis. It would be useful to d i g a b i t deeper to see what cogni t i ve mechanism might be i nvolved i n i nterpreti n g a s i m i le. In applying the description "These highways are l i ke snakes" to the h ighways, you h ave to figure out in what respects the highways are l i ke snakes. In i nter p reti ng the metaphoric parap h rase "These highways are snakes," you have to do the exact same t h i ng. You have to figure out how to i nterpret 'snakes' so that t hey m ight apply to h ighways. G i ven that many such i nterpretations are based on the simi larities between the source and the target , you have to deter m i ne how t hese h ighways might be l i ke snakes. Thus, both the s i m i le and i t s metaphoric paraphrase seem to require the same cogni t i ve process , except t h at the p rocess of comparison i s exp l i c i t l y ignaled by the presence of the word ' l i ke' i n a s i m i le. From t hi s vant age poi n t , we can also better appreci ate the difference be t ween the statements of l i teral s i m i l ar i ty and s i m i les. In applying 'd i ct ionary' ( an d its related concept s ) to encyclopedias, t he degree of unconventionality i s m u c h less t h a.n i n ap p l y i n g ' go l d m i n e s ' to e n cycloped i as ( i n i n t e rpr et ing the s i m i le "Encycloped i as are gold mines . " ) Thus, statements of l iteral simi larity are much less metaphoric than s i m i les, i f i ndeed t hey are metaphoric at all . (The con c lusion that the same cogni t i ve process u nderlies s i m i les and metaphors is bolstered in t he next chapter, where i t i s shown t h at s i m i les can also create s i m ilarities j ust l i ke metaphors . ) G i ven that s i m i les explicitly signal comparison s , i t m ight b e worth noti ng whether or not t hat m akes t hem special i n any way ( cogn i t i vely speaking) . There seem to be two poss i b i l it ies here. One is t hat the presence of t he word ' l i ke' can affect one's abil i ty to comp rehend the i ntended meani ng ( perhaps make i t easier ) . There i s some empirical research t hat has investigated this i ssue, t hough the results are quite i nconclusive, and at t i mes contradictory,
28
Part I: The Problem
as to exactly what the effect is. For i nstance, Verbrugge [1980] noted t hat simi les are often t reated as symmetric comparisons between X and Y ( the target is the l i keness between X and Y), whereas when paraphrased w ithout ' l i ke' ( "X i s Y" ) , t hey are t reated as asymmetric statements where the source Y is being used to describe the target X. Reynolds and Ortony [1980] noted t hat chi l d ren, 7- 12 years of age, when asked to choose an appropriate ending ( from a gi ven set of endings ) for a given short story, prefer similes to the "X is Y " form . Contrad i c t i ng this resul t , Winner et al. [1980], experiment i n g w i t h children aged 6 , 7, a n d 9 years, found that b o t h similes ( "Raindrops were l i ke tears fall i n g from the sky" ) and predicat i ve metaphors ( "Rain d rops were tears falling from the sky" ) have about the same degree of comprehensibi l i ty, w h i ch was less than the comprehensibility for topic-less metaphors ( "Tears fel l from the sky" ) . Later experiments by Vosn i adou , Ortony, Reynolds and Wilson [1984] con fi rmed Reynolds and O rtony's findings , and con tradicted t hose of 'vVi nner et al. The other possible way in which the presence of the word ' l i ke' might make simi les special is by taking away some of the emotional i ntensity t h at accompanies the "X is Y" form by red ucing the i mpact of the shock t h at we feel i n i tially due the seman t i c distan ce between X and Y . As t h i s emo tional i n tensity m ight be an im portant factor in poetry and l iteratu re, it is u nderstandab l e that l i terary theory would want to distinguish similes from metaphors, as is done in Nowottny [1962] .
1.6.2
M e t ap hors and Analogies
The term ' analogy ' i s used i n the l iterat ure in many different senses [In I woul d l i ke to d i st i n g u i s h two different senses of analo gy . One has to do with s i m i l arities between t he two si t uat i o ns w hethe r not i c i ng the existing si m i l arities or creating new ones-and the other h as to do w i t h predicting fu rther simi lari ties between the two s i t u a t i o n s based on the exi s t i n g ones . T hese two usages of analogy are usually not distingui shed, but it is very crucial to do so for t h i s s t udy, si n ce t here is a great epistemological chasm separati n g t hem . Conseq uently, 1 woul d l i ke to say a few words here elaborating each sense of analogy and relating it to my characterization of metaphors. durkhya 1 989] .
-
Chap ter
1:
Characterizing Metaph or
29
Simple Analogy
The fi rst sense of analogy concerns s i m i l arit ies between two objects or situ ations. A s I woul d l i ke to defer my discussion of t he creat ion of s i m i l arity to the next chapter, let us j ust focus on analogy as not i c i n g some existing s i m i l ar i ties between two s i t u ations. I refer to this sense of analogy as simple analogy. A simple analogy can take the form of a l i ngu i s t i c expression , as i n "White blood cells fight germs a s soldiers fight an i n vad ing army. " I n this way, t hey seem iden t i cal to simi les, and , consequently, the remarks I made above concerni n g s i m iles apply here also. In parti cular, s i m ple analogies couched i n l i nguistic terms do not req u i re u n conventional i nterpretations, tech n i cally speak i ng, but use t he same cogn i t i ve mech anism as the one used i n u n derstan d i ng meta phors . Of course, one shou ld note t h at simple analo gies are even more expl i c i t t h an si m i les. ( The s i m i l e correspon d i ng to t he above simple analogy would be "While blood cel ls are l i ke sol diers . " ) Though the more exp l i ci t for m m i ght m ake i t easier for one to arrive at the i ntended i nterpretation of the analogy, it still requi res t h at the sou rce ( soldiers i n t h e army and related concepts) b e gi ven a n u n convent ional i nterpretation i n order t o apply i t meani n gfully t o t h e target ( the i m mune system ) . S imple analogies are more often encoun tered i n cogn i t i ve setti ngs t han i n purely l i nguistic set t i ngs. For i nstance, one cou l d ex p l ai n t h e structure of the atom to a physics student by analogy to the solar system : "An atom i s l i ke a m i n i ature solar system . " O r t here is the parable of the sower t h at Jesus tells his d i sciples to m ake the poi nt t h at His teachi ngs wou l d be u sefu l on l y i f t aken to heart [ Mallhew 1 3; Mark 4 ; L uke 8] . ( A ccording to the parable, as a sower was sow i ng seeds, so me ( s eed s ) fel l along the pat h , some fel l on rocky grounds, some fell u pon thorns, and some fel l on good soi l . Those t h at fel l along t h e path were eaten up by the birds. Those t hat fell on rocky grounds sprouted i mmediately b u t , because they could not develop roots , were scorched when t h e s u n came out . Those t h at fel l u pon thorns were c hokes up by t h e t h o rn s . Only t h ose t h at fell on good soi l brought forth grai n . ) I am l i m i t i ng myself here to the u se of t hese analogies to i l l ustrate certain features of an object or situat ion ( t he t arget ) by poi n t i n g the featu res of an analogous s i t u ation ( the sou rce) t h at is easier to understan d . The usc of analogies to make further i n ferences about the target is discussed later. All such simple analogies make use of a cogn i t i ve p rocess t h at is l i ke t he one used i n i nterpreti ng metaphors. The more fam i l i ar sou rce concepts are appl ied to the less fam i l i ar target phenomenon , req u i r i ng an u n conventional i nterpretation of the c o n ce pt s i n the process. One t h i n g you
m i gh t n ot i ce
from t hese exam ples of s i m ple an alogy i s that
30
Part I: The Problem
there is less of an asymmetry ( than metaphor ) between the source and the target . The atom-solar system analogy can equally well be used to commu nicate the st ructu re of the solar system to someone who has studied some atomic physics b u t not astronomy. "Soldiers fight an i n vading army l i ke white blood cells fight germs" can be used to tell a m icrobiologist about warfare. The mean i ngs t ransferred when the simple analogy is used in one d i rection and when it used in the other d i rection are more or less the same, u n l i ke the situation with l i nguistic metaphors . Perhaps , extrapolating the findi ngs of Verbrugge [ 1 980] , t here is a gradual ecli pse of asymmetry from non-simile metaphors, t h rough simi les, and to simple analogies. This eclipse becomes total for certai n variants of simple analogies commonly known as pmpo1'lional analogies, which are completely symmetrical . P roportional Analog y
P roportional analogies are characterized as relations of the form " A i s to as C is to D." L i ke sim ple analogies, t hey might also come from verbal domai n , as in " G i lls are to fish as lu ngs are to humans . " In fac t , all si mple analogies can be paraphrased as proport ional analogies : "Defending soldiers are to an i nvad i ng army as white blood cells are to germs" and "Electrons are to the nucleus as planets are to the s u n . " The symmetry of proportional analogies is evident in the fact t h at the terms B , D can be i n terchanged w i t h the terms A , C , respecti vely, w i t hout affecti ng the meani ng o f the analogy. For instance, " L ungs are to humans as gills are to fish" cap t u res the same meaning as the version presented above. ( P roportional analogies are sym metric in another way. The terms B and C of an analogy can be i nterchanged w i t hout distur bi ng t he analogy. For i nstance, " G i l ls are to lungs as fish are to humans" also forms an acceptable analogy, t hough one coul d argue t h at t h i s analogy does not q u i te mean the same th ings as the version p resented above. ) P roportional analogies can also be formed in percept u al domai n s . For i nstance, Figure 1 . 1 shows a proportion al analogy relation i nvolving ge ometric figures . I n fac t , such analogies often form the staple of standardized intelligence tests, such as the M i l ler's A nalogy Test . B
We encounter some immediate problems i n ass i m i lati ng p roportional ana logies with our characterization of metaphor, for we ask : What i s the t arget of the proportional analogy? What is the analogy about ? What is the de scri ption? What are the symbols? What are the convent ional i nterpretations of the symbols? And so on. I t is im portant to clarify these issues , sin ce, as I show i n the next chapter, proportional analogies p rovide a key i n sight i nto solv i n g the riddle of creati ve metaphors.
Chap ter
1:
31
Characterizing Metaphor
0 D A
D B
c
D
FIGURE 1 . 1 : A proportional analogy relation ( ' A is to B as C is to D ' ) involving geometric figures.
A t least for proportional analogies i nvolving words , all t hese problems are easily addressed . For i nstance, in the gills-lungs analogy, fish and gills form one situat i o n , and humans and l ungs form the other s i t uation . W h i l e t he symmetry o f the proporti onal analogy precludes us from disti ngu i s h i ng the source from the target , one could regard either one as a complex symbol ( the source) that i s being app l ied to the other situation ( t he target ) . For i n stance, we could view the process of comprehending the analogy as that of i nterpreting the l u n gs- humans relationship i n the fish s i t u ation , or vice versa. This i nterpretation may well be regarded as lying at the middle, or even at t he conventional end, of the metaphoric-content cont i n u u m , because the relevant relationsh i p is 'organ of breat h i ng , ' w h i ch subsumes t he gil ls fish relation u nder its conventional meaning. H owever, l i ke the situation w i t h ' plow ' we encountered earlier, t here is some su bjecti v i ty i nvol ved in rendering this j u dgement , for , after all , the physiologies of humans and fish are quite d i fferent . Consider, however, a n i nteresti ng example provided by H ofstadter [ 1 98 1 85] : "Who i s t o G reat Britain as Nancy Reagan is t o t h e U . S . ? " ( N ancy Reagan was the w i fe of the then U . S . p resi den t . )
Here, the re l at i on s h i p
in question , 'the wife of the presi dent , ' cannot be di rect ly applied gi ven the
32
Pa.rt I: The Problem
pol i t i cal structure i n G reat Britai n , for t here i s no presi dent t here. Moreover , l i ke many metaphors, i t i s possi ble to come u p w i t h different , a n d yet q u i t e acceptable i n terpretations, leading to different answers. For i nstan ce, one could i nterpret ' president ' as ' prime m i nister' and answer ' Dennis That cher, ' who was t h e husband o f t h e then prime m i n i ster o f G reat Britai n . O r one coul d i nterpret i t as ' queen , ' lead i n g to the answer ' Pr ince P h i li p . ' Thus, we see t hat t he notion of metaphorical i nterpretation i s q u i te applicab l e here. We can now t u rn to proportional analogies in percept ual domains , such as the one shown in Figure 1 . 1 . Here the two situations can be i dentified based on the figures that form the fou r terms A, B, C, an d 0 of the analogy. For the example i n Figu re 1 . 1 , we might consider A and B to form one situation and C and D to form the other. Next , we figure out what i s the relation between the two terms of one si t u at i on , and then i nterpret it in the context of the other s i tu ation . Shoul d we choose to regard A and B as the source, the relation becomes ' move the ci rcle from the i nside of the upper triangle to the i nside of the l ower square. ' Note that this descri ption is essent i al ly a struc t u red set of symbols, for the terms ' inside, ' 'upper , ' ' t ri angle, ' and 'square , ' are symbols t hat are i nterconnected i n a certain way i n the description . I n i nterpreti n g t h i s descri p t ion i n the context o f t he t arget object consist i ng of figures C and D, we need t o i nterpret ' t ri angle' as ' p entagon , ' 'circle' as 'el l i pse, ' and 'square' as ' rectangle with rounded corners . ' This i nterpretation i s clearly non-conventional , and can be l i kened to the i nterpretation of the concept ' president ' in the context of the British system of governmen t . Thus, proport ional analogies i n volving geometric figures also reveal an u nderlying cogni t i ve mechanism t h at i s l i ke t he one respon s i b le for metaphors. I t is i m p ortan t to appreciate t h i s l i n k between t h e process of i nterpretation t hat is tak i n g place in perceptual domain s , as seen in Figure 1 . 1 , and verbal and cogni t i ve metaphors . As I show in the next chapter, t h i s domain of geometric proportional analogies provides t h e most con v i n c i n g evidence of the creation of similarity. I t also leads us to some key i nsights i nto how the creation of s i m ilarity takes p l ace. P redict ive Analogy
Finally, we come to the other sense of analogy t h at I ment ioned earlier, namely the process of predicting further s i m i l ar i ti es between two objects or events on the basis of some existing simil ar i ties between them. Here it i s assumed t h at the fact t hat t here are existing sim i l arities i s sufficient by i t self to 'j ustify ' the conclusion t hat there m i ght be other similarit i es as wel l . For i nstance, suppose a person has never steered a boat before.
Chapter 1 : Characterizing Metap h or
33
However, he h as driven automobiles, and from what he knows about boats and automobi les, he sees many simi lari ties between the two. From t hese s i m i l arities, he m i ght 'j ustifiably' conclude t h at pushing the rudder to t he left i n the boat-being analogous to t u r n i ng t he steering wheel to the left i n the automobi le-would cause the boat to turn left. I refer to this sense of analogy as predictive analogy, which i s also variously known as 'analogical reasoning' and 'analogical i n ference. ' This sense of analogy i s i n widespread use [ Carnap 1 962, p . 5 8 6 ; Gentner G i ck and Holyoak 1 98 0 , 1 98 3 ; Hesse 1 96 6 , pp. 1 0 1 - 1 29 ; Von Wright 1 96 5 , pp. 1 34- 1 3 6] . Cogni t i ve scientists have fou n d i n i t a val uable source of heuristics for problem solving, have conducted many experimental stud ies about it, and h ave prvposed a number of theories of predictive analogy. Logicians h ave done their part by taking seriou ly the chal lenge of providing some sort of logical fou ndation for predictive analogy so t h at an i n ference from pred i c t i ve analogy comes across as more probable than, say, a random i n ference, and have developed mathematical frameworks to j ustify i t . 1 98 3 ;
For m y part , I wou l d l i ke t o d istan ce m y use o f t h e term ' metaphor' from ' pred i c t i ve analogy. ' The reason is that , to me, metaphor is the process of meani ngful ly i nterpreti ng something as somet h i n g else, and in this process , the fact t h at some parts of the i nterpretation have been carried out success ful ly, does not j ustify i n any way t h at other parts of the i nterpretation can be carried out as wel l . For example, when you u nderstan d "The sky is cry i ng," the fact that you can iden t i fy tears with rai n d rops does not 'j ustify ' that other aspects of crying, such as 'salti ness of tears, ' 'sobbing noise , ' ' wet eye lashes, ' and ' wet ch eek s , ' can all be i nterpreted as wel l . Of cou rse, they might all be can d idates for i n terpretat ion , and one might be able to extend t h e in terpretation to a . varyi n g degree depend i ng on one's i m agi nation . But there is no 'j ustifica.t i o n ' here. In Chapter 7, I discuss a certai n mode of metaphor t h at ca p t ure s t h i s o p en-endedness, which i s very much l i ke pred ictive anal ogy m inus the 'j u st ificat i on . ' Lest t h i s might seem a small techn ical ity on w h i ch to base the c l ai m t h a t my ch aracterization of metaphor h as not h i ng to do w i t h predictive analogy, let me emphasize that this 'j ustification' is very much t he l i feblood of pred i c t i ve an alogy. Without it p red i c t i ve analogy loses all i t s force as a. problem solving heuristic-t he role w h ich is t he sole reason t h at pred i c t i ve analogy h as been so much i n the mai nstream of cogni t i ve science research . G i ven that analogy i s w idely used i n the sense of ' pred i c t i ve analogy, ' and its cogni t i ve potent i al i s highly rated , i t is only appropri ate to place it in the context of the framework of metaphor and cogn i tion that I am developing
Pa.rt
34
I:
The Problem
i n t h i s book . I undertake t h i s t ask i n Chapter 9, where I review the various attempts t h at h ave been m ade to j ustify predictive analogy, and argue t h at i t i s best seen as a cogni t i ve process that, w h i le useful at t imes, can also be a serious obstacle to cogn i tion at others. U n t i l then , however, let me emphasize once more t h at my term metaphor does not cover predictive analogy i n any way, and the two should not be confused . 1.6.3
M e t aphors and M o dels
By ' models' I mean t h i ngs l i ke a small scale replica of a ship, the Stone Age v i l l age i n a natu ral h istory museu m , a picture of a dress accompanied by a sample of the fabric i n a catalog, wind t unnels used by aircraft designers, an arrangement of colored marbles put together by a chemi stry professor to ex plai n the molec u l ar struct u re of benzene to her students, the hydrau l i c model of electrici ty, a computer simu lation of the t raffic flow at a city planner's of fice, the K eynesian model of the economy, and so on . I n each case t here i s an obj ect ( or situat i o n , or phenomenon ) being modeled (the t arget ) , and t here is another object ( t he source) , w h i ch can be regarded as a structured set of ymbols, that represents (or describes ) the t arget . There is also an element of i nterpretation i nvolved , si nce the parts of a model ( t h e symbol s ) must be i n terpreted appropri ately in the context of the t arget for the model to be meani ngfu l . This i nterpretat ion , at least for the examples presented above, is based on an underly i ng st ruct u ral sim ilarity between t he source and t he target . H owever, most models are deli berately constructed to represent the phe nomenon being modeled in certai n respects, and so t here is an i ntended i nterpretation that goes w i t h them . T hese interpretat ions are not u n l i ke i n terpreti ng the w i ne at the commu n i on as the blood of Christ . For instance, a scale model of a ship h a s a conventional i nterpretation t hat is a necessary con d i t ion of its being t he model ; wi thout the i nterpretation, it is not a model at all . Of course, t h i s i s not to say that different models of the ship m i ght not have different i nterpretations. O bviously, a model of the ship t h at i s used at a travel agen cy for showing i t s customers the types of available accom modat ions needs a different i n terpretation than the model used by a marine engi neer to determi ne how much the ship i s l i kely to roll during squalls. But for any given model , there i s a conventional i nterpretation t hat goes w i t h i t , and using t h e model w i t h that i nterpretation does not seem l i ke metaphor at all . Thus, i f such models were to be considered metaphorical at all , they would lie at the conventional extreme of the metaphoric-content continuum.
Chap ter
1:
Ch aracterizing Metaphor
35
Of course, a model might be i nterpreted in rather u n convent i onal ways, as noted by Goodman i n an amusing l i t t l e anecdote t h at I cannot resist recoun t i n g here: "Let me tell you two stories-or one story with two parts. M rs . M ary Tri c i as studied [ an u pholsterer's] sample book , m ade her selection , and ordered from her favorite tex t i le shop enough m aterial for her overstuffed chai r and sofa-i nsi st i ng t h at i t be exactly l i ke the sample. When the bundle came she opened i t ea gerly and was dismayed w hen several hundred 2" x 3" pieces with zigzag edges exactly l i ke the sample fl u ttered to the floor. When she called the shop, p rotesting loudly, the proprietor replied, in j u red and weary, ' B u t M rs . Tri c i as , you sai d t he m ater i al must be exactly l i ke the sample. When i t arri ved from the factory yes terday, I kept my assistants here half the night cutting it up to m atch t he sample. ' This i n c i dent was nearly forgotten some month s l ater, when M rs . Tri c i as , h aving sewed the pieces together and covered her fur n i t u re, decided to have a party. S he went to the local bakery, selected a chocolate cupcake from those on display and ordered enough for fifty guests, to be deli vered two weeks l ater. J ust as the guests were begin n i n g to arrive, a truck d rove u p w i t h a single huge cake. The lady r u n n i ng the bake-shop was u t terly di scouraged by the complai nt . 'But M rs Tricias , you have no i dea how m u ch trouble we went to. My husband runs the tex t i le shop an d he warned me t h at you r order woul d have to be i n one piece. "' [ Goodman 1 978, pp. 63-64] . The i nterpretations of the proprietor are certai n l y u n convent ional , and t hey can be considered metaphorical . In spite of their seem i ngly arbit rary nature, t hey do p r e se r ve cert a i n s i m i l arit ies between the model a n d the object being modeled . I n fac t , what this story reveal s i s t h at many of our conventional i nterpretations t h at we t ake for granted are not the only ones possible. I nteres t i ng as this example i s , such u n conventional i nterpretat ions are qu i te rare. So I must conclude by noting t h at while models do have t he poten t i al for sustai n i n g u n conventional i nterpretations, t hey are i nterpreted conventionally almost all the t i me. Noticing thei r potential for forming meta p hors i s i m portan t , hence the anecdote from Goodman, for s i m ilarity-creating metaphors can and do arise from models. B u t this is an issue I d i scuss i n the next chapter.
Part I: The Problem
36
1.7
C onclusions
The pu rpose of t h i s chapter has been to characterize metaphor and to expli cate i t s relat i onsh i p w i th s i m i le, analogy and models. The i ssue at stake is not that t here i s one correct mean i ng of metaphor, and we ought to fi n d out what i t i s , but rather that we must clearly demarcate the range of phenom ena covered by my use of the term . To do so i s i mportant because w henever I present an exam ple of metaphor in a later chapter, it would be helpful to you not to have to wonder whether the example really i s a metaphor. Also, clarify i n g my usage of the term metaphor reduces the possi b i l i ty of confusion and misunderstan d i n g of the argu ments in this book. W i t h t h i s goal i n mind, the ch aracteri zation of metaphor I use i s t hat a metaphor is an unconventional way of descri b i ng (or representing) an object , event , or situation ( real or i m agi ned ) as another object , event or s i tuation . The object being descri bed is called t he t arget , and the object that i s be ing used to u n convent ionally describe the target is called t he source. The source parti c i pates in the process essent i ally as a struct ured set of symbols that have to be applied to t he target in unconvention al ways so as to render the descri ption mean i ngfu l . The unconvent ionality of i nterpretat ion i s em phasized because t he objecti ve of t h i s book i s to study the process by w h i ch metaphors create new meani ngs and concepts, and create s i m ilariti es . I n exam i n i ng t h e relationshi p o f s i m i les, analogies, a n d models to my characterizat ion of metaphor, I noted that s i m i les m ake use of the same cog n i t i ve mechan ism as metaphors, t hough techn ically t hey can be regarded as convent ional . I d i s t i nguished between two senses of analogy. One, w h i ch I call s i m ple analogy, refers to comparing two objects or event s and not i c i ng t heir s i m i l ar i t ies . S i mple verbal analogies behave i n the same way as s i m i les; t hey h ave the same underlying cog n i t i ve mechanism as metaphors . S imple non-verbal analogies and proport ional analogies (a variant of simple analo gies ) , especi ally t hose i nvolving perceptual domains such as geomet r i c figures, are m ore overtly metaphori cal . The other, more popular sense of analogy, which I call pred i c t i ve analogy, refers to the process of i nferring fur ther sim i larit i es between two objects or events based on the exi s t i n g simi larities, and i s q u i te d i fferent from metaphor. Considering models, we saw t hat while t hey have t he potential to sustai n an unconventional i nterpretat i o n , their i nterpretat ions are usually conven tion al . As a. last note, I would l i ke t o emphasize t hat most o f the metaphors discussed in t h i chapter, i ncluding s i m iles, analogies, and t he u n convent ional i nterpretat ions of Mrs. Tri c i a.s ' proprietor, are based on some u n derlying
Chapter
1:
Characterizing Metaphor
similarit ies between the source and the t arget . For the rest of the book ,
37
I refer
to such met aphors as sim ilarity-based m etaph ors, in contrast to sim ilarity
creating metaph o rs, which are i n t roduced in the next chapter .
Chapter 2 E nter S i milarity- Creat ing Metap hors
2.1
Int ro d u c t i o n
As I mentioned i n the prologue, the i nteraction t heory of metaphor has been p roposed primarily to account for the creation of simi larity that , it is clai med , accompanies certain metaphors . The proponents of t h i s t heory however almost all of them philosophers-take the phenomenon of creation of simi larity more or less for granted . That i s , while they use t h i s phenomenon to discred i t the comparison theories of metaphor, and articulate their version of the i nteraction t heory to account for i t , the fact t h at certai n metaphors can, i ndeed , create similari ties i s i tself not established i n any reasonable fashion, beyond occasionally mentioning a fleeti ng example. As a result of t h i s, what I consider to be essent i ally a methodological s l i p , we h ave on one hand philosophers trying to formulate t heories of a. phenomenon that h as not been empirically demonstrated-a factor that may h ave been the primary cause of the fuzziness surrounding most versions of the i nteraction t heories . And we h ave, on the other hand , psychologists and cog n i t i ve scientists all focusing their attention on comparative, similar i ty-based metaphors, notwi thstanding the cri t i cisms of t he i nteractionist philosophers, since here they h ave a phenomenon t hey can put their hands on. Indeed , t here h ave been q u i te a few empirical studies of how existing similari ties be tween t he source and the t arget form the basis of a metaphor, what k i n d of similarities c a n form t h e basis o f a metaphor, how t hese similarities can be computed from t he given representations of t he source and the target, and so on . ( See, for example, Gentner, Falkenhainer & S korstad 1 987; Gen39
Pari I: The Problem
40
t ner & Clement 1 988; Gick & Holyoak 1 980; 1 983; Malgady & John son 1 980; O rtony 1 979. ) So great has been the i mpact of t hese studies , t hat the cogni t i ve science research on metaphor has been com pletely dom i n ated by s i m i lari ty- based accounts . I n order to no t make the same mi stake a nd have a book focusing on a phenomenon of the existence of w h i ch you may not be convinced , I devote t h i s chapter to demonstrat i n g t hat s i m i l ari ty-creati ng metaphors are quite real , and t hat t h ey p l ay an i m portant role i n cogn i t i on . I do so by i nt roducing s i m i l ar i ty-creat i n g metaphors w i t h several examples i n Section 2 , and argui n g t hat t hese metaphors d o , i ndeed , create s i m i la ri t i es between their source and their t arget. Then , in Sect ion 3 , I review the few psychological studies that have sought to demonst rate the creat ion of s i m i larity. I n Section 4 , I show t hat t he creat ion of s i m i lari ty can also result from the phenomena of s i m i le, analogy, a n d models that were related to metaphor in t he last chapter. In Section 5 , I cont rast the roles of s i m i larity-creati ng metaphors and s i m i lari ty based metaphors in cogn i t ion , and argue t hat si milari ty-creati ng· metaphors are evi dent in many of the c rea t i ve acts of cogni t ion. Final ly, I s u m marize t he main points of this chapter i n Sect ion 6 , and highlight the key p roblems posed by s i m i lari ty- creat i ng metaphors . 2.2
S ome Examp les o f S im i larity- C reat ing M e t ap hors
As ment ioned in t he prologue, i t is somewhat tr i cky to demonstrate the cre ation of s i m i lar i ty convinci ngly, s i n ce even in a s i m ilarity-creating metaphor, there are always s i m i l ar ities after the metaphor. So, if a metaphor i s simply presented , i t i s hard to be convi n ced that t here were no s i m ilariti es before t he metaphor. After I p resented Carl Sandburg's Fog in the prologue the way I did, i t wou ld not su rprise me if some of you t hought : "Of course, fog and cat are si m i lar-t hey both creep on you silently. I j ust d i d not see t h is s i m i l ar i ty before. " B u t t h i s i s preci sely my poin t . Objecti vely speaking, any two objects are s i m i l ar in some respect . By creation of similari ty, I mean the creation of s i m ilari ty i n the conscious mind of a cog n i t i ve agent . I p resent several more examples here to convi n ce you of the fact t h at cert a i n metaphors can create s i m i lari t ies between their source and the target . I n doing so, I follow the same approach as i n the prologue. I provide you w i t h pairs o f objects, a n d you are i n v i ted to t ry to articulate a l l possi ble ways i n w h i c h you consider the t w o objects i n each pair to be s im i lar. ( Take your
Chapt er
2:
Similari ty- Creating
Metaph ors
41
time i n doing t h i s experi men t . ) Here are the pairs: ocean a n d ch i cken , pi ano and far m , w i l d flowers and water, river and com puter, com puter and harp, ocean and harp, h arp and spaces h i p , spa. c eshi p and b o n e , b o n e a.n d ocean . Now consider the beaut i ful poem liVh ite Ha wthom by Ea.va.n Bolan d .
in
the
We s t
of hela n d
I drove West in the season between seasons. I left behi n d subu rban gardens . La.wn mowers . s m a l l t a.lk . U n der low skies, p a.st splashes o f col t s foot , I assumed the h a.rd shyness of Atlant i c l ight a.n d the supersti tious a. u ra. of hawthorn . A l l I wanted t hen was to fi l l my a. r ms w i t h sharp flowers, to seem, from a. d istance, to be a . pa. r t of t h a. t i vory, dow n h i l l rush . But l k n e w , I h a. d a.l wa.y s know n , the custom wa.s not to touch hawthor n . Not to bring i t i ndoors for t he sake of the l u ck such const raints would forfeita child m i ght die, perhaps , or a. n unexplai ned fever speckle heifers . So I le ft it stirring on t hose h i l l s w i t h a. fl uency o n l y water ha.s . A n d , l i ke water, able to redefine l a.n d . And free to seem to b efor anglers, and for travellers astray i n t h e u n m arked l i ghts o f a May d usk the only language spoken i n those parts. The p o e m
is
fi lled w i t h vibrant and
creat i v e metaphors .
I n fact , the poem
Pari I: Th e Pro blem
42
as a whole can be i nterpreted metaphorically i n more t han one way. W h i le I leave the purs u i t of s u ch i nterpretat ions and their analyses to you r i n d ivid ual leisure and fan cy, I wou ld l i ke to draw you r attention to one parti cu l ar metaphor that i s dom i n ant t h roughout the poem : n amely wild flowers as wa ter. The metaphor is evident in ph rases such as "splashes of coltsfoot" and "ivory, downh i l l rush," but it c l i m axes, to my feeli ng at leas t , in the sixth verse: "st i rr i n g on those h i l l s . . . redefine l an d . " T he si mil arit ies between the wild flowers ( hawt horns here) and water that the metaphor m akes u s see are very m u ch created s i m i l arit ies, for I would be very surprised if t hey were a part of you r earl ier com parison of water and w i ld flowers. As another example, consider the following l i nes from Stephen Spender's well-known poem Seascape: There are some days the happy ocean l ies L i ke an unfingered harp, below the lan d . A fternoon g i l d s a l l t h e si lent w ires I nto a b u rn i ng music for the eyes. O n m i rrors flas h i ng between fine-strung fires The shore, heaped u p w i t h roses , horses , spi res Wanders on water tal l above ri bbed sand The motionlessness of the hot sky t i res A n d a sigh , l i ke a woman 's from i nlan d , Brushes t h e i nstru ment w i t h shadowy hand Draw i n g across those wi res some gull's sharp cry O r bel l , or shou t , from d i s t a n t , hedged- i n , s h i res; These, deep as anchors , the h u st l i ng wave buries. Here agai n , after read i n g the poe m , we are at once struck by the s i m ilari t ies between the harp and the ocean . Yet , these s i m i lari t i es coul d not have been a part of your earlier comparison of the h arp and the ocean . Let us now t u rn to art s . Consider Piet Mondrian 's Co mposition with Bht e and Yellow [Plate 3] . The pai nt i n g l i terally contains eighteen rect angles, two of w h i ch are colored, one blue and one yellow , and n i ne t h i ck black l ines, five of w h i ch are horizontal and the other fou r vertical . What can t h i s pain t i n g be about ? What c a n i t ' m ean , ' i f anyth i ng a t all ? There seems to be no way to i nterpret the pai nt i ng convention ally. A second look a t t h e pai n t i ng , however, reveals a tension between various components. We see that the arrangements of l i nes and rectangles , and of colors, exh i b i t s a certai n dynamics and equ i li b ri u m . ( See W h i t ford [ 1 987] ,
PLATE 3 : Piet Mondrian, Composition with Blue and Yellow, 1 93 5 , Hirshhom Museum and Sculpture Garden , Smithsonian Institution .
Chapter
2:
Similarity- Creating Metaphors
43
p p . 1 2-20 ; and Champa [ 1 985] , Chap. 12, pp. 1 1 3- 1 26. ) I n fact , t h i s dynam i c equilibrium is a. characteristic o f many o f Mondrian 's com posi tions. W hat can t h i s dynam i c equi li b r i u m be about ? What cou ld it be say i n g about l i fe, or anyth i n g else for that matter? VVe need not go very far, for Mondrian h imself h as w r i t ten a lot about h i s art , and how h i s art rel ates to l i fe. For i nstance, i n one art i cle he wrote: "Good and evil-the two princi pal oppositions of l i fe-all the world k nows t hem , all the world suffers or is h appy because of the one or t he other. B u t not everyone real i zes the true value of t h i s opposi tion , and in genera.J we do not even see t heir necessity: we demand good , and avoid evi l as much as possi ble. I n t u i t i vely, man wants the good: u n i ty, eq u i l i br i u m-especi al ly for h i mself. Thus he fal ls back i n to the search for false ease and stat i c equ i l i b riu m , w h i ch i s i nevi tably opposed to the dynam i c eq u i l i bri u m of t rue l i fe. He sat i sfies h i msel f with the false u n i ty an d in seeki n g i t rejects t h e dual i ty o f opposi tions, which , w h i le d i ffic u l t to per ceive, i s nevertheless very real to us. It is evident t h at u n t i l the present man generally h as fel t t he profo un d u n i ty of true l i fe, b u t l i v i n g i n this d i seq u i l i brated world he does not accept the two oppositions simul taneously: he does not l i ve l i fe as a w hole so t hat the dual i ty can be resol ved . . . . H owever, l i fe shows us t h at i t s beauty resi des i n the fact t hat precisely t hese d i seq u i l i brated oppositions compel us to seek equ i valent oppositions: t hese alone can create real u n i ty, whi ch u n t i l now h as been real ized only i n t hought and i n art . " [Mondrian 1 9 3 4 , p p . 283-284 . ] The same t heme i s echoed i n many other p laces i n M o n d r i a n 's writi ngs. T h is i nterpretat ion , however, w h i ch is rem i n i scent o f B u d d h i st metaphysics, m akes the Mondrian pai n t i ng deeply mea n i ngfu l at once. M oreover, the s i m i l arities b et ween t h e un i ty of l i fe and t h e p a i n t i n g t h at the i n t e rpr e t at i o n s uggests are created ones. F i n al ly, let us t ake a q u i ck l ook at the sym bolism in fi l m s for the evidence of s i mi larity-creati n g metaphors . l n Stanley K u brick's classic fil m 200 1 : A Space Odyssey, t h e movemen t of a bone t h rown i n the ai r by Moon- Watcher ( an ape- m an ) is transformed i n to the movement of a space-sh i p in the twenty first cent ury by means of a c u t t hat m ay wel l be one of the most d ramat i c cuts i n t h e h istory o f films. Though t h e c u t seems t o have t h e character o f an unobtrusive j oi n , for the movement of the spacesh i p is closely matched w i t h t he movement of the bone, i t s effect , o n the cont rary, is q u i te shocki ng. ( See also W h i t tock [ 1 990] , p p . 5 1 -52. ) We rea l i ze tha. t they are both expressions of
44
Part I: The Problem
human technologi cal prowess-a prowess that, i n the light of the subsequent events of the fi l m , seems quite hollow. In fac t , t hat single cut serves as t he anchor for l i n k i ng the Moon- Watcher sequence to the rest of the fi l m . For i n stance, cri t i c Thomas A l len Nel son notes : "At H i lton Space Station 5 , i n the Howard Johnson Earth light Room , Floyd 's empty ritual of sounds i n the company of So viet scient ists hardly h as any more value as com m u n ication t h an Moon- Watcher's grunts of bewilderment or screams of triumphs. A t t h i s second waterhole, Ku brick shows t h at batt les for terri tory and tribal dom i n ance persist even in t he rarefied air of space; . " [ elson 1 982, p . 1 08 . ] .
.
T h u s , the s i m i l arities that the j uxtapos i tion o f the bone a n d the spaces h i p evoke g o far beyond whatever you m ay have come up w i t h earlier. I n fact , the use of j u xtaposi t ion to create s i m i lari ties is consi dered an accepted technique in ci nema. A l fred H i t ch cock comments on it in his con versat ions w i t h Francois Truffaut , while di scussi ng his film R e a r Window: "In one of [ Pudov k i n 's] books on the art of montage, he descri bes an experi ment by h i s teacher, K u l eshov . You see a close-u p of the Russian actor I van Mosj o u k i ne . This is i m medi ately fol lowed by a shot of a dead baby. B ack to Mosjoukine again and you read compassion on his face. Then you take away t he dead baby and you show a plate of soup , and now , w hen you go back to Mosjouski ne, he l ooks h u ngry. Yet , in both cases , t hey used the same shot of the actor; h i s face was exactly the same. In the same way, let 's take a close- up of Stewart looki ng out of the w i n dow at a little dog that's bei ng lowered in a basket . B ack to Stewar t , who has a k indly s m i le. But if in t he place of t he l i t t le dog you show a half- na ked girl exercising i n front of her open w i n d o w , a n d you go back to a smiling Stewart again , t h i s time h e ' s seen a s a di rty o l d m an ! " [ Truffaut 1 984, pp. 2 1 5-2 1 6] This example u nambiguously demonstrates t hat s i m i l arities can be created , for one cannot say, i n t he case of Mosj ou kine, t h at the same face contained both compassion and hunger, or i n the case of James Stewart's smile in Rea r· Win dow, t hat i t contai ned both kindli ness and lust at the same t i me, and that the other i m age was merely highlighting the appropriate emotion . The s i m i larit i es between the two i mages t hat are seen after t he secon d i m age is presented are created-i n every sense of the word-by j uxtaposition.
Chap ter
2:
2.3
P s y chologi cal S t udies of t he C reat ion
Similarity- Creating Metaphors
45
of S i mi larity T h e examples presented i n the l ast section suggest the existence of s i m i larity creati n g metaphors. G i ven that , it seems reasonable to wonder i f any system ati c study h as been done to provide empirical evidence for their existence. I should emphasize here t h at while t here have been m any empirical studies to show t h at metaphors are based on some underlying s i m i l ar i ty between the source and the target , t hese studies do not refute the creation of s i m i l ar i ty i n any way, for their approach i s to present a metaphor to the subjects, and t hen ask them to explain t he metaphor. If the subjects then explai n it on the basis of the s i m ilari ties between the source and target , t h i s i s evidence of t he fact t h at t here are s i m ilarities after the metap hor. Not h i ng w hatsoever can be concluded about w hether t hese sim i lari ties were created or not , u n less i t i s know n what the sim i lari ties were before t h e metaphor. The problem in demonstratin g t he creation of s i m i lari ty i s to find out what the similar i ti es between t he source and the target are prior to the metaphor, b u t w i t hout giving away the metaphor . In the study by M cCabe ( 1 983] , the problem was partially solved by having one group of su bjects rate s i m i l ar i ties between given pairs of nouns, and another group rate the aptness of metaphors formed by using the two nouns i n each pai r. I am saying ' par t i ally' because one m i ght quite reasonably wonder if the subj ects in the group t h at is assi gned the t ask of rating the sim i lari ties m ay not be trying to i nter p ret the noun p ai rs metaphorically. S t i l l , M cCabe's results were surprising. S he fou n d t h at when the metaphors were presented i n i solated , formulatic sentences ( "Dew i s vei l " ) then t here was a sign i ficant correlation between s i m i l arities and aptness of metaphors. H owever, when the metaphors were presented i n exten ded , natural contexts, then the aptn ess of metaphors was not correlated at all w i t h the s i m i l arities between the source and the target . This suggests that , at least i n their extended contexts, existing s i m i l arities between t he source and the target have no bearing on whether their j u xta position will fo r m an appropriate metaphor or not . I n a l ater study, Camac and G lucksberg ( 1 984] sought to show the cre ation of s i m ilarity d i rectly. They used the lexical decision paradigm to solve the problem of determi n i ng s i m ilarities between sou rce- target pai rs wi t hout giving away the metaphor. I n this paradigm the subject i s presented wi t h p a i r s of random strings of letters , a nd for each pai r she h as to respond 'yes' when both stri ngs form English words, and ' no' when either or both of the stri ngs do not for m Engli s h words. The response t i me is measured for each
46
Part I: The Problem
pai r , w h i ch is t aken to be an i n d i cation of the associations between t he two words i n the pair ( when both strings in t he pair do form words) . The response t i me i s shorter when both stri ngs in the pai r form words t han when either of t hem does not ; and i t is even shorter when the two words are associated . Thus, the response t i me for doclor- n u 1·se would be shorter t han the response t i me for docto r-lion, which in turn woul d be shorter t han the response t i me for koot- akel. I n t h i s paradigm , using a n umber of word pairs t h at are k nown to be associ ated , one can deter mi ne w hether a new word pair i s associated or not by comparing i t s response t i me to the average response t i me of the associated word pairs. Camac and G l u cksberg used this paradigm to test the hypothesis t h at metaphors can be used to create associ at i ons between words, words which were not associated prior to the metaphor. They presented ten subj ects with fou r sets of word- word pai rs. One set contai ned metaphor pairs, w here both the words in every pai r cou l d for m a metaphor. This set included pairs l i ke job-ja ils, surgeon-butch e rs, etc. The second set cont ai ned scram bled metaphor pairs, w h i ch were words t aken from the first set and randomly p a i red, w i t h the restriction t h at t hey did not form a metaphor. This con tai ned pai rs such as surgeon-jails . The t h i rd set had stan dard associated pairs l i ke docto1·- n u rs e . Finally, t he fourth set had scrambled standard asso ciates , which were words from set t hree t hat were randomly paired , w i t h the restriction that the words i n a pair were not associated . When t he response t i mes for all these fou r sets were measured and av eraged over the pairs and across the subjects, a surprising result emerged . Whereas the mean response time for t h e the standard associated pairs was 782 m i l l i seconds, it was 9 1 0 m i l l i seconds for the scrambled [standard associ ated] pairs. There i s a 1 28 m i l l i seconds d i fference in processing t i me between word- pairs t hat are associ ated and word- pairs that are not . For the metaphor pairs however , the metaphor pai rs set had an average response time of 954 m i l l i seconds, and the scrambled [metap hor] pairs had the average response time of 971 m i l l i seconds, showing only a 17 m i l l i seconds difference. This suggests that the metaphor word pai rs were not associated . However, since each p a i r i n t h i s set for m s a reasonable m e t a p h o r , as i n " S u rgeon s are b u t ch ers," the experi ment s uggests that metaphors can create associations between words t hat were not associated before. In a different study, Kelly and Keil [ 1 987] asked t he subjects to compare two semantic domai ns before and after some metaphors connecti n g the two domains were presented . In order to measu re the subj ects' percep t ion of similarity between the two domains before the metaphors , and w i t ho u t giving
Chap t er
2:
Similarity- Creat ing Metaphors
47
t h e m any h i nt o f t h e metaphorical connection between the t w o domains, t hey came up w i t h t he following methodology. The subjects were gi ven a number of concepts from one domain , and they were asked to rate each concept on a given set of semantic d i fferent i al scales . Then they were given a number of concepts from the other domai n , and asked to do the same, w i t h the same set of scales. The s i m i l arity between any two concepts, one d rawn from each domain , was then taken to be s i m p l y their degree of correspon dence on the seman t i c different i al scales. For i nstance, one pai r of domai ns was periodicals an d food . The subjects were gi ven i tems, such as Ne w Yo1·ke1·, Reade1· 's Digest and Wall Street Jour nal, from the periodical domai n , and were asked to rate each i tem on a given set of d i mensions, i n c l u d i ng tasteful-tasteless, h eallhful- unh eallh y, and sp icy bland. Then , t hey were given a number of concepts from t h e food domai n , w h i ch i nc l u ded quich e, sp inach, and hamburger, a n d asked t o d o t h e same t h i ng. From t h i s i n formation , the difference between, say New Yorker and quich e, along the tasteful- tasteless di mension wou ld be the absol ute val ue of the d i fference between the rat i ngs of these two i tems along t h at di mension. Adding the differences along all the d i mensions wou l d provide a measure of how d i ss i m ilar these two concepts are percei ved to be. This procedure was repeated twice for the same pai r of domai n s , and with two groups of subjects. For one of the groups, however, fou r i nstan ces of metaphor i n vol v i ng the two domai ns were presen ted before the procedu re was repeated t he second t i me. For i n st ance, a. metaphor for the periodicals food domai ns that was used in this experi ment was "The New Yorker is the q u i che of newspapers and m agazines . " I t was found t h at , for the subjects who were in the group t hat was presented with the metaphors, t heir perception of s i m ilarity between the two domai ns changed considerably after the meta phors, thereby demonstrat i ng tha. t metaphors can change one's perception of similarity between the two domains. Technically, K e ll y a nd Kei l's experiment demonst rates t h at t h e s im ilar i ties between the domai ns change, and not t h at new s i m i l arities are cre ated . I ndeed , the authors themselves i nterpret thei r results in t he context of O rtony 's model [Ortony 1 979] , where a metaphor is seen as using the h ighly salient att r i b utes of the source to highl ight the less sal ient att r i b u tes of t he t arget . I n t h i s model , the attributes of the source an d the target are all t here to beg i n w i t h , only their relati ve sal ience is changed by the metaphor. H owever, this i s easily explai ned by the fact t hat Kelly and K e i l ' s subjects were p rovided with a. fi xed list of semant i c d i mensions, from w h i ch thei r percept i on of s i m i l arity was determ i ned . There
was
no mechan i s m in t he
48
Part
I:
Th e Pro blem
design of the experiment to test if new attri butes were created . B u t one thing the experiment did demonstrate i s that similarities are not objecti ve, mind-i ndependen t , properties of two gi ven objects, situations, or domain s . For otherwise, how could the si m i l arities between t h e m change? A n d i f s i m i larities along a certain fixed set of semanti c di mensions c a n change, i t i s q u i te conceivable t h at new d imensions of s i m ilarity can be created as wel l . 2 .4
C reat ion of S i mi larity i n Met ap hor- Relat e d P henomena
In the last chapter we saw that the p henomena of s i m i le, simple analogy ( and its vari ant proportional analogy ) an d models are closely related to metaphor, for each has the potential to sustain an u n conventional i nterpretation in describ i ng the target as the source. G i ven that , i t i s natural to wonder i f the creation of s i m i l arity can also arise from t hese phenomena. I n deed , as I show i n t h i s section , each of these phenomena can create similarities between two disparate obj ects or situations. 2. 4 . 1
S imile
The case of s i m i l e i s easily settled . I n the verses of Boland and Spender, t here were two i nstances of metaphor that coul d technically be considered s i mi les, for t hey exp l ici t ly i n d i cate that a comparison i s being made by i ncluding the word ' l i ke. ' H owever, this does not d i m i n ish the emoti ve and cogni t i ve force of the metaphor in any way, and the s i m i l arit ies t h at we see remai n very much t h e created ones. For i nstance, i n Seascape, even t hough the word ' l i ke' is mentioned i n the secon d l i n e , i f, on your first readi ng of t h e poem , you were to pause t here, and ponder on how could the ocean be l i ke an unfingered harp, you woul d probably not be able to come up w i t h the similarities between the two t hat the l ater li nes of the verse evoke. I n fact , t h e presence of t he word ' l i ke' seems to have no i mpact on the emotional i mpact of the metaphor. ( K i tL ay [ 1 987, pp. 1 7- 1 9] makes essentially the same point by considering T . S . Eliot 's s i m i l e "The eveni n g is spread out against the sky �ike a patient etherized upon a table" i n Love So ng of J. A lfred Pruj1-ock, which creates simi larities between the evening and a pat ient . )
Ch apter 2.4.2
2:
Sim ilarity- Creating Metaphors
49
A nalogy
Let us consider si mple analogies now . Clearly, as far as verbal simple analo gies are concerned , all the examples of s i m i l ari ty-creati n g metaphors provided so far constitute evidence t h at simple analogies can also create s i m i larities. T h i s i s because each exam ple can be paraphrased as a s i m ple analogy, as in "The afternoon sun was reflecti n g on the waves i n the ocean l i ke someone was strumming the strings of a harp . " As noted in the last chapter, this parap h rasi n g might make i t easier for someone to arrive at the i nterpreta t ion of the metaphor. W h i le t h i s may rob t h e metaphor of some (or even mos t ) of i t s emoti ve force, it does not alter the fact t h at the s i m i l arities i n the metaphor were t h e created ones, for t hey were not p resent i n t h e earlier comparison of ocean and harp. S i mple analogies i n non-verbal cogni t i ve sett i ngs can also create s i m ilar i t ies. Consider computer software and myt h . What are the possible s i m i lar i ties between the two? They seem quite d i sparate t h i ngs at first . However, Joseph Campbell recalls that whi le he was learn i n g to u se com puter software, he had a sud den revelation about mythology [Cam pbell 1 988, p 20] . J ust as comp u ter software req u i res the user to fol low certai n steps i n order to get the desired effects, a myth also requ ires i t s symbolism to be i nterpreted i n a certai n way i n order t o become ali ve and mean i ngfu l . A n d j ust as the se quence of signals t h a t pro du ces some desired effect with one piece of software m ay not work w i t h another piece of software, t h e way a particular myth i8 i nterpreted may not work w i t h another myth . This an alogy, which had a sig n ificant cogni t i ve value for Cam p bell , created s i m i larities between software and myt hology i n h i s m i n d . For otherwise, it wou l d not have appeared as a revelation to h i m . As an even more bi zarre anal ogy, consi der Jean M et z i nger ' s L e Gou l e r [Plat e 4] and compare i t with quan t u m mech an i cs . L e t you r i m agi n at i on soar, and see i f you can come u p w i th any s i m i lari t i es . Well , Metzi nger's pai n t i ng p resents perspec t i ves from d i fferent angles at once. For instance, t he head s h ows a full-face v iew and a pr o fi l e s i m u l t aneously, a n d t h e t e ac u p combines the view from the t o p w i t h the eye- level v i ew , whereas quantum mechanics lets u s see the same thing s i m u ltaneously as a parti cle and as a wave. You m i g h t h ave had a hard t i m e see i n g t h e s i m i l a r i t i es i n t i1 i s exnm ple, or maybe t h e y were obvious at once. B u t i f you try to t ransport yourse l f back i n h i story t o j us t before qu ant u m mechan i cs was developed , i t wo u l d c e r t ai n l y be i m possible to come u p w i t h any s i m i l arities between the Metzi nger a n d a parti cle. Yet , a Metzinger ( not Le Caut er but another-t he exact Metzinger
50
Part I:
The Problem
does not matter for t h i s argument ) might well have been t he driving force behind N iels Bohr's search for a t heory that allowed the concepts of wave and part i cle to be i nterchangeable, so t hat a particle can be a wave at once, and v ice-versa. ( See A ndersen [ 1 967] , p. 322; and also M i l ler [ 1 978] . ) If we accept t h i s clai m , t hen the quantu m theory i t self becomes a product of analogy, i n w h ich there were n o s i m i l arities between the source and t h e target t o begi n w i t h , b u t after a new theory was created , then t here were s i m ilari ties between the two. ( See also the fasci nat i ng st udy by S h lain [ 1 99 1 ] , w here it is shown how many of the revoluti onary ideas in physics, especi ally modern physics, were preceded by movements in arts that seem to have a.nti c i pa.ted them . ) I n order t o cont rast all these i nstances of analogy where the s i m il ar i t i es are created , [ use t he term aea live analogy, and restrict the term 'simple a n al ogy ' so that i t only appl ies to s i m i l ari ty-based analogies. Let u s now t u rn to p roportional analogies. W h i le verbal proportional an alogies can create s i m i l arities i n t he same way as s i mple analogies ( "What are to the ocean as t he stri ngs bei ng strummed are to t he harp?" ) , it seems that percept u al proportional analogies are not capable of exh i b i t i ng t h i s phe nomenon . Looking at the figures A and C i n Figure 1 . 1 ( Chapter 1 ) , one wonders how is i t possible for anyone not to see t he s i m i l ar i ties between the two figures i n i t i al ly, but t hen see them i m med i ately after the figures B and D are added . The apparent problem here, i n admi t t ing the hypothesis that perceptual proport ional analogies m i ght also create s i m i l arities, must be appreciated for two m aj or reasons. F i rs t , the resolu tion of t h i s problem can provide the most convincing evidence yet of the creation of s i m i lari ty. Second , i t can gi ve us some refreshing i nsights into how the creat ion of simi larity takes place. So let me el aborate on why it seems that p e r c e pt u a l p r op o r t i o n a l an alogies m ay not be capable of creation of s i m i lari ty. It seems quite reason able to concede t hat verbal concepts usually have so many associat ions t hat a person might not be able to bri ng all the associat i on s t o mind a t once. G i ven t h i s , a cogni t i ve s c i e n t i s t w h o wishes to clai m t h at a l l metaphors are s i mi larity- based might offer the followi ng explanati on of what I have been cal l i ng the creation of s i m i l ari ty. When a. person i s asked to com pare, say a cat and the fog, she cannot bring to m i nd all the d i fferent t h i ngs associated w i t h the concepts of cat and fog. Conse q uen t l y, n o t a l l t h e s i m i l ari t i es b e t ween t h e two wou ld be i n c l u d ed in her i n i tial accou n t . H owever , when a n appropriate context i s p resen t e d , a s b y Sandburg's poe m , these h i dden associations are h i gh l igh ted a t once, a n d the person i s able t o see the s i m i larit ies . But the s i m i l arities were t here a l l the t i me, a comp a r i s o n
P L ATE 4 : Jean Metzi nger, Le Gouter (Tea Tim e) , 1 9 1 1 , P h i ladel phia M u seum of A r t : The Loui se and 'vValter A rensberg Collecl ion .
Chap t er
2:
51
Similarity- Creating Metaphors
EE (a)
(b)
(c)
FIGURE 2. 1 : Three geometric figures. You are to compare each pair of figures: (a) with (b) , (b) with (c), and (a) with (c). Write down all possible ways i n which each pair seems similar.
t heorist would argue. When we look at the perceptual proportional analogies i n the l ight of t h i s argument , i t seems t hat the objects i n question ( such a s the figures A and C i n Figure 1 . 1 ) are simple geometric figures , and t hey are right i n front of the person in all their enti rety. T here are no h i dden mean i n gs or associations. The figu re s are reasonably simple. There is no symbol i s m i nvol ved , as i t wou l d be if the figures were o f animals or houses. So, a l l t he person has t o do i s to compare the two figures, a n d come up with the s i m i l arities. And w h atever i s i ncluded t here must be the possible s i m i l arit ies between the two figures. Context can pick out d i fferent s i m i l arit ies from t h i s l i s t , but i t cannot add new t h ings to i t . Well , I hope you get the poi n t . N o w , consider Figure 2 . 1 . It shows t h ree figures . Take figures ( a ) and ( b ) , and compare t hem . Write down if t h ey ap pear s i m i lar to you , and if so, t hen in w h at ways. T h e n do t h e same w i t h figures ( b ) and ( c ) , and then w i t h figu res ( a ) and ( c ) .
geo m et r i c
Now look a t F i gure 2 . 2 . Do
t h e r e form a p r o p o r t i o n a l D ? " l f you a n s wer " N o ' " takt> another look . Do you see the relations involved? Do you see how figures A and C are s i m i lar? But t h ey are t he same as fig u r e s ( a ) and ( b ) , respect i ve l y, in Figure 2 . 1 . A re the s i m ilarities you see in Figure 2 . 2 i ncluded in what you wrote down after seeing Figure 2. 1 ? Repeat the same experi ment with F i gure 2 . 3 , w h i ch uses figures ( a ) and ( c ) of F i g u re 2 . 1 to form a p ro p o r t i on al ana l o g y re l at i o n . ana l ogy re l ation "A is to
the fou r figu res
B as C is
to
Pa. r t I :
52
A
B
c
The Problem
D
FIGURE 2.2: A proportional analogy relation ( ' A is to B as C is to D ' ) involving geometric figures. Note that the figures A and C are the same as Figure 2. 1 (a) and (b), respectively. Compare the similarities between the figures you see now with what you wrote down after seeing Fi gure 2. 1 .
A
B
c
D
FIGURE 2 . 3 : A proportional analogy relation ( ' A is to B as C is to D ' ) involving geometric figures. Note that the figures A and C are the same a s Figure 2. 1 ( a ) and (c), respectively. Compare the similarities between the figures you see now with what you wrote down after seeing Figure 2. 1 .
Chap t er
2:
Similarity- Creating Metaphors
53
I hope this experiment i s the last nai l in the coffi n of any doubts that m ight still l inger i n you r m i n d about the p henomenon of creat ion of s i m i l ari ty. Let me now address, i n the light of this example, the not-so-hypothetical account of t he creation of s i m i l ar i ty in a compari son theoreti c framework mentioned above. To explai n the creation of s i m i l ar i ty as merely h i ghl ighti ng and downplaying of certain attributes of t he source a n d the t arget that were t here to begin w i t h , the descri p tion of every object and s i t u ation (a poten t i al source or t arget of a metaphor) must i nclude n u merous-potent i al i n fi n i te attributes. The descr i p tion of a relati vely si m ple figure, such as Figu r e 2 . l (a ) , must i n clude all possi ble ways of descri bing i t : that i t has fou r parallelog rams in i t arranged in such-and-such fashion , i t bas t h ree t rapezoi ds w i t h t hei r axes 1 20 degrees apar t , i t bas six triangles w i t h thei r verti ces coi nciding and their axes 60 degrees apart , and so on and on. A n d [ d i d not even consider att r i b u tes l i ke the t h ickness of the l i nes, the tex t ure of the paper on w h i ch t hey are draw n , etc . , t hough any of t hese can easily be m ade relevant for a proportional analogy by choosing the terms B and D appropri ately. A n d p lease bear i n m i n d t h at t h i s i s a s i mple fi g ure! The point here is t h at if the s i m i l arities are assu med to be there from t he start , t hen every object must be gi ven a descri ption t h at i s astronomical in s i ze, if not i n fi n i te. O therwise, t here would always be altributes left out t hat m ay be needed in com p rehen ding some metaphor . H owever, w i t h the descrip tions so huge, they become com p letely u n workable in any reasonable model of cogni t ion. First, there i s the obvious memory space problem . Sec ond, t here is t he i nefficiency of having to search t h rough t h i s huge description l i s t to fi n d the right descri ption for any given context . With the descri ption of Figure 2 . l (a.) t h at i ncludes all possi ble ways of look i n g at it, i t m ay be a. very long time before one sees i n i t a hexagon w i t h al l i t s m ajor d iagonals connected . H owever, i f we adm i t the possi b i l i ty of creat ion of s i m i lari ty, t h en t here is no such problem . O ne can have small workable descri ptio n s of objects and situations, and t here woul d be similarity- based m e t a pho r s t h at arc bas ed on t h e u n d e rl y i n g s i m i lar i t i e s b e twe e n t he se g i ve n d e s c r i p t i o n s . At t i me s , however, new sim i la r i ties are c re at e d s i m i l ar i t i e s n o t s e e n f r o m t h e existing descri ptions. ,
T h e examples of Figures 2 . 2 and 2 . 3 also p rovide a. val u able c l u e to t h e source of the created s i m ilar i ties . Not i ce t h at to u n derstand the an a log y relat ion i n each case, one must look at Figure 2 . l ( a ) d i fferently. I t h as to be descri bed d i fferently. For the analogy of Figure 2 . 2 , it needs to be descri bed as four parallelograms in a certai n configuration . For Figure 2 . 3 , it needs to
Part I: The Problem
54
be seen as t h ree t rapezoids with their axes 1 20 degrees apart . Thus, each t ime, the descript ion of the figure is changing, and a new description is being c reated . The created s i m i l arities are with respect to this new descri ption . Thus, the p roblem of creation of s i m i l arity collapses i nto the p roblem of redescription . This foreshadows the account of s i m i lari ty-creat i ng metaphor to be p ro posed i n Chapter 7. However, two t h i ngs should be noted here about rooting the creation of s i m i larity i n redescri ption. One i s t hat t h i s observation is not something new, but can be fou n d i m p l i citly or exp l i c i tly i n the writings of M ax Black, M ary Hesse, and Paul Ricoeur, among others. The other is that t h i s observat ion alone merely passes the buck, and does not address the p roblems raised by the p henomenon of creation of s i m i l arit ies; p roblems such as : Where do created s i m i l ar i ties come from? What constrains cre ated s i m ilari ties from being arbi t rary? A n d so on. For s i m ilar i ssues can be raised about the redescription process: H ow does the new description emerge? \Vhat p revents the new description from being arbitrary? A n d so on . 2.4.3
M o dels
I n the last chapter, we saw that a model i s usually a deli b erate creat ion meant to represent certai n aspects of the object , s i tu ation , or p henomenon being modeled . Consequently, there is a convent i onal i nterpretation t hat goe s with each model , though i t is possible t hat one might not be aware of it, and decide to i nterpret the model in an unusual way. Thus, with my emphasis on u n conventional i ty in metaphors , models are generally non-metaphorical , though they have the potential to become metaphors . T h e term model , h owever , is also app l i ed to what might be termed as ' p re- theoreti c model s , ' w h i ch are models before t h ei r i nt e r p r et a t i o n is fixed and becomes conventional . These pre-theoretic models can be fou n d by h i s torically tracing the origi n of what are now regarded as convention al mod els. There i s usually a target phenomenon that i s not well u nderstood, and a source that i s more concrete and well u n derstood . But t here is no good connection, or t ransference between the two, so that the sou rce can be mean i ngfully i nterpreted in the target domai n . There is only some vague i dea. i n t he m i n d o f t he s c i e n t i s t . Somet i mes , t here i s not even a vague idea but an emotional d r i ve that keeps the scientist seeki n g some connection . However, once the connect ion i s foun d , the model starts to become entrenched . If we compare t he states of t he source and t h e t arget before and after the model
Ch ap t er 2: Similari ty- Crea t ing Metaphors
55
became entrenched , the creation of simi lari ties can be seen quite clearly. The i n fluence of Metzinger on Bohr's theory of quantum mechan i cs men t ioned above serves as a good exam pie of a pre-theoret i c model . Here the creation of s i m i l ariti es can be seen rather starkly, s i n ce t here was no quantu m theory before t h e metaphor. Several other examples of pre- theoreti c mod els h ave been noted by h istorians of science. Gru ber [ 1 978] , on analyzing D arw i n 's notebooks in w hi ch he kept notes while work ing on h i s celebrated t heory of evolution, noted t h at the i m age of an i rregularly branchi n g t ree kept on recurring i n h i s t houghts , and may have served as the primal metaphor for his natural selection principle. Rothbart [ 1 984 , pp. 6 1 1 -6 1 2] h as noted t h at Newton 's i n vestigat i on of opti cs was greatly i n A uenced by the theory of acous t ics-that i s , the t heory of acoustics was a pre-t heoreti c model for op t i cs . M ore examples are presented in the next section along w i t h a d i scussion of the role of s i m i lari ty-creati n g metaphors i n creat i ve problem sol ving and cogni t ion . I should emphasize t h at all t hese examples of pre-t heoretic models can not be explained from a s i m i lari ty-based accoun t , though every p re- theoreti c model , i f i t i s successfu l , always gi ves rise to s i m i larities between t he phe nomenon being modeled and the model . [ t i s i mportant to u nderscore this point because the proponents of what I call predi c t i ve analogy often cite the same exam ples as evidence t h at not i c i n g existing s i m i l arities between two s i tuations i s a j us ti fication for pos i t i ng that t here might be other s i m i lari ties as well . However , the so called existi n g s i m ilarities are always s i m i larities after the fac t , at least i n all the examples p resented here. It i s not as i f Bohr saw certain s i m ilari t i es between t he cubist style of pai n t i n g and the behavior of atom i c p ar t i c l e s . Rat her, cubism p r e s e nt ed h i m w i t h an i d ea, n a m e l y t h at a parti cle can be a w ave at the s ame t i me. Finding t h i s i dea aestheti cally p leasing, he worked hard to see i f such a t heory might in fact be developed . The same can be said about Darw i n ' s i m age of the i rregularly branchi n g t ree. M i l ler's account ci tes several excerpts from Darw i n ' s notebooks to show t hat it was not some exi t i ng s i m i l ar i ties between the t ree i m age and whatever was k nown about the evol u t i on at t h at time t hat k e p t Dar w i n s ea r ch i ng for w h at other s i m ilarit ies m i ght be foun d . O n the cont rary, i t was an emotional d r i ve t h at kept up his i n tellectual comm i t ment to articulat i ng an account of evolution that m atched t h e t r ee i m age . lt w as not as if D a r w i n was searc h i ng for si milar i ties, r a t h e r be w a s for m u l a t i n g them . This p rocess w a s ac t u al l y fraught w i t h several p ro b l e m s that appeared t o i n va l i d a t e t h e m od e l , b u t D a r w i n ' s i ntellectual comm i t ment to the i dea kept him from t h r o w i n g away the image altoget her . I nstead , he im provi sed and sought differen t ways to
56
Part I:
Th e Pro blem
render t he i m age meani n gfu l . 2.5
S i milarit ies and C reat ive P r o b lem S o lv i ng
Now l h a t we have seen t h at s i m i l ari ty-creati ng metaphors are real, we need to assess what role, if any, they play in cogni t i o n ; and to contrast t h i s role w i t h that of s i m i larity- based metaphors . This is the task u n dertaken in t h i s section . I n highlight i n g t he role of s i m i l ari ty-creati ng metaphors i n cogni tion , I focu s on creati ve problem sol v i n g as the domain of cogni ti ve acti v i ty. By using t he qualifier 'creat i ve' I am restrict i n g myself to those problem-solv i n g act i v i t ies lhat req u i re some n ew i n novat ion , new idea, or new way of t h i n k i ng. It i s now cons idered an estab l ished fact t h at metaphors play a key role in creati ve p roblem solving [B road 1 985; Cangui l hem 1 963; Gentner 1 982; Gentner & Jeziorski 1 989; G i ck & Holyoak 1 980; 1 983; G i t ter e t al. 1 964 ; Gordon 1 96 1 ; Gordon 1 965; G ru ber 1 978; Hesse 1 966; 1 974 ; 1 980; Holstei n 1 970; I
Chapter 2.5.1
2:
Similari ty- Creating Metaph ors
57
S im ilarit ies B e fore and A ft e r t he M e t aphor
In t h i s case, one notices some existing s i m i l arit ies between the source and the target . These exi s t i n g s i m i l arities provide a way to map parts of the source to parts of the target . Based on t h i s i n i t i al mapping, hypotheses can be transferred from t he source to the target . These hypotheses, i f veri fied i n t h e target , might prov i de usefu l add i tional know ledge o f t h e target domai n . A n exam p le i s prov i ded b y Gentner and Jeziorski [ 1 989] . I n creat i ng the t heory of thermodynamics, Carnot used an analogy from the flow of fl uids. Gentner and Jeziorski prov i de a long quotation from Carnot that lays out the a nalogy. From the existing s i m i lari t ies between the fl u i d- flow and the heat-flow , namely t h at fluid flows from the h i gher level to lower level and the heat flows from the h i gher temperat u re body to the lower tem perat u re body, Carnot suggested the hypothesis : Cou l d it be t h at t h e rate of hea t - flow is p roportional to the temperat ure d i fference between the two bodies? ( J ust l i ke the rate of fl u i d-flow is proportional to t he d i fference in level s . ) T h is exam p le i s clearly an instance of s i m i lari ty- based metaphor. More over, the suggestiveness of metaphor can be seen as a man i festation of the open-endedness of metaphor that we saw i n Chapter 1. ( I n understan d i ng "The sky i s cry ing," one may attach a fee l i n g of u n i versal sadness to the mean i ng of the metaphor. ) T h is parti c ular role of metaphor i n cogn i tion comes closest to predi c t i ve analogy, and t herefore i t i s crucial to distinguish between t h e two. I n pre d i c t i ve analogy, the existing s i m i l arities between the sou rce and the target are seen as j ustifying that the hypotheses t ransferred from the source are l i kely to hold i n the target as wel l . Whereas, i n s i m i l ari ty- based metaphors, the s i m ilarities t h at h ave been found so far carry no such j ustification about whether addi tional similarit i es would be fou n d or not . Lest this seem a trite t ech n i c ali ty let me point out that t h i s t e c h n i c al i ty i s the basis of a major point of d i ve rgence between how s i m i l a r i ty - b a s e d m e t a phor s and p r ed i c t i ve analogy m ight be used i n cogn i t ion . I f the exi s t i ng s i m i l ar i t i es are seen as j ustifying additional similarities, then this, at once, suggests that when we are faced with an unsolved problem w i t h the target , our best bet may be to find the most similar source, based on whatever i s k now n about the tar get so far, and t hen to i m port hypotheses from the source to the target. But similarity-based metaphor, si nce i t carries no j u s t i fica t i on suggests no such mechan i s m . O f c o u rs e the fal l acy o f see i n g a h y p o t h e s i s a s j us t i fied ,
,
,
j ust because t here are some simi lari ties between the two domai n s works as a cogn i t i ve b l i n d spot , as i s show n i n C h ap t e r 9. For n o w , t h i s i m p o r t a n t d i f
ference must be kept i n mind so t hat t h i s o p e n e n d e d use of s i m i l ari ty-based -
58
Pari
J:
The Problem
meta.phor is not confused w i t h pred i c t i ve analogy. The use of s i m i l arity-based metaphors i n t h i s way i n volves l i t t le creat i v i ty. I f we adm i t the hypothesis that the s i m i lar i ties between fl u i d- flow and heat flow were know n , as in Gentner and Jeziorski 's accoun t , then it does not req u i re a particular deep i n sight to generate the above mentioned hypothesis. It seems obvious at once! A somewh at more creative use of s i m i larity-based metap hors can be seen in what W i l liam J . J . Gordon calls ' d i rect analogy ' [Gordon 1 96 1 , p p . 42-45] . Here, faced w i t h some problemat i c situation, one searches one's experience and memory for an i m age t hat i s l i ke the problem at han d , and m akes a conscious comparison of the parallel facts between the problem and the source image. This is perhaps best demonstrated by an example provided by Gordon w here a gro u p was faced w i t h the task of designing a dispenser for various products such as glue, nai l pol i s h , etc . The d ispenser was to be i n one piece ( w i t h out a reclosable top ) , and therefore i t s mouth must open for d ispensing and t hen close tightly after each use. The d i rect analogy t h at led to solving t h i s problem came from t h at of a horse excreting. As a member of the group remi n i sced : "vVhen I was a k i d I grew u p on a far m . I used to drive a h ayrack beh i n d a pai r of draft horses . W hen a horse wou l d take a cra p , first h i s outer . . . I guess you 'd call i t a k i n d o f mou t h , would open . Then the anal sphi ncter would dilate and a horse ball wf u l d come out . A fterwards, everything would close u p ag a i n . 1\h e whole p i c t u re woul d be as clean as a w h i s t l e . " [G o rdo n 1 96 1 , p . 42] .
Here i t i s easy to see t h at there were s i m i lari t i es between the source and
the pr obl em to be s ol ve d before the solution was achieved . Moreover , t hese s i m i l ari t i e s w ere pr e s e r ved in the solution p rocess. Here, once more, I must
em phasize that Gordon 's d i rect analogy should not be confused with predic t i ve analogy. When one finds a source t h at is s i m ilar to the problem at h an d , t here is absol u tely n o guarantee-not even a n increased l i keli hood-t h at t h i s w i l l lead to t he sol ution . Also, i f t here are t w o sources , a n d o n e of them i s more s im i lar to the problem t han the other, d i rect analogy does not by any means suggest t hat the more s i m i lar source is more l i kely to lead to the sn l u t ion ( wh i ch is one of the p redi ctions t h at pred i c t i ve analogy m akes ) . The poi n t of di rect a n a logy is s i mply t h at somet i mes recall i n g a s i m ilar i m age_ may suggest a new way to solve t he problem .
Chapter 2.5.2
2:
Similarity- Creating Metaphors
59
S im ilarities A ft e r but N o t B e fore t he M e t aphor
Even t hough most of the recent research h as concent rated on what role, i f any, s i m i l ar ity-based metaphors and p redictive analogy play in problem sol v i ng, there exist a few studies of how many creati ve and origi nal i deas origi nated from metaphors t hat created the s i m i larities between their sou rce and the t arget . What is even more i nteresting i s t h at al l t hese stu dies are from ' real world' problem-solving si tuat ions-t hat is, sit uations w here the sol ution of the problem was not k nown a priori . ( This is i n cont rast w i t h somewhat contrived experiments that have been done to support predictive analogy. I n t hese experiments a group of subj ects are p resented w i t h a problem , the solu t i on of w h i ch i s know n , and a n umber of sources, one of which i s an alogous to the problem and also leads to the sol u tion of the problem . I discuss such studies, and the fallacy of conclu d i ng from them that pred i ct i ve analogy is t he key to creati ve problem solving, i n Chapter 9 . ) Let u s look at one such example i n detai l . The exam ple i s taken from Schon 's excellent study of creati v i ty i n Displace m e n t of Co n cepts. One of the main concerns of Schon in t h i s st udy was to remove h i mself from the fallacy of ' after-the-fac t ' analysis of creati ve acts . A fter a creati ve i dea h as been s uccessfully app lied to solve a certai n problem, i t is al ways easy to analyze i t , to see the u n derlying simi larit i es between the source of the i dea and the problem at han d , and attribute the success of the i dea to t hose s i m i l ar i ties. However, t h i s analysis sheds l i ttle, if any, l ight on how to solve anot h e r prob l e m . What is c r u c i al for studying creat i ve problem sol v i ng is a 'during- the-fac t ' analys i s : What i deas came to mind i n sol v i ng the problem ? W h i ch i deas were rejected and which ones were tried out? A n d so on . The example from Schon 's st udy that I h ave chosen to p resent he re con cerns a g ro u p of researchers who were engaged in i mprov i ng the performance of a synthetic-bristle pai nt brush . ( See Schon [ 1 963, p p . 74-76] , and also Schon [ 1 979] . ) Compared to the natural-bristle pai ntbrush, the synthetic fi ber brush delivered the pai n t to the surface i n the form of d isconti nuous stripes, gi v i ng i t a gloppy ap p e aran c e. Their model of pai n t i ng a surface and the role of a paintbrush in i t-accounted fo r t h e p rocess as t h e b r u s h s m e ari n g t h e pai n t on t h e s u rface .
The m o d e l , o b v i o u s l y , w a s s u ffi cient for
pai n t i ng various surfaces w i t h n at u r a l p a i n t b r u s he s H o wev e r , w h e n a sy n thet i c bru s h was u sed , the model could not e x p l a i n why t he painted surface woul d not be as smooth as w h e n a n a t u ral b r u s h w as u sed . fn vai n , t h e r e s e ar ch e rs t ried to extend their model by m a king some o the r feat u res o f n at ural b r u sh e s relevant to the process of sm e a r i ng and t hen i n corporat i n g t hem in the synthetic brush . For i nstance, they not i ced t h at t he n a t u r al b r i s .
60
Part I: The Problem
ties h ave spl i t ends an d , t h i n k i ng t h at t h i s feat u re might affect the smearing process, they t ried to split the ends o f the synthet i c bristles, b u t w i t h no i m p rovement in the performance. Finally, the breakth rough occurred when a t heoret i cally oriented p hysical chemist suggested an unorthodox model t h at a paintbrush might work l i ke a p u m p . I n proj ecti ng the pumping model on t he process of painting t he researchers noted t h at the pai nt i s not smeared on t h e surface, b u t act ually forced , by a pumping action , t h rough the space between t he bristles. This perspec t i ve gave a total ly d i fferent ontology to t he process of pain t ing, and t he role of a pai ntbrush i n t he process was radi cally t ransformed . A n d t h e s i m ilari ties between the pai ntbrush a n d a p u m p were created i n t h is process of t ransform i n g the perspecti ve on pai nt i ng and the role of paintbrush i n i t. Thus, t here were n o s i m i larities before the metaphor, but t he s i m ilar i ties were created by the metaphor. From this transformed view of pai n t i ng, when the actions of nat ural and synthet i c pai ntbrushes were com pared , it was foun d t h at whereas the natural brist les formed a grad ual cu rve when pressed on t he su rface, the syntheti c bristles formed a. sharp ben d . N ote that t h i s d i fference becomes relevant only with the new ontology. When pai n t i ng i s seen as t h e process of smearing pai n t on the surface, the angle o f bend of the bristles i s i rrelevant s i n ce i t plays no role in the process . Specu l at i ons t h at the sharp angle of bend of t h e synthet i c brist les m i g h t b e t h e reason for gloppy appearance o f t h e painted surface led to a n umber of i n novat ions. Some of these i nnovations were i m plemented to p roduce a gradually ben d i n g bristle, and the resul t i ng brush d i d , i n deed , produce a smooth pai nted su rface. Schon presented several other exam ples l i ke t h i s . H e used the term p ro jecti o n to refer to the process of j uxtapos i ng two dissimi lar s i tuations as a means of gai n i ng fresh i n sight i nto one of them . W i lliam J . J . Gordon , whose direct a n a lo g y was c i ted above as an e x am p le of creat i v e use of s i m i l arity-based metaphors, h as p r ov i d e d m any more exam p l e s of real-world problem-solving s i tuations w here similarit ies were created [ Gordon 1 96 1 ] . He p roposed two mechanisms t hat are often useful in creati ve problem solvi ng. One of t hem i s m aking the strange jam ilia 1·, w hi ch works by i m posi n g a fam i l i ar poi nt of view on a problem w i t h w h i ch one i s u n fam i l i ar . T h e role o f cubism i n Bohr's development o f quantu m mechani c s and t h e role of t he t ree image i n Darw i n 's arti culation of evolutionary t heory can both be seen as examples of t h i s mechan ism . ' M ak i ng t he st range fami l i ar ' can also be evidenced when we are faced w i t h a problem from a domain about w h i ch we k now very l i t t le , a n d we i mpose a fam i l i ar per s p e ct i v e on the domain
Chap t er
2:
Similarity- Creating Metaphors
61
t o solve t he problem. Some examples of this phenomenon are p rovided i n Gordon [ 1 965] , i n cluding one of a student who, when asked t o prove a t he orem about endomorph isms ( a function w i t h the same domai n and range ) , constructed a n analogy o f looki ng a t oneself i n t h e m i rror to arri ve a t the p roof. In all these examples the simi lari ties are created , since i n i tially t here is so little known about the domai n that few s i m i l arities , if at all , can be seen between it and whatever fam i l i ar domai n happens to be the source of the theory. Gordon 's other mechanism is even more i nteresting, and he refers to it as m aking the fa m ilia r slmnge. Here one is fami l i ar w i t h the problem domai n , but t h e fam i li ar perspecti ve can not help i n reach i n g t h e sol ution . S o the thing, Gordon suggests, is to view it strangely by j u xtaposing i t with st range domai ns. The j u xtapositions i n i tial l y seem quite crazy, b u t then one of them might lead to an i ll u m i nat i n g i n sight t hat can prove to be the key to the solution . This mechanism is, in fact, quite t h e opposite of predictive analogy, w h i ch looks at the most similar source to i m port hypotheses i nto the problem domai n . A ccording to Gordon 's view-a view that is supported by many case studies p rovi ded t here-any such attempt would on ly lead to m u ndane an d not parti cu l arly i nsightful hypotheses . This i s because a si mi lar domai n i s n o t goi ng to change the perspec t i ve on t h e problem domai n . Schon's pai ntbrush example ci ted above serves as a good exam ple o f this mechan i s m . The p u m p i ng domai n was not chosen for its existing s i m i l arities w i t h pain t ing, and had the researchers limited themsel ves to seeking sources that were s imilar to the painti ng domai n they would h ave been stuck with the pai n t ing-as-smearing point of view. I n another example of ' making the fam i l i ar strange' one presented by Gordon-a group of researchers was faced with sol v i ng the problem of h aving a s h aft t u r n a t t h e con s t a n t s p eed o f 400 revol u t i o n s per m i n u t e ( rp m ) , w h i le
400 to 4000 r p m . A b l a.c k box 4000' e n t e r i n g and a sh all l ab e l ed the r e s ea r c h group t r i ed to m ake t h i s
t h e speed of t h e power-sou rce s h aft var i e s fro m was d r aw n w i t h a s h aft
l abeled '400
to
'400 co n s t a nt ' exi t i n g . T h e m e m b e r s of fami l i ar problem strange by metaphorical ly entering the box and attem p t i ng to maintai n the required speed constancy of the outgoing shaft by using thei r bodies. Here is, for instance, an excerpt from one member of the group : " . . . I ' m i n t h e b ox and
I
a m trying t o b e a governor . . . t o b e a
feedback system . . . b u i l t i n . . . . Let ' s s ee .
If 1 grab t h e o u t - s h aft w i t h my hands . . . and let 's say t here's a plate on the i n-shaft so t h at my feet can press agai n s t i t . I p u t my feet way o u t on t h e periphery of the plate and . . . what 1 real l y wou l d l i ke i s for my
62
Pa.rt I: The Problem
feet to get smaller as the speed of the i n-shaft i ncreases because then the friction would be reduced and I would hold on to the out shaft for dear l i fe and its speed m i ght remai n constan t . . . . The faster the i n-shaft went t he smal ler my feet would become so t h at the driving force would stay the same." ( Gordon 1 96 1 , p . 39] . Based on t h i s i dea, one member of the team designed a hydraul i c c l utch , w h i ch t urned out to work as expected b u t was q u i te i nefficient and not suit able as a power t ransm i t t i ng devi ce. B u t then, another member of the team designed a mechan i cal clutch from the analogy w i t h the hydrau l i c clutch tha.t proved to work q u i te sati s factori ly. H ere the approach to the problem is q u i te unorthodox , to say the least. Moreover, i t i s not i n s p i red by any existing s i m i lari ties. H owever, once the mechanical c l utch is built, one can see that the actions of the person i n s i de the box are quite a nalogous to i t . Some other stud ies o f creat i ve problem solving that fi t t h i s category can now be noted in passi ng. Libby ( 1 922] c ites several examples, i ncluding that of 1\:ekule who came u p w i t h the i dea t h at the carbon atoms i n the benzene molecule might be arranged in the for m of a ring when he d reamt of a serpent swallow i ng its own t ai l . H ere t here was an i m age t hat led to the sol u tion of a problem . A ft e r the sol u t ion , one cou l d see the s i m il ar i ties between the molecu lar struct u re of benzene and a snake swallowi ng i ts t ai l . B u t before that, t here were no s i m i lari ties. The i m age of the snake suggested an i dea t h at t u rned out to be fru i tfu l . O ne cannot say t h at Kekule was aware of some exi s t i ng s i m i l arit ies between the snake and benzene that led h i m to the hypothesis t h at the snake swallowi ng its tai l m ight be the molecular structure of benzene.
of similarity he traced B e nj a m i n Fran k l i n 's invention of the light n i ng cond uctor, conclu d i ng w i t h : ( 1 964, pp. 1 99-207] h as p r o vi d e d metaphors in p r oble m sol v i ng. I n o n e
I\ oestler
creat i n g
m any examples
par t i c u l ar e x a m p l e ,
"There are two successive Eu reka processes i n vol ve d in t h i s story. t h e fi r s t , the bisociative l i n k was what Fran k l i n called ' t h e power o f poi n t s ' ; i t g ave rise to t h e a n alogy : poin ted fi n ge r d i s c h arges Leyden j ar , poi nted rod d i scharges cloud . lt m ay h ave been attained by i deation on a r e la t i vely conscious level, probably w i t h t h a t a i d of visual i m agi n a t i o n . The second stroke of gen i u s was the u s e of t h e k i te to reach the t h underbolt . I t i l l u strates t h e argument I have p u t forward earlier in t h i s chapter: o n e can hardly say t h a t a h i d de n a n a l ogy was p re - ex i ste n t in the u n i verse In
Chapter
2:
Sim ilarity- Creating Metaphors
63
between a k i te used as a sai l by a boy float ing on a l ake, and a l ightn i ng conductor." [Koestler 1 964 , p . 204 .] All t hese examples provide plenti fu l evi dence that s i m i l ari ty-creat i n g meta phors do, i n deed , play a central role i n cogn i t i o n . They even suggest t hat , i n any act o f cogni tion i nvolving creat i v i ty, s i m i l arity-creating metaphors might p l ay a much more promi nent role than s i m i lari ty-based ones . 2.5.3
S i milarit ies B e fore b u t not A ft e r t he M e t aphor
A few examples of t h e rol e of metaphor i n creati ve p roblem sol ving fit this category. Here, a s i m i larity-based metaphor provides an i n i t ial sol ut ion of the p roblem, w h i ch i s not very sati sfactory. The i n i t i al sol u tion i s then modified u n t i l it becomes sat isfactory. In the modification p rocess , however, the source is no longer used , so that the final solu tion of the problem ends up bearing l i t t l e or no resemblan ce to the source. B road [ 1 985] provi des some classic examples of t h i s phenomenon i n Edi son's p roli fi c i nventions. For i nstance, Edison 's i nvention of the k i netoscope, a. motion p icture mach i ne, was made from analogy with h i s earlier i nvent ion of the phonograp h . One of t he earlier designs of the k i netoscope showed a. cyl i n der on w h i ch a sequence of i m ages were laid out spiral ly. The cyl inder was meant to be v iewed t h rough an eyepiece, so that as the cylinder was rotated , the i m ages woul d be v iewed i n sequence. The design was rather awk ward , and so he made many further modi fi cations. The final k i netoscope bore l i t t l e resemblan ce w i t h the phonograph . T h u s , we see t h a t the role of metaphor here is basically to provide a first foothold in an unfami l iar domai n . After t h at t h e con n e c t i o n w i t h t h e source i s severed , and later deve lo p m e n t s d es t roy the s i m i l ar i t i e s t h at were the basis of the foot hold . The pr oc e s s i s , perhaps , n o t u n l i ke t h e series painted by Piet Mondrian as the stud y of ob j ects l i ke a t r ee or a l ighthouse. In the t ree series, for i n s t a n c e , the i n itial pai n t i ng looks very much l i ke a tree, b u t each subsequent painting becomes more a n d more abst ract , until the fi n al one, w h ich hardly looks l i ke a tree. 2.6
Conclus ions : T he P roblem of S i m i lari t y- C reat ing M e t aphors
We have seen i n this chapter that the phenomenon of creation of s i m ila r i ty is quite real , a n d t hat i t c a n be e v i d e n ced i n m a.ny crea.t i ve act s of cognition.
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Part I: The Problem
G i ven t h i s , the problem for any theory of metaphor i s to explai n the creation of s i m i lari ty. W here do the created si m i l ar i ties come from? What was left i m p l i c i t i n al l the exam ples of s i m i lari ty-creat i ng metaphor p resented i n t h i s chapter i s t h at the creation o f s i m il arity i s far from arbitrary. That i s , j uxta posing any random domai n may not res u l t i n any creation of s i m ilarity, and even when i t does , the created s i m i l arities may not be particularly insightful ones, and even when t hey are, the i nsights may not be helpful i n solving a cer tain problem with t h e target domai n . For instance, Gordon [ 1 96 1 , pp. 45-48] noted t h at when a group of researchers were engaged in developi ng a j ack ing mech a n i s m t hat would fit into a fou r by fou r i nch box, and yet would extend up to t hree feet a n d support fou r tons, t h e researchers tried to use a b iologi cal metaphor ( " [A] biologi cal j ack w here the power source would be a k i n d of virus c u l t u re. You d rop some ' food ' i nto t he c u l t u re and the ani mals breed and occupy more space thus offering a power source . " ) and a chemi c a l metaphor ( " [A ] slow b u rn i ng powder that woul d develop energy a s you added oxygen to i t . " ) but in vai n . ( The final solu t i on was arrived at by the analogy from the Indian rope trick , which is another example of s i m ilarity creat ing metaphor. ) Schon noted that the group working on t he pai ntbrush problem also con sidered ' pai nting as m as k i ng a surface' metaphor, but it led to no u sefu l insights [Schon 1 979, p . 259] . I n the case of H i t chcock 's Rear Window, while J ames Stewart' s face can be made to express k i n d ness or lust by j uxtaposing i t w i t h an appropriate image, i t cannot be made to express horror, anger, or frustration . A l l these exam ples demonst rate t hat the cre at ion of s i m i lari ty seems to work in mysterious ways. Someti mes it works , a n d somet i mes i t does not . It is a s i f every domain h a d a m i n d o f i t s own , a n d i t wou l d d o u n pred ictable t h i ngs when j uxtaposed w i t h another domai n . T h e problem for any t heory o f metaphor, a n d certai nly for t h e one de veloped in P ar t II of the book , i s to shed some l i g h t on t h i s mystery, and to answer questions such as : What cons t rains the creat ion of s i m i l arity? When two domains are j u x t aposed , what i s act u a l l y go i ng on? This i s not t h e first t i me, however, t h at these quest ions have been rai sed . A s I me n t i o n ed in t h e prologue, the i nteract ion t heories of metaphor have been p roposed primar i l y to account for the creation of s i m i l ari ty, and to answer these questions. G i ven that, i t wou ld be useful to exam i ne how far such t heories have come to provi ding an adequate explanat i on of t he creation of s i m ilarity. This i s t h e subject o f t h e next chapter.
Chapter 3 A p p roaches to S imilarity- Creat ing Met ap hors
3.1
Int r o d u c t i o n
We s a w at the e n d o f the last chapter that si milarity-creating metaphors present us w it h a paradox. On the one h an d , they show that si milarities h i therto u nseen can be m ade real . On the other h an d , the creation of simi larity seems to be quite constrained . The p roblem i s to resolve t h is paradox somehow and to show how the similarities are created , where they come from, and to make explic it the invisible h and that constrains this creation . Of course, an attempt i s made to solve thi s problem i n the comparison theory of metaphor [ K i ttay 1 982] . You may recall that, according to t h is the ory, all metaphors are based on some existing similari ty between the source and the t arget . The existing similar i ty i s also seen to constrai n the creation of s i m ilarity. I t i s argued t h at the ' creation' is i n merely h igh light i ng simil ar ities w i t h respect to less sal i e n t attributes and relations of the target . T h i s process i s not ar b i t r ary, s i n ce t h ere m u s t be some e x i sting similarities, albeit not prominently v i s i b l e due to t h e i r low salience, between the source and the t arget i n order for thei r j u x t apos i t ion to be meaningfu l . But this account en c ount e r s the p r oblem t h at the represe n t a t i o n (or des c r i p t i o n ) of any object h as to be infinitely l arge, as it must i nclude every possi ble attribute, every relat i on and every possi b le way thi s object can be seen as s i m i l ar to any o t h e r object . I have emphasized t h i s point in the l ast chapter in t he context of proportional analogies i nvol v i n g g eo m e t ri c figures. This fail u re of the comparison theory and i t s variants t o explai n t h e ere-
65
66
Par t
I: The Problem
ation of s i m i l arity has been one of t he key factors beh i n d the development of what is generall y known as the i nteraction t heory. rr:hough the roots of it can be t raced back to l . A . Richards ' Ph ilosophy of Rhetoric, the i nteraction theory is most often identified with the views presented by Max Bl ack i n t wo t houghtfu l essays written about t wenty years apart [B l ack 1 962; 1 979] . B lack 's articulation of the i nteraction theory, however, is quite vague at its very bes t . W h i le he provi des some analogies and metaphors to communicate the key concepts of the theory, t hese analogies and metaphors are not elabo rated sufficiently to add ress the creat ion of simi l ari ty satisfactorily. To make m a t ters worse, h i s account contai ns some paradoxes and the i m ages prov ided by his metaphors and analogies are sometimes in conflict w i t h one another. Severa l other scholars have proposed variat ions of the i nteraction theory in order to remove the problems i n h erent in B l ack's version . H owever, most of t hese accounts are equal ly vague, often i nt roducing more i l l - defined concepts in t heir at tempts to clarify and elaborate the i nteraction theory. In all this confusion , i t i s h ard t o k now what exactly any part icular version of the i n t eraction theory entai l s . One of my objecti ves i n th is chapter i s to reveal the vague, paradox- ridden nat u re of the i nteraction t heories, thereby j ustifying the need for a concise framework such as the one I p resent i n Part II of this book .
l n spite of t h i s m u d d led picture of i nteractionism, some of the i m agery t hat has been used to articulate it is quite i nsightfu l , given some elaboration and a sympathetic i nterpretat ion . My second objec t i ve in this chapter i s to clearly iden ti fy such i nsights ( w i t h m y elaborations a n d ' sympathet i c ' i nterpretations) , for t hey have been i ncorporated i n my o w n framework . This also allows me to acknowledge an i ntellectual debt to t hose i n teractionists whose views have great ly i n fl uenced my own . The few works I d i scuss here have been chosen o n the basis o f their no tab i l i ty and relevance to my framework . G i ven the promi nence enjoyed by B l ack's i n t eraction theory, I begin by d i scussing it at some length in S ec tion 2 . I fol low t h i s i n the su bsequent two sections, w i t h a b rief pres en tation of the i nteraction isms of Paul Ricoeur and Carl Hausman , respect i vely, who have also w rest led with t h e problem of the creat ion of s i m i l a rit y I n Section 5 , I take note o f Wheelwright 's epiphor-diaphor d i st inction , a n d M ac Cormac's attempt to formal i ze it by using fuzzy set- theory. ,
.
A non-i nteractionist approach to the creat ion of s i m i l ar i ty comes from t he work of George Lakoff an d h i s colleagues [Johnson 1 98 7 ; Lakoff 1 98 7 ; Lakoff and Joh nson 1 980; Lakoff a n d Turner 1 989] , which I refer to a s t he Lakoffi an approach . A lt hough Lakoff and h i s colleagues have l argely focused
Chapter
3:
Approa.ches to Creative Metaph ors
67
on what m i ght be called conventional , frozen , or dead metaphors, show i n g h ow m any o f our everyday concepts are struct u red by these convent i onal metaphors , t hey have not only duly recognized t h e poten t i al of metaphors to create s i m ilarities, but also shed some light on how the similarities are created . Consequently, I p resent the Lakoffian approach to the creation of s i m ilarity in Section 6. We see t here that the Lakoffi an approach can , i n fac t , b e easily seen as a variant of the i n teraction theory, even t hough Lakoff and Turner [ 1 989, pp. 1 3 1- 1 33] explicitly reject the i nteraction t heory ; their rej ection turns out to be based on a quite myopic view of i nteractionism. We also see t h at the Lakoffian approach is i t self put forward quite vaguely, leaving fun damentally u nresol ved the paradox of the creation of si m i l ari ty. I n spite o f th i s , a key insight o f t h e Lakoffian approach is t o explicitly recognize t hat i n order to exp l ai n the creat ion of si m i l ari ty, one needs to look at i t i n t h e b roader framework o f cogn i tion , and reexam i n e some fundamental assumptions about the n at u re of cogni t i o n . Not i ci n g the ambigu i t i es i n herent i n the interact ion theory, several at tempts have been made to art iculate it precisely using some mathemati cal formalism or another. There is my earlier attempt [ I n d u rkhya 1 986; 1 987] that, al t hough i t does not ful ly resol ve the paradox of the creation of simi larity, does have certai n i nteres t i ng featu res that have been preserved i n the t heory developed i n t h i s book . Therefore, I briefly review my previous ap proach to metaphor in Section 7. Then t here is K i t tay's perspecti val theory [ K i t t ay 1 987] . Though her theory is embedded in a framework of compo sitional semantics that makes i t l i m i ted to l i nguistic metaphors, K i t t ay's explanation of the creation of similarity comes q u i te close to resolving t he paradox . I review K i t t ay's approach i n Section 8 , since i t i s d i rectly relevant to the account of metaphor I am goi ng to present in Part I I of this book . F i n al ly, i n Section 9 , I summarize the mai n points of t h i s chapter. Often various scholars use different terms to refer to w h a t I h ave been cal l i n g the source and the t arget . The t arget i s var i o u s l y re fe r r e d to as t he top i c . The sou rce is somet i mes called s u bsi d i ar y su bject and someti mes the veh icle. To avoid
p r i m ary or p r i n c i pal s u b j ec t a n d as t he the second ary or t h e
the u nnecessary confusion that might result from using different terms to refer to the same thing, I conti nue to use the terms source and t arget i n d iscussi ng other aut hors' approaches t o metaphor.
Part
68 3.2
I:
Th e Pro blem
Max B lack
The fi rst detai led account of the i nteraction theory was p resented by M ax Black i n his classic essay ' Metaphor' [Black 1 962] , which , i n a nutshell , can be explai ned as fol lows . The two subj ects of a metaphor, n amely the source ( t he subsidi ary subject ) and the target ( t he princi pal subjec t ) , are to be regarded as ' system s ' rather t han isolated words or predicates . For instance, in "Man i s a wolf," i t is not j u st the word ' wolf' t h at act s as the source, but a lot of our general knowledge an d conventionally held beliefs about wolves that must be brought into play. B l ack refers to all thi s k n ow ledge and these beliefs as ' associ ated common p l aces, ' and it is the associated commonplaces of wolf t h at wou l d serve as the source system in thi s example. I n understan d i ng a metaphor, the source and the target systems ' interact ' w i t h each other, a p rocess i n w hi ch the associated commonplaces of the source system organ i ze the t arget system , selecti ng, emphasizing, and suppressing feat u res of the t arget system in the process. For i nstance, in the man-wolf metaphor, the associ ated com monplaces corresponding to wolf, w h i ch might i nclude beliefs l i ke wol ves are ferocious, territorial , and possessive, organize our view of man . In this process, certai n human characteri s t i cs , such as walk ing on two leg s , are pushed i n the backgroun d , while other characteristics, such as ferociousness, are ren dered promi nent. The creation of s i m i l arity is explai ned here by arguing t h at , i n organizing t he target i n terms of the associ ated commonplaces of the source, the target is m ade to look si m i l ar to the source. Moreover, since the target h as its own associated com monplaces, they serve to constrain the creation of similarity. B u t t h i s explanation is rem i n i scent of the comparison theoreti c account to the creat ion of s i m i l ar i ty that I mentioned at the begin n i ng of t h i s chap t e r , as i t essent i al l y explai n s the creation of s i m i l ar i ty i n terms of highlighting do w n p l a.yi n g feat u res of the target . So o n e n a t ura l l y wonders : What , t hen , is new about t h e interaction theory? What is i t t h at makes the i nteraction d ifferent from mere com parison ? Interestingly perhaps , the most i l lumi nating answer to t h i s question i s provided by Black i n terms of a metaphor: " S u p p ose I look at the night sky t h rough a piece of he av i l y smoked glass on which certai n l i nes h ave been left clear . Then I shall see only the s t ar s t h at can be made t o l i e on the l ines previously pre pared u pon the screen , and the stars T do see w i l l be seen as or gan i zed by t h e screen 's structure. We can t h i n k of a m e t a pho r as such a screen and the system of ' associated commonplaces ' of the focal world as the network of li nes upon the screen . We can say
Chapter
3:
69
Approaches to Creative Metaphors
t h at the [target] i s ' seen t h roug h ' t he metaphorical exp ression or i f we prefer, that the [target] is ' proj ected u p o n ' the field of the [source] . ( I n the latter analogy, the i m p l i cat ion-system of the focal expression must be taken to determine t he ' law of p rojec tion . ' ) " [Black 1 962, p. 4 1 ] . This an alogy contai ns two key i nsights. First of al l , it provi des an account of the creation of s im ilarity that i s q u i te d i fferent from the com parison theory. When we see the stars t h rough the smoked glass, and see t hem arranged a l o n g certain l ines, it i s t he smoked glass (the source ) t h at is imposing an organization on the stars ( t he target ) . The s i m i l ar i t ies ( between the s m oked glass and the stars) are created because t h i s new organ ization is not a part of t he t arget . For , if we remove the smoked glass, then there are no l i nes i n the sky. I t cannot b e said that the l i nes were al ready there, but less salient, and t h e smoked glass i s merely making t hem more p ro m i nen t . I n fac t , there might be an i n fi n i te number of geometric patterns t h at can be t raced on the smoked glass, and the stars in the sky might be seen in the corresponding patter n . One cannot argue t h at all t hese patterns are al ready t here in the sky. This creation of s i m ilarity is const rai ned , however, because j ust hol d i n g a smoked glass w i t h certain l i nes etched on i t i s n o t sufficient b y i t self t o see t hat pattern i n the sky. There m u s t be stars i n the sky. Moreover, t he stars must be i n certain positions i n the sky w i t h respect to the smoked glass so as to be v i sible t h rough the etched l i nes . Both of t hese are attributes of t he t arget t h at are i n dependent of the source, and can block the creation of similarity. T h e other i l l u m i n at i ng i n s i ght of t h i s analogy is t h at it presents metaphor as an i n he r e n t ly asym metr i c process. For one c a n n o t look at the smoked glass t h rough t h e s t arry s ky. Even i f we ass u m e t h at one co u l d reverse t h e source and t he target-suppose t hat t he 'sky' is a huge black screen w i t h tiny holes and i l l u m in ated from beh i n d-what you w i l l see when you view the smoked glass t h rough the black screen is certai n l y not the poi nts of l i ght arranged along the l ines etched on the glass . U n fort u n ately, however , B l a ck
italize on the
d i d not elaborate on t h i s analogy and cap
val uable i n s i g h t s i t contai ned .
To worsen the m a t t e r , some
of h i s other remarks in the same essay serve only to h i d e t h ese i nsights, and someti mes even contradict t hem . For i n s t an c e , i m m e d i ately aft er t he smoked glass a n a l o gy B l ack presented another exam ple to clarify the n at u re of i nteraction : ,
70
Part I: The Problem
" O r take another example. Suppose I am set the task of de scribing a battle in words drawn as largely as possi ble from the voca bulary of chess. These latter terms determine a system of i mplications w h i ch w i l l proceed to control my descr i p t i on of the bat t l e . The enforced choice of the chess vocabulary will lead some aspects of the battle to be emphasized , others to be neglected , and all to be organi zed in a way that would cause much more strain i n other modes of descri ption . The chess vocabulary filters and transforms: it not only selects, it brings forward aspects of t he battle that m i ght not be seen at all t h rough another med i u m . ( Stars t hat cannot be seen a t all , except t hrough telescopes . ) " [ B l ack 1 962, pp. 4 1 -4 2 . ] T h i s example seems to fal l back i nto explai n i n g t h e role o f metaphor as highlighting a n d downplay i ng the existing attributes of the t arget , and a key i nsight of the first analogy is obscured . B l ack , of course, mentions t h at new aspects of the batt le m ight be made visi ble t h rough the source, but i n the absence o f a concrete exam ple, h i s arguments d o not appear convincing. The analogy with a telescope i s not very apt , for a telescope brings in new i n formation i n a different way. The asym metry of metaphor that was i n herent i n the smoked glass anal ogy is also expl i c i t l y cont radi cted by Black at another place in the same essay : "If to call a man a wol f is to put h i m i n a special light, we must not forget t h at the metaphor makes the wolf seem more human t han he other wise wou l d . " [ B l ack 1 962, p. 4 4 . ] The remark suggest s t hat metaphor is sym metric, and t hat the res u l t of i nteraction also affects the source. This pattern of i n sightfu l observations i nterlaced w i t h contradi ctory state ments is repeated in B lack's elaboration of t he i nteraction t heory in his later essay ' M ore about Metaphor' [B l ack 1 979] . T h e most insightful part of t h i s essay i s the se c t i on t i t led ' T h i n k i ng i n Metaphors ' [ p p . 32-34] . Consider t he figure of t h e S t ar of David shown i n F igure 3 . l (a) . The figure can be de scribed , or t hought of, in various ways: as two equilateral t r i angles, one of w h i ch is i n verted and set u pon the other [Figure 3 . l ( b )] ; as a regular hexagon with an equ i l ateral t riangle on each of i t s edges [Figure 3 . l ( c ) ] ; as three p ar aJlelograms superim posed on each other w i t h their axes 1 20 degrees ap a r t [ Figure 3 . 1 ( d )] ; e t c . In eac h c a s e , the r esu l t i n g description of t h e figure of the Star of Dav i d is a result of an i n teraction between the figure i tself ( t he target ) and the concepts chosen for the description: triangles , hexagon a n d t r i a n gles paral lelograms, e t c . ( t he source ) . In this example, the deep insights o f t h e starry-sky- t h rough-the-smoked,
71
Ch ap ter 3: Approach es to Crea t i ve Metaph o rs
(a)
(b)
(c)
(d)
FIGURE 3 . 1 : Black's lllustration of 'Thinking i n Metaphors . ' The familiar figure of the Star of David (a) can be thought of (or described) in terms of two equilateral triangles (b), a hexagon and six triangles (c), and three p arellelograms (d).
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Part I: The Problem
glass analogy resurface. We get a gli m pse of exactly how the i n teraction t akes place, and t h at i t i s not a comparison . I n seei ng t he figure of the S t ar of Dav i d as t h ree parallelograms, we are not comparing the parallelogram w i t h the figure. I n stead , we are reorganizing, or redescr i b i ng the figure of the Star of David i n terms of the paral lelogram . The example also clearly shows t hat both the source and the t arget part ici pate in the i nteraction process. Fi rst of al l , one can see how d i fferent sources affect t he description of the same t arget , highl ighting the role played by the source in t he i nteraction process. And, of course, the same source woul d give different descri ptions to different targets. Figure 2 . 1 ( a ) [Chapter 2] can also be described in terms of equ i l ateral t r i angles, in terms of hexagons and equi l ateral triangles , and i n terms o f paral lelograms. B u t each o f these descri ptions is different from the correspond i ng descri ption of Figure 3.1. Moreover , certain t argets may be such that t hey cou ld not be described at all in terms of a given source. For i n stance, Figure 2 . 1 ( c ) [Chapter 2] cannot be described i n terms of hexagons, equi lateral triangles, or parallelograms. Thus, we see t hat t he t arget also affects the res u l t of i nteraction. A l l these exam ples provide valuable clues to resolv in g the paradox of the creation of similari ty. 1oti ce t hat the S t ar of David example is also i nherently asymmetric. For i n organi z i ng the fi gure of t h e S t ar of D av i d as t h ree parallelograms , t he parall elograms ( the source ) do not start to appear Star-of- D av id - l ike. Yet , a t another p l ace i n the same essay, B l ack again i nsists o n the symmetry of i nteraction : " [The i n teraction] reci procal ly i n duces parallel changes i n the [source] . " [ B lack 1 9 7 9 , p . 2 9 . ] T h ere are other contrad i c t i o n s a s wel l , a n d some o f B l a ck s ot he r e x a m p l es and analyses i n t h i s essa.y make the i n teraction theory look l i ke a vari ant of the comparison theory. 1 mention two such instances here. '
First, B lack vehemently mai ntained t hat t he basis of a metaphor is an i so morphism between the source and the target [Black 1 979, pp. 29-3 1 ] . That is, the i m plicat i ve com plex of the source, when projected on the t arget , m irrors an i dentical i m p licat i ve complex i n t h e target . For exam p l e , in "Marriage is a zero- s u m gam e , " t h e p a r t of the i m p l i cat i ve com p lex of the s o u r c e , n a m e l y "A game is a contest," is projected onto t he i mplica t i ve complex of the tar get , namely "A m arri age is a sustai ned st ruggle," and so on . This account however, makes the i n teraction theory a. vari ant of the comparison theory. It al so com pletely fai l s to ad d ress the creation of s i m i l ari ty, and the i l l u m i nati ng i n s i ghts o f t h e s t arry-sky- t h rough - t h e-smoked-glass i m agery a n d t h e St a r of David e x a m pl es a r e hop el e s s l y los t S ec o n dly, w h i le i n t h e i n i t ial for m u l a t i o n of t he i nterac t i o n t heory both .
Chap t er
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73
the source and the target were regarded as 'system s , ' Black retracted this requ i rement for the target i n h i s later accou n t . H e clai med th at t h i s requ ire ment is "needlessly paradoxical , though not plai n l y m istaken" [ B l ack 1 979, p . 28] . The only j ustification he provided for changing his p c s i t ion was an ex ample, Wallace Stevens ' "Society is a sea," w i t h Black argu ing t h at Steven s was not viewing society as a system of social relationshi ps. There i s a r i ng of truth here. We do not regard the fig u re of the Star of D av i d as a system of triangles or parallelograms . For i f we d i d , t hen t here woul d be l it t le or no poss i b i l i ty of reorgan i z i n g it in krms of different sources . For i nstance, if the figure of the Star of Dav i d is regarded as a system of parallelograms, and the source contai ns the con cept s cf hexagons and equi l ateral triangles, t hen t here is no way that the figure can be reorgan i zed as i n Figure 3 . l ( c ) . Th is problem , however , can be addressed by regarding the source and the target as systems a.t diffe rent levels . I n the Star of David example, the target can be considered a system of l i n e segments, w h i ch , w h i le it can be organi zed in terms of hexagons, tri angles , an d parallelograms , resists arb i trary organ i zations. For instance, i t cannot be organ ized or descri bed i n terms of ci rcles and ellipses. I n deed , t h i s is the way that the problem is approached in my own account , as we see in Chapter 7. The problem w i t h B l ack's soluti on of not regardi n g the target as a system at all is t h at then it is hard to exp l a i n how the creat i o n of s i m i l ar i t i e s i s c o n s t r a i n e d . Recal l t h at i n my i n t er p re t at i on o f t h e s t a.r r y - s k y - t h rou g h - t h e s mo k ed - g l ass a n a . l o g y I argued t h at i t i s the ar r a n g e m e n t s of t h e s t a r s i n the sky, an i n dependent attribute of the target, that acts as a constrai n i n g factor in the creation of the s i m i l a r i t y . ln t h i s i n terpretation , t h e t arget i s s e en as a system of s t ars w h i ch i s being or g a n i z e d by the system of l i nes o n t h e s m oked gl ass . However, if t he t a rget is not re g a r d ed as a system , t h e n t h e const rai n t on t h e creat ion of s i m i l arity must b e exp l ai ned i n some oth e r w a.y . B u t Black does not provide any alternat ive expla n a t ion . To s u m u p , we see t hat B l ack ' s i n t e r ac t i on t heory, w h i l e i t contai ns a n umber of i l l u m inating i n s i ght s , i s fraught w i t h p a r a d o x e s a n d l oose e n d s . A few other scholars , drawn to the i nteraction theory for various reasons, have also noticed t h i s and m ade various attem pts to c l ari fy a. n d el aborate the i nteraction theory. I n ow turn to a n ex arJJ i J J a.t i o J J o f s o m e o f t h ese a t t e m p t s .
Part I: Th e Problem
74
3.3
Paul Ricoeur
Ricoeur's development of i nteractionism h as been markedly i nfluenced by Black's views. However, i n spite of the fact that Ricoeur h as written much more on metaphor t han B lack [Ricoeur 1 976, Chap . 3 ; Ricoeur 1 977, esp . Chap. 7; Ricoeur 1 978; Ricoeur 1 982] , h i s version o f t he i nteraction t heory i s even more vague than B l ack 's. Here, I present two key features o f Ricoeur's accoun t t hat are particularly germane to my own framework . One major feature of R i coeurian i nteractionism is i t s notion of split ref e re n ce . The allusion here is to the fact t hat a metaphor i n volves a non conventional i nterpretation. S i n ce this means t h at the metaphor must h ave a conventional i nterpretation as well ( w h i ch i s ruled out by the contex t ) , the t wo i nterpretations together constitute what Ricoeur calls t he split reference. For example, in Spender's Seascape, t here is the conventional referent , t he harp, and the metaphorical referen t , the ocean . Now i t may seem t hat Ricoeur is merely coin i n g a new p hrase for some t h i ng that is already well established, for most scholars of metaphors wou l d readily agree that every metaphor i n volves a d u a l reference. However, R i coeur u ses his notion o f split reference i n a novel way to explai n h o w meta phors, particularly creat i ve metaphors, are made meaningfu l . U n l i ke B lack , i n whose account the tension i n a metaphor arises from the i nteraction be tween the source and t he target ( regarded as systems ) , in Ricoeur's view the t e n s i o n i n a metaphor comes from the two i nterpretations of t he metaphor. Moreover, i t i s these two apparently conflicting interpretat ions t hat sustai n a metaphor and make i t meani ngful by bringing the referents of the two i n terpretations into semanti c prox i m ity. Thus , i n read i ng Spender 's Seascape, the harp and t he ocean t hemselves are b ro u ght together. That is, t he harp and the ocean are seen as i f they belonged to the same category. This observat ion i nvolves a bold step i n i nvolving the referents of the { I n alm ost all of t h e earlier approaches , i n cluding that of Black , the referent s were n ot explicitly i n volved . ) However, i t fails to address the main problem of creation of similarity: How is it t h at some referents can be brought into semanti c p rox i m i ty but not others? source a n d t h e t arget .
The second major feature of Ricoeur's theory provides a parti al answer Here, R i c o eur makes an implicit dist i n ction between the obj ects i n t h e worl d a n d t h e l i ng u i s t i c m e a n s t h rough w h i ch we c a n access and descri b e t hese o b jects. T h e i dea is t h at the l i ngu i s t i c ex p ressi o n s work like models in giving us a cognitive access to t he th i n g s in t he world . I n t h i s process, t hey present us with certain aspects of the world . And metaphor to t h i s quest i o n .
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Approaches to Creative Metaphors
permi t s u s to change the models , t hereby allowing us to change the way of seeing t h ings and percei ving the world [ Ricoeur 1 982, p. 1 886] . 1 In other words, metaphor works by changi ng our representations of the worl d , and i n doing so, offers us new i n formation about t h e world [ R i coeur 1 976, p p . 5253] . I t i s of i nterest to note that Black also adopted a s i m ilar stan ce i n his later essay on metaphor: " [ T ] he world i s necessarily a world under a certain description-or a world seen from a certai n perspec t i ve. Some metaphors can create such a perspective . " [ B l ack 1 979, pp. 39-40. Em phasis Black 's. ] The framework for metaphor I present in Chapter 7 sharply reflects t h i s theme. C arl Haus man
3.4
The paradox raised by t h e creation of simi larity occupies the centerstage i n C arl Hausman 's approach to metaphor [ Hausman 1 983; 1 984 ; 1 989, esp. Chap. 3] . However, i n his solution to the paradox , which i s more elaborate and less ambiguous than Black 's, Hausman i n t roduces several new con cepts t h at are t hemselves somewhat vague. Moreover, H ausman , in break i ng away from B l ack , also lets go of some of the key i nsights that are i mplicit i n Black's account . I now briefly discuss the maj or featu res of Hausman's theory. H ausman i nt ro duces t hree new concepts to explai n the creation of simi larity. The first i s the uniqueness of referen t . I t i s argued that a metaphor creates a new and u n ique referent that is d i fferent from the referents of the source and t h e target . It wo u l d b e h e l p fu l to read H ausman 's term ' u n i q u e ' as ' au t ono m o u s , ' for h i s p o i n t i s t h at t ho ugh t h e new re ferent m i g h t. h ave acqu i red some of its attributes t h rough the referents of the sou rce and the t arget , t h e n e w referent i s quite distinct a n d h as i t s o w n a u t o n o my. Fo r i n s t an c e i n S h akespeare ' s " J u l i et i s t h e s u n " t h e r e fe r e nt i s not the sun and ,
not J uliet , but someth i ng t hat can at best be descri bed
as ' J u l i e t - t h e- s u n '
He r e , H a u s m a n considers h i s acco u n t as paral l el i n g t h at of H.i coe u r , t hough
his i nterpret at i o n above .
of
R.i coeur
i s somewh at differe n t from the one
J presented
S t i l l , to me at least , i t is not quite c l ear w h at the u n i q u e referent
i s . T h e b es t p o s s i b l e l i g h t in w h i ch l can p r e s e n t it is by say i ng t h a t t he j uxtapos i tion of the two referents brings to view certai n aspects of the two re fer e n t s t h at are n o t t h ere w h e n each referent i s v i ewed i n d i v i d u a l ly S i nce t hese as pects h ave been created solely t h r ough the juxtaposition , one can v i e w thi:s proce�� 11.s i f 11. n e w referent h as been c reated w i t h p r e c i sely t h ose .
aspects.
1 1 a m gratefu l to P rof. M arie- Dominique G i neste for translating p a r t s of this p a p e r for 1ne.
76
Part I: The Problem
The second key concept of H ausman's account is the extmlinguistic con d i t i o n . He argues t h at the u n i que referent t h at is created h as att r i b utes t h at are not all li nguist i c . I n ot her words, t he new referent bri ngs i n new i n for mation t hat cannot be exp l ai ned in l i nguistic terms. A major consequence of t his pos i t ion i s t hat a metaphor is seen as not amenable to a p u rely l i nguis t i c analysi s . Also, i t i s these extral i nguistic attributes of the metaphorical referent that are seen to const rai n the creation of s i m ilari ty by the metaphor. The t h i rd concept t hat Hausman i n t roduces i s that of in dividuality. The referent created by the metaphor i s seen as an i n d i v i d ual in the sense of bei ng ontologically real . H ere, H ausman evokes Pierce's concept of dyna mical objects, w h i ch are objects that can be apprehended by senses, and yet are grounded in objective real ity so t h at they resist bei ng descri bed arb i t rarily [ H au sm an 1 989, A ppendix ] . The i n d i vidual i ty con d i tion is proposed so that the creation of s i m i l ar i ty does not become a p u rely subjecti ve p rocess , s ince the extralinguistic att r i b u tes of the created referent are determined in part by its objecti ve nat u re. W h i le some of Hausman's ideas are clearly echoed i n my account of metaphor i n C h apter 7, these ideas are p resented on l y vaguely by Hausman . The general themes of h i s appro ach can be understood easi ly, but when one tries to get more specific, his t heory leaves much to be desi red . For i nstance, what exactly is t he u n i que referent ? How does i t acq u i re extral inguistic at tributes? W h i ch ones come from the source referent and w h i ch ones from t he target referent ? And where do the others come from? These are only a few of the many questions not fully answered i n H ausman 's account . Finally, H ausman 's version of i nteractionism i s quite sym metr i c . I n posit ing that a new referent i s created a s a res u l t of the i n teraction , there i s an i m p l ied symmet ry. Lest t here be any dou bt , Hausman ex p l i c i t l y endorses a rad i c al version of the sym met ry view , arguing that t h e sou rce- t arget d i s t i n c tion i s meani ngless , and i t i s best to j ust say t hat a metaphor i n volves two domains [ H ausman 1 989, p . 67] . 3.5
Wheelwright - Mac C o r mac
Wheelwright [ 1 962] suggested a t heory of metaphor that recognized the com aspect present in some metaphors, while at t he same t i m e fully re alizing the creat i ve aspect of other metaphors t h at sprout new meanings a n d n e w b a s e s for s i m i l a r i t i es . He d i v i ded metaphors i nto two kinds: epi phors and d i aphor s . Epi phors i nvolve "outreach and extension of meani n g through parat i ve
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comparison" [ p . 72] but the "si m ilarity need not be obvious and compari son e x p l i ci t " [ p . 74] . Thus, epi phors correspond to what I h ave been cal l i ng similarity-based metaphors . D i ap ho r s , on the other han d , create new meani ngs t h rou g h j uxtaposition, corresponding to my similarity-creating me t aphors . Wheel wrigh t , however, does not offer much in the way of explanation as to how d i aphors create new meani ngs. A vague analogy i s offered with chem istry: "The essent i al possi b i l i ty of d i aphor lies i n the broad onto l ogi cal fact t hat new qual i ties and new mean i ngs can emerge, s i m ply come i nto being, o u t of some h i therto u n g ro u p ed comb i n ation of elements . . . J ust as d i fferent atoms , molecules, etc. exist i ndepen dently but give rise to i n teres t i ng compounds when put together under proper condi t ions ( temperat ure, p r essure, etc . ) ( l i ke H2 0 from fh and 02 ) , si m i l ar l y various mean i ngs can exist alone but new meani ngs can be created by j uxtapos i tion of previously un j oi ned words and phrases. This i s a d i aphoric synthes i s . " [ W h eel wright 1 962, p. 85-86] . This analogy does l i t t le to i l l u m i n at e the creation of s i m i lari ty, save poi n t i ng to the facts t h at the creation of si m i l ar i ty works somet i mes , w hen some mys terious con d i tions are right , and not at other t i mes; and , which s i m i l arities are created depends on w h i ch parti cular words or p h rases are j uxtaposed . B u t t h i s mere l y amounts to ack nowledgi ng that t h e creation of s i m i larity t akes place someti mes , and does not p rovide any mechan isms t hat explai n how and w hy. About twenty years later, M ac Cormac [ 1 982; 1 985] u n dertook to formal ize W heel wright ' s i deas using t h e fuzzy set-t heory o f Zadeh [ 1 965) . In fuzzy set-theory, t he membersh i p function of a set i s not a t w o - va l ued b oolean fun c tion, but a conti nuous val ued fu n c t i o n t h at maps every member of the u n i verse to some rca.! n umber in the range 0 to 1 . The val u e of this function for an obj e c t i s t h e degree of membersh i p of t h a t obj e c t i n t h e set .
Zadeh
p r e d i c at es we use in our everyday lang u age , such as ' t al l , ' t h at adm i t degrees of members h i p i n stead of part i developed t h i s t h eory to form al i ze m any
tion i ng the u n i verse of all objects into members and non- members. U s i ng the fuzzy set-members h i p funct ion , i t i s s t i l l possible to define a. belo ngs to t h at can be used to determ i n e the extent of the s e t . It wor-h by Bpecify i n g t wo b o u n d 5 a 11.nd b, w i t h 0 :::; b :::; a :::; l. Now gi ven 11. fu zzy s e t - memb e rshi p function fA , and some o b j e c t i n the u n i verse, say x , x belo ngs lo t he set A i f, 11.nd only i f, JA ( x ) .2:: a ; x docs n o l b e lo ng lo the set A
notion of
Pa.rt
7
I:
The Problem
i f, and only i f, fA ( x ) ::; b; and x is indele1·minate w i t h respect to the set A i f, and only i f, b < fA ( x ) < a . This system gives rise to a t hree-valued logic i n w h i ch every expression evaluates to 'true,' ' false , ' or ' indeterminate. ' M ac Cormac extended t h i s t hree-val ued logic system to a four-valued one by using th ree bounds a, b, and c, w i t h 0 ::; b ::; c ::; a ::; 1 . The i nter vals ( 0 , b) and ( a , 1 ) are i dentified w i t h membership and non-membership as before, resulting i n t rue and false expressions respecti vely, but the m iddle ' i n determinate' i n terval i s broken i nto two parts . The i nterval [b, c] gives rise to diaphors and the i n terval (c, a] gives rise to epiphors . Thus, accord ing to this t heory, if a predicate i s attributed to an object , and t he membersh i p fun ct i on o f that predi cate returns a value between b and c t hen t h e predi cate i s said to be metaphorical ly att r i b uted to the obj ect . I n particular, i t wou ld be a d i aphor. S i m i l arly, i f a predicate is applied t o a n object w i t h i t s degree of membersh i p lying between c and a t hen a n epiphor woul d res u l t . Perhaps needless to say, Mac Cormac 's theory also i ncludes elaborate mech anisms for locat i ng various terms in a m u l t i - d i mensional semantic space, and for determ i n i ng the seman t i c distance between two given terms so t hat the rnetaphoricity of t heir j u xtaposit ion may be determined. One can already see that this account is so far removed from B lack 's i nter action theory that i t i s hard to see it as a variant of i t , t hough Mac Cormac i nsists on i t q u i te the same [ M ac Cormac 1 985, p . 5 ] . More i mportantly, i t does n o t explai n the creation of s i m i larity a t all , a fact that M ac Cormac h i mself acknowledges [ Mac Cormac 1 985, p. 1 40] . The reason for t h i s is that M ac Cormac 's approach takes a stat i c view of language, si nce the seman t i c d istances between various words are all predetermined , a n d t hese distan ces form the bases for determi n i ng the degrees of metaphoricity. Of course, one could raise other grounds for cri ticizing t h i s approach, such as its j u dging d iaphors as less true t h an epiphors, w h i ch in turn are deemed less t rue t h an li teral statements, b u t t h at does not seem to be relevant here. 3.6
T he Lakoffian A p proach
approach to metaphor t h at h a s become i n creas i n g l y i n fl ue n t i al w as de by George L akoff and h i s col leagues. The focus of t heir study h as been what are generally regarded as conventional metaphors. Lakoff and his colleagues have put up the most i mpressi ve empirical demonstration of how many of our everyday concepts are structured by conventional meta phors [Lakoff & J oh n son 1 980] , and how many of t he novel metaphors i n poetry can b e analyzed as new exten s i o n s o r new combinat i ons o f convenAn
veloped
Chap t er
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79
t iona! metaphors [Lakoff & Turner 1 989] . Nevertheless, these schol ars have also emphasized that metaphors can create s i m i lari t ies wh ere none exi sted before, and h ave t ried to explai n how this creat ion takes p l ace [Lakoff and Johnson 1 980, Chap . 22] . These views have been fu rther el aborated in John son [ 1 987] , Lakoff [ 1 987] , and Lakoff & Turner [ 1 989, Chap. 2] . Though their exp l anations do not ful l y resolve the paradox of the creat ion of s i m i lari ty, t hey are successfu l in poi n t i ng out t h at the roots of t h e paradox run much deeper than i t m i ght first appear, and t h at i t s reso l u tion requi res certain views about cogn i ti o n to be reexami ned . A t the core of the Lakoffian explanation of the creat ion of s i m i larity is a d i s t inction between objective simila rities and experi e n t ial similarities. Their contention i s that objecti ve s i m i l ari ti es do not exi s t , and only experien t i al s i m i l ar i ties are real . T h at i s , we cannot ask whether two objects are s i m i l ar or not i n dependentl y of how these two objects are experienced and conceptual ized. And s in ce "The essence of metaphor i s u nderstan d i n g and experiencing one k i n d of thi ng in terms of another" [Lakoff & Joh n son 1 980, p . 5], i t fol lows that i n conceptual i z i n g the t arget as the sou rce, the two are made to look s i m i l ar . Thus, a metaphor c reates experiential s i m i l arities between the source and the t arget . This point can be i l lust rated w i th the examples of geomet ric figu res that were introduced i n C h apter 2 [Figure 2 . 1 ] . Comparing Figures 2 . 1 (a) and 2 . 1 ( b ) , the obj ecti ve s i m i larities, i f t hey were to exi s t , woul d i n clude all pos sible ways in w h i ch these two figures are s i m i l ar independent of any obse1·ve1· or a n y conceptual 0 1-gan iza tio n . C learly, no such thi ng can exi s t , for i t is the concepts t hat m ake two d i fferent objects appear s i m i l ar . We see t h at they are both ' t ri angles , ' or they are both ' t rees , ' or the river and the s nake are both ' wavy . ' Look i ng at Figures 2 . l ( a) and 2 . l ( b ) one m ight say that t hey are both 'closed figures . ' B u t ' c losed figure' i tself is a concep t . If concepts are n ot a d m i tted , then even two congruent t r iangles cannot be seen as si m i l ar .
So we conclude t hat in order to see w hether tw o objects are s i m i l ar or not, t hen in what respects, requires t hat the objects be concept u al ized in some way. The figures i n Figu res 2.l ( a) and 2.l ( b ) can be t hought of in terms of triangles, squares, hexagons, ellipses, etc. However, as soon t he o b j e ct s are conceptualized, any s i m i l a r i t i es that are gleaned between them now be come very much dependent on the concept ual i zat ion chosen . Tn other words, t hey become experienced sim ila rities. and if so
And conceptualizations are subj ect to change. We can concept ualize Fig ure 2.l ( a ) in terms of t riangles, trapezoids, or paral lelograms , among oth ers. As the con ceptualization o f one o r both o f th e ob jects being compared
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FIGURE 3.2: The figure used in the quotation
from Whorf. (From Whorf [1941].)
changes , the experienced s i m i larit ies also change, as they are dependent o n the conceptual izat ion s . Thi s i s precisely how s i m i l arit ies are created . Every i nstan ce of creation of s i m i larity is accompanied by a change of concept u al ization of one or both objects . There are t hree thi ngs about thi s explanation that I must emphasize. F i rst of al l , i t essent i al l y rearticulates a poi n t made about forty years earlier by Benj am i n Lee Whorf. Whorf ( 1 94 1 ] presented em piri cal evi dence to argue that different c u l t ures can concept ualize t he worl d d i fferently so t h at t hei r s i m i l arity metrics are d i fferen t . That i s, two si tu ations that are consi dered s i m i l ar i n one c u l t u re can be regarded as very different in another culture. For i n stance, to Engl ish speakers, the sentences ' 1 pull the branch aside' an d 'I h ave an extra toe on my foot ' seem quite dissi m i l ar. Set t i n g aside t he l i nguistic descriptions, even the two phenomena that the sentences describe woul d not be consi dered s i m i l ar . Yet , in Shawnee, Whorf writes: " ( T ] hese two statements are, respect i vely, n i-l'Oa wa- 'ko-n-a and n i-l'Oawa-'koOit e ( the(} here denotes th as in 'thi n ' and the a pos t rophe denotes a breath catch) . The sentences are closely si m i l ar ; i n fact , they d i ffer only a t the tail end. I n Shawnee, moreover , the begi n n i ng of a con struction is generally the i m portant and em phati c part . Both sentences start w i t h ni- ( ' I ') , which is a mere prefi x . Then comes the real ly i m portant key word, l'Oa wa, a com mon Shawnee term , denot i n g a forked outl i ne, l i ke ( Figu re 3.2]. The next element, - 'ko, we can not be sure of, b u t i t agrees in form with a varian t of the suffix - a 'kw or - a 'ko, den o t i ng t ree, bush, tree par t , branch, or anything of that general shape. In the first sentence, -n- mea.ns 'by h and act io n' and m ay be e i t her a causa tion of the bas i c condition (forked outline) manually, an increase of i t , or both. The final -a m ea n s t h at the subject ('T') d oes t h i s action to an a p propr i a te object. Hen ce the fi r s t sentence means 'I pull i t ( somethi ng l i ke branch of tree) more open or apart where it forks.' In t he ot her sentence , t he suffix -Oite means p e rt ain i n g to the toes ,' and the absence of fu rther suffixes means that the subject mani fests the condition in his own person. Therefore, the '
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Approaches to Creative Metaphors
81
sentence can mean only 'I h ave an extra toe forking out l i ke a branch from a norm al toe. "' [ Whorf 1 94 1 , p . 234.] From m any other exam p les l i ke t h i s , Whorf argued t hat one's language i m poses an organization on the world accord i n g to which certai n t h i ngs are seen as s i m i l ar and certai n others as dissi m i l ar. However, different languages can i mpose d i fferent organizations on the worl d , t hereby creat i n g d i fferent s i m i larity metrics. Thus, we see t h at the i dea t h at the creat ion of s i m i l arity is brought about by a change i n conceptualization i s not so new after al l . Even though Whorf was not focusing on metaphors, his account contains a clear and u n ambiguous explanation of the c reat ion of si m i l arity t h at is essenti ally the same as the Lakoffian explanation. The second t h i n g about the Lakoffian account i s that i t echoes the t hemes that were at least i m p l i c i t , if not quite exp l i c i t , in Bl ack 's and Ricoeur ' s ac coun t s . Though the Lakoffian approach rejects the i n teraction theory [ L akoff and Turner 1 989, p p . 1 3 1 - 1 33] , fau lting it for its stand on the symmetry of metaphor, t h i s rej ection i s based on tak i ng the symmetry to be the one and the only character i z i ng featu re of i nteraction i s m , a view w h i ch is very shortsighted in l ight of what I h ave already discussed in t h i s chapter. Black's starry- sky- t h rough-the-smoked-glass analogy and t he Star of Dav i d example are both i nstan ces of the t arget being experien ced t h rough the source. More over, B lack 's account of how the s i m i l arit ies are created in each of these cases is very much l i ke the Lakoffian explanat ion . F i n ally, both Ri coeur and B l ack m ade a d i s t i n ction ak i n to w h at the Lakoffian approach refers to as experi ential and objecti ve real i t ies by argui n g that metaphors are models through w h i ch we h ave cogni t i ve access to real i ty. A II these facts strongly suggest t h at the approach of Lakoff and h i s coll eagues is much closer to i nteraction ism t hen t hey are w i l l i ng to adm i t . F i n ally, w h i le the Lakoffian approach i s better art iculated . aided w i t h nu of interactionism, a careful a n alysi s reveals t hat i t does not real ly resol ve t h e parad ox of creation of si m i lar i ty. To appreciate t his p o i nt , let me elaborate the Lakoffian approach with a few ex amples. Consider first a c ase where t he creat ion of similarities is n ot i nvolved , just to u nderstand how a metaphor works in the Lakoffian account. In the ' m o r e i s u p and less i s down' metaphor, exemplified by "House prices plum meted following the stock market cr as h , " Lakoff argues, the source 'vertical i ty ' i s already understood ind ep enden t ly of any m et a p h or. In t he Lakoffian approach, s uch concepts are refe r red to as ' d i rectly emergent,' w h i ch means t hey come about due to our h aving bod ies of a certain sort , and are d i rectly understood as such. While the concept ' di r e c tl y emergent' itself r aises sevmerous examples, than the other versions
Part I: The Problem
82
era! questions and contributes to the vagueness of the Lakoffian approach
[Mac
Cormac
1985,
pp.
66-70],
let us grant them that notion here. Now, the
target 'quantity' is seen as having the following structure: Whenever we add more of a substance, the level rises, and whenever we remove some quantity of the substance, its level falls. In fact, this structure is already described in terms of the metaphor, and shows structural correlations of 'more' with 'up' and 'less' with 'down.' Lakoff takes this structural correlation to be the key factor that makes the metaphor work. He even goes on to state that there is an isomorphism between the metaphorical mapping and the structural correlation [ Lakoff
1987,
pp.
276-278].
There is a small but crucial assumption here that must be brought out, namely that the target domain must also be independently structured before the metaphor. [[it were not, then the correlation condition does not make sense.
T hat is, if the metaphor caused the correlation (and there was no
structure to 'quantity' before the metaphor), then Lakoff's account does not explain why 'verticality' is an appropriate source domain. Why can another source domain not introduce a different structural correlation? Why can the 'container' domain, another one of the so called directly emergent concepts in the Lakoffian account, not structure the 'quantity' domain by inducing the structural correlation?
The 'verticality' domain just did. What makes
the 'verticality' domain so privileged?
All these questions undermine the
Lakoffian explanation unless one admits that the target domain has a struc ture before being conceptualized by the source domain and the structure is independent of any metaphor. Because then the correlation business can be explained by pointing out that it is the autonomous structure of the t ar ge t
domain that resists arbitrary
But if the target correlation betwe<'n
source domains being applied to i t.
already has
a
structure, then
existing similaritie s between
L ako ffi an approach becomes essentially a variant
but finding some
acco u n t , i n spite of their se v ere criticism of it.
establishing
of the
the two domains.
u c t ura l
To be fair, 1 should stress that Lakoff did not cit e
t his e x amp le
But this an alysis was merely to
as a
example that is conside red
an
am not sure if he would view it as one.
c rea t ing metapho r in the Lakoffian approach. Lakoff and Johnson
the
expose the hidden assumption in the Lakoffian I
N ow l et us look at
And
comparison theoretic
similarity-creating metaphor, and a ccount.
a s tr
it and the e xi sti n g structure of t he sour ce is nothing
a similarity
[1980, pp.l47-148] present th e example of the
'ideas
are food' metaphor to argue that this metaphor creates the similarities be tween 'ideas' and 'food.' In particular, they argue th a t the concept of 'swal-
Chapt er
3:
Approach es to Creati11e Metaphors
83
low i n g ' i deas comes only by virtue of the metaphor, and does not exist in dependently of it. But then why do i deas not generate some waste product after being digested? Why do ideas not start rot t i ng if you leave them out side for a long t i me? Why can only some aspects of the ' foo d ' source domai n be i m ported b u t ot hers not? A n d why wou l d any other sou rce domai n , l i ke ' vert icality' not do as wel l ? It must be that the target h as an i n dependent struct u re t hat resists arb i t rary correlat ions. Or, if the target does not h ave an i ndependent structure, then what is it that resists arbit rary correlations? These problems creep u p everywhere Lakoff and his col leagues try to get more specific about t heir account of the creat ion of s i m i l ari ty. For instance, Lakoff and Turner [1989, pp. 63-64] state t hat a metaphorical schema maps slots , relations, propert ies and k nowledge of t he sou rce domain to the slots, relations, properties and k nowledge of the t arget domai n . They also state t hat w h i le some of the slots, relations, propert ies and k now ledge of the t arget domain m ay have existed before t he mapping, some are aeated expressly by the metaphorical process for t he p u rpose of the mapp ing. For i nstance, in the ' l i fe i s a jour ney ' metaphor, t he ' course of l i fe ' slot i s created i n the t arget domain of ' li fe' so t h at the slot ' path ' i n the source domai n 'journey' can be mapped onto it. But t hen why are not slots created for ' cond uctor , ' or ' steward , ' 'luggage , ' and so on . Of course , it i s u nderstood t h at the mappi n g i s p artial, a n d n o t every t h i ng i n the source domai n is m apped . B u t t h e p o i n t i s t h at w h e n i t comes to i nducing slots a n d relations, i t seems quite arbitrary why certain slots an d relations of the sou rce domai n can i n du ce their counterparts i n the t arget domai n , b u t other slots and rel at ions sim ply cannot.
T hus, e i t h e r the Lakoffian approach has to admit that Lhe t arget has a structure t h a t is independent of any metaphorical structu ring, so that it can be used as a constrai nt to determine which metaphors work and which ones do not, whi ch seems to contradict the very foundation of t he Lako[fian approach t h at vehemently maintains t h at many of our everyday concepts are inherently metaphorical, and cannot be characterized non-metaphorically. Or the L a k offi an a p p roach must re mai n mysti cal fo r not bei ng able to explain why onl y certain source domains can struct u re a given target-a target that can only be exp e r ien ce d thro u gh a metaphor, a nd not directly-and w h y even w hen they do, t he y can only s t ru cture the target in certain non-arbitrary ,
ways.
failure of t h e Lakoffian approach to fu lly address t he cre of s i m i l ari ty, i t contains a cruci al i nsight t h at is only cu rsorily presented in Black's later paper [1979]. Th is is the realization that the creation of simiIn spite of this
a t io n
84
Part I: The Problem
larity is rooted i n a more fundamental cogni t i ve phenomenon , and t hat t he creat ion, i n i t s essence, i s really the creat ion of attribu tes ( and relat ions etc . ) o f obj ects . I ndeed , Lakoff and Johnson 's experient i al account i s act ually a framework of cogn i t ion. Bu t I defer a further d iscussion of their cog n i t i ve framework u n t i l the next chapter, where J exam i ne various i nteractionist view s of cogni t i on .
3. 7
My Earlier Approach
Ever si n ce I started being i nterested in metaphors, over ten years ago, I h ave been i n t rigued w i t h the i n teract ionist approach to metaphor-especially t h at of B l ack-and concerned w i t h i t s ambigui ty. My first attem pt at formali z i n g t he i nteraction t heory, outli ned i n I n d u rk hya [ 1 986; 1 98 7], o n l y part ially ad dressed the phenomenon of creation of s i m i l ari ty. Nevertheless, it h as some i nteresting aspects worth not i n g here, especially si nce my approach to the creat ion of s i m i larity presented i n t h i s book can be seen as an evol ution of my earlier theory. Moreover, I used a mathemati cal formalism to art i c u l ate my i deas preci sely then , someth i n g t hat l do here in C h apter 6 as well , and i t i s i m portant to emphasize that the use of formal tools i s not a s l i m i t i ng as some researchers, such as Lakoff [ 1 987, Chap. 1 4], take them to be. E ven i n my earlier approach, which made use of F i rst-O rder Logi c , some key char acteristics of m etaphors, such as how d i fferent metaphors can organize t he same targ et d o m ai n d ifferen tly , cou ld be neatly ca pt ured .
The s o ur c e and the t a r g e t domains, in my earlier approach, were char acteri z ed as s ystem s of axioms that were closed under entai lmen t . Thus, each domain ha.d a ' vo c ab u l ary,' which was a set of constant and pred i cat e symbols , and a 'structure,' which were the axiom s t h at showed how the sym bols we r e interrel ated. Certai n axioms of a domain were called 'deri vations,' where every derivation d e fi n e d some symbol in terms of ot h er s y m bo l s. For instance, in the domai n of fam i ly relat ionships, a derivation for 'ch ild ' might be "X is a child of Y i f, and only i f, Y is a parent of X."
A key feat u re of the t heory was t hat the deri vat ions were a.llowed to be ci1·cular. That i s , i t w as pe rm i ssibl e to h ave a derivation for X i n terms of Y, w h i l e at the same t i me h av ing another derivation for Yin terms of X. In the a bove example, that the symbol 'parent' can also be defined in terms of 'child.' An important consequence of i n cor p orati n g this feat u re was t hat a domain coul d adm i t of several possible choices of primitives. For i n st ance, the domai n of fa m i l y relat ionships could b e described from the set of p rimitive s { 'm a l e , ' 'female,' 'ch i l d '} and also from the set of primitives { ' m a l e ; ' 'female,'
Chapt er
3:
Approaches to Creat i ve Metaphors
85
' p arent ' } . A metaphor was defined as a part ial struct u re-p reserv i n g mapp i n g from the vocabu l ary of the source domai n to the vocab u l ary of the target do m ai n . That i s , a metaphor was seen as rel at i ng some of the symbols i n the source domai n with some of the symbols i n the target dom ai n i n such a way t h at w hen the structure of the symbols ( how they are i n terrel ated ) i n the source domai n was t ransported to the target domai n , i t did not contradict the existi n g struct ure t here . This account might seem quite simplistic, but it cou l d explain some im portant characteristics of metaphor. For i nstance, the role of a metaphor i n reorgani z i n g a dom ai n was explai ned a s fol lows. A metaphori cal mappi n g o n l y chooses certai n symbols i n the target domai n , and the v i e w o f the tar get domain , as seen t h rough the metaphor, is essentially as if those symbols were the pri m i t i ves and the rest of the target dom ain were bei ng descri bed in terms of t hem . A n d since d i fferent metaphori cal mapping cou ld choose d ifferent symbols from the same target domai n , t hey wou l d suggest d i fferent ways of organizing i t . It also explained how a metaphor can i n duce n e w struct ure i n the t arget domai n . A metap horical mapping al lows ad d i t ional struct u re to be im ported i nto the t arget domain as long as it does not cont rad ict whatever structure i s t here already. Two operators were exp l i ci t l y proposed t h at extended the metaphorical m apping by i n d u c i ng structure i n the target domai n . One op erator, called 'augmentation,' made use of der i vations in i n d uci ng structure. For i n stance, La koff an d Tu rn er 's e x am p l e of a 'course of life' slot being in d uced i n the ' l i fe' domai n by the source domain j ou rn ey can be seen as
Here, the induced slot is quiLe '
in instance of augmentation.
constrained
by
been m a pped an d it is merely a new name for a q u ant i t y relation, etc.) t h at is already t h ere in the target domain. The
what has already (attribute,
'
,
secon d operator, called 'positing structure,' was could induce any arbitrary structure as
long
as
much l es s
it w as
constrained and
consistent with the
exist i ng structure of the target domai n . I n spite o f bei n g able t o formally capt ure some int u i t ions about metaphor, h as a. major limitation a.s far as t h e phenomenon of c rea t ion of si m i l ari ty i s con cern ed. The stru ct ure of the target domain was always i ncren.sed monoton i ca. l ly. That is, new stru cture was added as long as it was consistent with the existing structure of the target domain. But t hi:s proce:s:s woul d n ever invalidate the exi s t i n g stru ct u re T h us t h i s approach wou l d not b e able t o explain Schon's 'paintbrush a s a . pump' m e t aph or where i t was this approach
.
,
necessary to discard the existing structure of the tar ge t doma.in 'painting,' ,
86
Part 1: The Problem
si nce the metaphori cal restructu ring was i n consistent w i th the i n i t i al struc t ure. Being aware of this l i m i tation , I offered the follow i n g explanation a.t the t i me: "In genera l , i n com prehending a metaphor , there i s t hree- way ten sion goi ng on rather than two- way tension as we assumed in our theory. The i n teract ion tak i ng place in un derstan d i n g a metaphor i s not merely between the source domai n and the t arget domai n b u t among the source domai n , the t arget domain and the object or the concept t hat i s represented in the t arget domai n . Thus i n i nterpret i n g t h e metaphor ' t he s h i p plowed t h rough t he sea' the domai ns plowing and sailing i nteract with each other and w i t h t he actual process of sai l i ng t o produce an i nterpretat ion of the metaphor. The reason for this d i s t i nct ion i s that our representa tion of an obj ect or a concept reflects a certai n perspec t i ve and i n that sense i s a n approx i mati on t o the real nature o f that object or concept. A metaphor can , by mere j u xt apos i tion or other tech n i ques, force u s to look beyond our representation of the object in order to make sense of the metaphor. This process can give rise to a new perspect i ve on t he object t h at was missing from our representat ion . " [ Indurkhya 1 986, pp. 546-547]. I i nclude this long quote here because the approach to metaphor developed in this book is really a fru i t ion of t h i s i dea, and it m ight be helpful to s ee its origin . Moreover, t h i s is really an echo of w h at h as been i m p l i ci t i n the i n tera ct i on i s m s of Black, H ausman , and Ricoeur.
3.8
Kittay's Perspectival Theory
A nother n o t a ble attempt at formalizing t h e interaction theory has bee n made [1987]. Ki ttay refers to the interaction theory as t h e perspecti val theory, for, as she sees i t, the essential i ngred ient of i n terac ti onism is i n arguing t h at metaphors fu nction by prov i d i n g perspecti ves o n the target . (Bl a c k h as h i mself endorsed this view, as n ot e d at the end of Sect i o n 3.) Taking this vantage point, Kittay went on to develop an elaborate and formal framework to exp l ain the working of me t ap h o r , including the creation of by Kittay
similarity.
Kittay's theory is articulated i n the l inguist i c framework of comp os i t i on al to which the meani ng of any ph r ase or sen tence i s a
semantics, according
Ch ap t er
3:
Approach es to Creative Metaphors
87
function of the meani n g of its consti tuents. ( For example, the mean ing of "The sky is crying," in compositional semantics, wou l d be a function of the m eani ngs of 'the, ' ' sky, ' ' i s , ' and ' cryi ng. ' ) P resented i n t h i s way, K i ttay's account becomes essen t i ally a theory of t he metaphors of language. More over, her theory regards conventional meanings as more fu n damental t han metaphorical meani ngs in at least two ways: Con ventional meani ngs are arrived at befo re metaphorical mean i ngs, and it is some i ncongruity with re spect to the convent i on al mean i ngs that , at least i n part , triggers the process of constructing metaphorical meani ngs. This, in turn , h as two major con sequences : (1 ) U nderstand i ng conventional meani ngs becomes a p rerequisite to u nderstanding metaphorical mean i ngs, and ( 2) con vention al mean i ngs are seen as cognitively easier to understand , si n ce the extra stage of processing where the second-order i nterpretations are deri ved i s not n ecessary. Though the empirical research on this matter has not yet reached a consensus, there seems to be some evidence that, g i ven a proper contex t , metaphori cal mean i ngs are no h arder to comprehend than convention al mean i n gs [ Gerrig 1 989; Hoffman and Kemper 1 987]. Fu rther, the empi rical research also suggests t h at an attempt to focus o n the conventional mean i n g often turns out to be counterproducti ve in figuring out the metaphorical mean i ng . In both these respects , ]{ittay's theory cont rad icts empi rical findi ngs. Embedded in the l i nguistic framework, however, is a cogn iti ve d i mension , and Kittay's explanation of the creation of si milarity runs primar i ly along thi s cog niti ve d imension . As my m ai n i nterest here is i n the phenomenon of creation of s i m i l arity, I p resent h e re Kittay 's approach to i t , which can be understood w i t hout recou r s e to the c o mp os i t i onal semantics framework i n w hi ch it, is emb ed ded .
At the heart of KiLLay's account of the creation of similarity is the concept semantic field. A se ma n t i c field ca p t u res the i nt ui t i on that the meaning of a word cannot be specified in i so l at i o n , but i s invariably connected with the mean i ngs of the other words. Furt h er , the meanings of d i fferent words are structurally r e l ated to each other, and it is these structural relationships t h at are referred to as semantic fields by Kittay. For i nstance, the meaning of 'rock ' has a sem antic featur e ' s ol i d .' But the featu re 'solid' is re l ated to the features 'liquid' and 'gas' that m ig h t occur i n the meanings of other words. Moreover, the features ' sol i d ,' 'liquid,' and 'gas' form an ordered c ontr as t set. Any materia.! is in one, an d only one, of t hese three forms, an d there is an ordering from 'solid' to 'gas' Thus, th ere is a structural relationship among t he features 'solid,' 'liquid,' and 'gas,' that can be cal led i nto p l ay whenever the meaning of 'rock' is bei ng processed.
of
Pari
88
I: The Problem
Formally, a semantic fiel d is comprised of a lexical field and a cont e n t The lexical fiel d i s a s e t o f u n i nterpreted ( not y e t meani ngfu l ) labels t hat are structu red . For i n stance, a lexi cal field m i ght con t ai n t h ree l abels ' sol i d , ' ' l i q u i d , ' and ' gas ' t h at are struct u red in t h e sense t h at t hey are pai rwise m u t ual l y excl usive, and there is a gradat ion from ' sol i d , ' t h rough 'li qu i d , ' and to 'gas . ' The content domai n is the realm in which the labels are to be i n terpreted . An exam ple of content domai n wou l d be material objects . A seman t i c field i s formed when a lexical field i s i nterpreted in a content domai n . Thus, when we deci de to c l assify all m ateri al obj ects as 'sol i d s , ' ' l i q u i d s , ' and 'gases , ' a semantic fiel d is created. T h i s p rocess of i nterpretat ion is cal led articula ting t h e co n t e n t dom a i n . do m a i n .
With t h i s backgrou n d , t he process of i nterpret i n g a metaphor i s descri bed as fol lows. The conventional i nterpretations of t he expressions occurring i n t he metaphor identify two d i stant sem antic fields, t he source ( t he veh i cle) and the target (th e topic ) . I n overcoming t he distance between the two fields, t h e field of the source i s u sed to art i c u l at e t h e content domain of the t arget fiel d . The process is struct ur e preserving in that it must not violate the ex i s t i n g structure of the target content domai n . However, t h e articulation may i nduce ad d i t ional structure from t h e sou rce field to t h e t arget content domai n . The creat ion o f s i m i l arity is explained i n t h i s account as fol lows. I n re struct u r i n g t he t arget content dom ain, it is m ade s i m i lar to t he semantic field of the source. Moreover, t h i s rest ruct u r i n g i s constrained by th e ex isting structure of the t arge t content domain, which re sist s being o rgan iz e d arbit.rari ly.
Thus, we see that l\i t t ay ' s account qui te expl i c i t ly assi g n s a role to the referent of the t arget dom ai n in the i n teract ion. The content domains can best be identified as the pieces of real ity th at h ave been presented to our perceptual a n d conceptual system t o be 'articulated,' o r given form. Kittay ' s
own explanation of what exactly a content domai n i s clearly suggests t h i s : "[Content domai n s ] m ay b e perceptual a n d as general a s the do main of colour o r s h ape, or as specific as that of ice-cream flavours. An identifiable activity, su c h as wo o d wo r k i n g or fish i n g , may con s titute a content domai n, as m ay something as generally experi ential as t h e l i fe cycle. A d o m a i n cou l d h ave its sou rce i n cul t u ral i nst i t u tion s-for exam ple, m arri a g e and the s o cia l l y sig n i ficant k i n s h i p relation s . A d om a i n may b e conceived of as conceptual, h aving i t s u n i ty deri ve d not from an act ivity or a perceptual mode b u t from an i nterrelation of concepts. Scientific t h eories \�ould
Ch ap t er
3:
Approaches t o Creative Met aphors
89
be paradigmati c conceptual content doma i n s . As these examp l es suggest, a content domain is an area of thought , of in qui ry, of ac t i v i ty about which we req u i re or desire
inform a t io n . . .
. In short,
a content domain is whatever a sel of label s that have contrasti ve and affini t i ve relations may be
abou t . "
[ K il t ay 1 987, p .
225] .
T here i s a crucial issue here, though: Is a conte n t domai n s t ruc t u red prior to, and independently of, being articulated by a lexical fiel d ? Thi s issue is crucial because i f one answers it affirmati vely, then one is co m m itted to realism where reality has i ts own obj ect i ve str u c t u re prior to co nce ptual ization . But then i t is hard to argue that a source seman tic fi.el d that is not s i m i lar to this obj ecti ve structure can actual ly make the content domain s i milar to the field . A nd if one answers the question negat i vely, then one is comm itted to a relat i v ism where any arbitrary source can induce sim ilari ties by articulat ing the target content domain. K i ttay is quite aware of t h e d i l e m ma , but evades the issue altogether : " P ut simply, whether we consider a conte n t d o m ain t o have an objecti ve structu re, which we need to capture with a set of con trasts and affinities, or whether w e conceive o f the co n t e n t domain as a continuum upon which we impose a scheme of contrasts and affinities, it is the requi rements of i n formation t hat d i ctate the articulat i on of the doma i n by con t ras t s a n d affi n itie s . "
[ K it tay
1 98 7 , p. 226] .
Here, ' t h e requ i rements of i n for m at i o n ' are t h at t h e a r t i c u I at ion somehow
p rov i d e ' con d i t ional and d i fferent i al i n fo r m at i o n ' about the c on ten t d o m a i n . A n d a d i s c ussion o f w h at exactly t h i s con d i t i o n a l an d d i ffe re n t i al i n for mat io n is [ K i t t ay doma i ns
1 987,
resist
pp.
bei ng
1 2 1 - 1 39] fa i l s to shed art i c u l ated arb i t rari l y.
any
l ig h t
on how the content
Thus , we see t h at K i t t ay ' s i n corporation of t h e referent of t h e t arget i n to the metaphori cal p rocess fai ls to resolve t h e paradox of c reat i o n of s i m i l arit y. S t i l l , i t does come qu i te c l ose to i t by p oi n t i n g o u t t h at t h e key to t h e
resolution of the paradox lies in u n derstan ding t h e interaction between
lexical fields and the
t.hc
c o nt e n t domains. T h e paradox o f c re a t i o n o f s i m i l n.rity
can now be s t ated a.s : How i s i t t h at different lexi cal fie l d s can art i c u l at e a. content domai n
di!Terently,
but
no
t a rbit r ari l y ?
T h i s agai n suggests that the
problem of creat i o n of s i rn i l a.r i ty i s reaJ i y a p rob l e m of cogn i t i o n .
Part I: Th e Pro blem
90
3.9
Conclusions
We saw in t h i s chapter that despite numerous attempts at explai n i ng the creat ion of si m i l ari ty, i t s paradox i s s t i l l not ful l y resol ved . I n particu l ar , no t heory h as sat i sfactori l y demonst rated how i t i s t h at a metaphor can create s i m i l ar i t ies between the sou rce and the t arget , s i m i l arities t h at were not there before the metaphor, and how the creat ion of si m i l arities i s not arbi trary, but i s constrai ned somehow . We also saw that, i n s p i te of t h e wi de variation among d i fferent scholars' approaches to the creat ion of s i m i l ari ty, t here are two key concepts t h at are i m p l ici t ly or explicitly contained in most of them. F i rst, there is the i dea t h at the i nteraction involves not j ust the conceptualizations of t he source and the t arget , b u t also thei r referents-at least the referent of the t arget . Second, there i s the argument t h at s i m i l arity-creati n g metaphor i n variably works by changing the fam i l i ar perspect i ve on the t arget referent and creati n g a new one. A nd the sim i l a rities are created w i t h respect to t he new perspecti ve on the target . That i s , t h e sou rce and the t arget do not appear s i m i l ar from the fam i l i ar perspect i ves , but when the metaphor changes the perspecti ve on the t arget , t hey become s i m i l a r . Lurking underneat h t h i s exp l anation are t w o crucial assumptions t h at are partially analyzed by a few scholars. One assumption, explicitly recognized in the Lakoffian approach , i s t h at s i m i lari ties are characteristics of the per specti ves and not of the object s . That i s , we can not ask if two obj ects are s i m i lar or not i n dependently of how they h ave been conceptual i zed . The second ass u m ption is that i n changi ng perspect i ves on an object
( event , situation , etc . ) new att r i butes and struct u res can emerge . Thus, the
creat ion of s i m i l arity essent ially b ecomes the creat ion of at tribu tes. B u t this i s a c og n i t i ve c l ai m . T h e problem of c reat ion of s i m i l arity becomes a problem of cogn i t ion . The realizat ion t h at the paradox of the creat i on of s i m i larity must be w i t h i n a cogn i t i ve framework , wh ile i t i nvol ves a deep i n s i ght , does not , however, re s o l ve t h e paradox. lt merely t r a n s l at e s it i nto a cogn i t i ve p aradox : H ow is it t h at an object can be concep t u alized differently, with new at tributes and struct u res being created , but this creation i s not arb i t rary? What const rains the creat ion of at tri b utes a n d s t r u c t u res ? U nti l these q uestions are satisfactorily ans wered , the paradox of t h e c reat ion of resol ved
s i m i larity r em ains untamed .
lt is exactly t h i s p a r ado x of cogn i t ion t h a t has b een a c e nt r al t heme in the works of those schol ars who h ave t ried t o find a compromi se between the
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extreme views of subjectivism and objectivism . Perhaps not surprisi ngly, the view of cognition proposed by these scholars is sometimes known as the inter action view of cognition. Various articulations of this view, however, suffer from a lack of precision not unlike the vagueness surrounding the i nteraction t heories of metaphor. This is what I endeavor to show in the next chapter.
C hapt er
4
C ognit ion as Interact ion 4. 1
Intro duct ion
At the end of the last chapter we saw that the creation of simi larity points to a more fundamental cognitive phenomenon, namely that of the creation of attributes of an object , event or situation. This phenomenon ha.s sprouted a certain view of cognition that is becoming increasingly prominent . I refer to i t as the i nteraction view of cognition. A ccording to this view, our concepts do not reflect some pre-existing structure i n the environment , they c1·eate the structure. Yet , this conceptual organization cannot be arbitrary, and is somehow constrained by reali ty. The i nteraction view of cognition has been spec u l at ed u p on wi dely, es pecially in this century, by philosophers, psychologists, anthropologists, and linguists alike. There h ave been m any em p i rical studies contributing to this view . a
A n d many t h eoreti cal frameworks h ave b e e n proposed to elaborate
n d articulate
the exact nature of the i nteracti o n _
T h e i n t er a c t i on
view of c ogn i t i on
i nvolves a p aradox t h at i s very much
like the paradox of creation of similarity: How can t he a t t r i b utes be created, but not arbitrarily? The paradox is in positing a reality t h at can c o n s t r ai n our con ce ptu al organ i z ation , and yet denying t h i s reali t y a mi nd in d e p e n den t ontology and structure_ A n d if one maintai n s t h at real i ty does have a mind i n d e pend e nt ontology and structure, t hen t he quest ion naturally arises : Why is this o n to logy and structure not k now ab l e ? A n d if i t wou l d be kno wab le, then this woul d i mmed i ately le ad to the view that r e al i ty ha.s a p r e exi s t i n g o ntol ogy and structure and our concep t s can reflect i t . B u t s u ch a v i e w wou l d -
-
cont r ad i c t t h e fun d amental prem i se o f i n teraction i s m .
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This paradox has not yet been resol ved , t hough elaborations of the i nter action view h ave i m p licit ly dealt w i t h it to varying degrees. I n t his chapter, I consi der t hree d i fferent versions of i nteractionism and d i scuss what light, if any, each of t hem sheds on the paradox . The t h ree versions, which are cho sen for their notab i l ity and relevance to my own approach , are: Goodman 's worl d m aking, P i aget 's constructi v i s m , and Lakoff and Johnson 's experien t i al accoun t . A s each of t hese versions origi nated i n a d i fferent field-one i n p h i losophy, o n e in psychology, a n d o n e i n l i ngui sti cs-a d i scussion of t hem also provi des a m u l t i d i sciplinary perspecti ve on the i nteraction view. This chapter is organi zed as fol lows . I n Sect ion 2 , I present some empir ical evi dence i n support of the interact ion view of cogni t ion . I n the s ubse quent t h ree sections I review the t h ree versions of interact ion i s m mentioned above. I start out, in Sect ion 3, by consi deri ng the p h ilosoph i cal approach to interactionism that started in Kant , mat u red in Cassirer, and climaxed in Goodman . I n Section 4 , I discuss P i aget 's construct i v i s m at' some lengt h , because m y own a p p roac h to interactionism, l aid o u t in chapters 5 and 6 of t h i s book , i ncorporates m any i deas of P i aget . I n Section 5 of the current chapter , I present Lakoff an d Johnson 's experient i al account t hat emphasizes the bodily basis of cognit ion . Finally, in Section 6, I summarize the mai n points of the chapter.
4.2
E mpirical S upport for t he I nteraction View of Cognition
Many empirical studies support the view t h at our concepts do i ndeed con struct our wor l d v i e w , and are not reflections of some pre-existing, m ind i n dependent structures i n t h e wo r l d , and yet t hat t h i s construction is not a r b i t r a r y M y ob j e c t i v e i n this section is to give you some feeling for t he e mp i rical foundation of i nteractionism. I do so by breaking up the i n te r ac tion view i nto t h r ee se pa r at e hypotheses and reviewing empirical evidence fo r each hypot h esi s . Then I d i s c us s t he issue of 'universal s , ' which are st ruct u res t hat are a necessary part of any c o ncept u al organizati o n . As an illustration, I t he n review the search for the existence of color u n i versals and t h at attempts to ground them i n the physiol og i c a l s t r u c t u r e o f t h e brai n . .
,
Needless to say, my review is n o t meant to b e exhaust ive. T here are many emp i ri cal studies that corroborate the i nteracti on view, or refute the alternat i ve views of cogn i ti on , and even a somewhat s uperficial survey of a l l t h ese stud i es wou l d easily fill a whole volume. In fact , given the over-
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whelming evidence supporting the interaction view, I wonder how anyone can reasonably subscribe to any other view of cognition. Unfortunately, cog nitive science research abounds with approaches that completely disregard this mass of evidence. The research on metaphors, which has been dominated by similarity-based approaches that assume that attributes of an object are all given, provides one source of flagrant examples . G i ven that , my modest goal here is to review some of the evidence so that you do not regard interac tionism as a far-fetched i dea; and , if you already find it intuitively appealing, to provide some empirical grounding for this intuition. 4.2.1
C o ncept s are More t han Aggregates o f S e nse
D at a
It is through o u r sense organs , b y a process called perception , that we receive i nformation from the world . Given that , it may seem reasonable to assume that sense dat a accurately reflect the state of the world. Moreover, it might also suggest that concepts are really aggregates of sense data. That is, the concept 'tree' is merely a label for a class of visual stimuli . This view implies an atomistic approach to cognition, so that any concept can be analyzed i n terms o f its component sensory stimuli . Arguments refuting this atomistic view of cognition can be found as far back as Plato. In Th ea e t e tus, the doctrine 'cognition is perception' is elab orately refuted [ 1 84b-186e ] . It is argued that concepts such as ' sameness,' 'existence, ' and 'difference' are themselves not di rectly apprehended t h ro u g h our senses . That i s , you might see an object A and another object B and de clare that they have the same color. But the concept of ' same color as' is not something that you can sense. From our modern perspective, Plato's point is easily made by citing the p h eno m e n on of color blindness. If the concept ' s ame color as ' can be sensed , then we merely need to expose a c o l o r -b l i n d person to this sensation as a cure.
Towards t he end of the nineteenth cent u ry , Christian von Ehrcnfels , an Austrian psychologist , pointed out that the wholeness of a concept cannot
a wholeness to i t , namely the melody, that cannot s imply be e x pr essed as the sum of its parts, namely the individual notes appearing in the tune. We can shift the whole tune upward or downward on the musical scale, and yet it appears the same . In the process of shifting, howe v er , all the i n d i v i dual notes ( t h e ' p arts ' ) are ch anged . So what we reco g n i ze to be the same melody
always be expressed as the s u m of its p ar t s . When we hear a t u n e , there is
in the shifted t u n e
(its
' whole'
)
cannot be the same as the sum of i ts ' parts '
Part I: The Problem
96
( See Kohler [ 1 930] , p p . 1 64- 1 65 . ) B u t i t was t h e gestalt movement i n psychology t h at dealt a death-blow to t h e atomi s t ic view of cogn i t i on . ( See Koh ler [ 1 969] for an overview of gestalt psychology. ) The origi n of t h i s movement can be traced back to 1 9 1 2 , when Max Werthei mer, a German psychologi s t , did experiments on apparent mo tion . Werthei mer fou n d t h at when two dots are flashed near each other in quick su ccessi o n , t h e su bject viewing i t reports a movement of t h e dot from t h e fi rst posi t ion to t h e second. Lest this m ay be dismissed merely as an error of j u dgement on t h e subj ect 's part , Werthei mer d i d another set of experiments to demonstrate the ' real ' nat u re of t h i s percept u al experience. T here i s a phenomenon known as the negat i ve aftereffect of mot i o n . If a subject views a u n i form motion in a part of her visual field cont i nuously for some d u ration of t i me, i m med i ately fol lowed by viewing some stationary obj ect in the same part of t h e visual field , t hen t he stationary obj ect seems to be mov i ng in a d i rect ion opposite to t hat of t he previously v iewed u n i form motion . Werthei mer was able to demonstrate t h at the apparent motion exh i b i t s negati ve aftereffects j ust l i ke t he real motion . These experi ments clearly demonst rate t h at w h at we percei ve in a given s i t u at ion can be more t h an t h e sensory sti m u I i . This process o f local sensat ions com b i n i ng i nto a mean i ngful whole t h at is more t h an t heir sum is referred to as gro uping by the gestalt psychologists. Kohler did more experiments to show t hat ( 1 ) t he grouping p rocess i s not al ways learned, an d ( 2 ) the same grou p i n g process t h at creates a w hole out of t he parts, can also make a whole disappear u nder s u i t able con d i tions. His favori te exam ples demonst rat i ng bot h t hese points are shown in Figure 4. 1 . The figure i n 4 . l ( a ) contai n s t h e geometric form correspon d i n g to t h e n umeral 4, but su bj ects fai l to see it at al l . Clearly, the subject i s used to recogni z i n g t he n u me ral 4 i n i solation, but t h i s abi l i ty does n o t help i n recogn i z i ng i t in Figure 4 . l ( a ) . In fad , K o h l e r expli citly tes ted this hypothesi s i n another e x p e r i ment , where t he subject i s fi r s t repeatedl y presented with the figure of a hexagon [ F i g u r e 4 . 1 ( b )] . After that , when the su bject i s presented with Pig u r e 4 . 1 ( c ) , he completely fai l s to see that i t includes the hexagon [4. l ( b )J u n less he i n t e n t i ona l ly searches for i t . One m i ght still object i n t hes e exam ples t h at the fam i l i ar figure is presented in an u n u s u al and unfami l i ar set t i n g i n each case, w h i ch affects i t s recogn i z ab i l i ty. Kohler countered i t w i t h the exam ple of Figure 4 . 1 ( d ) where the numeral 4 is also p resented i n an u n u s u a l and unfam i l i ar set t i ng , and yet i t i s easily recogni zed . ( See Kohler [ 1 930] , p p . 1 49- 1 52. ) The original a pp a ren t motion experi ments of Wert heimer were e x p a n d e d
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(a)
(b)
(c)
(d)
FIGURE 4. 1 : Examples used by Kohler to demonstrate some characteristics of ' groupin g ' . Figure (a) contains the familiar figure ' 4 ' , but it is ' dissolved ' in the background. Figures (b) and (c) explicitly show that p ast experiences do not affect this dissolution. Even after the subject is conditioned by showing figure (b) repeatedly, she fails to rec o gnize its occurrence in (c), unless she is explicitly seeking it. Figure (d) shows that the dissolution is not always due to the unfamiliar background. The figure '4' is again presented in
a ' strange' setting, yet it is easily recognized. (From Kohler [ 1 930] .)
Part I: The Problem
98
more recen tly by Kolers [ 1 972] to reveal the complex ways i n w h i ch our v isual apparat us adds to what i s i n front of the eye. He fou n d , for i n st ance, t hat w hen a circle and a square were fl ashed near each other in q u i ck succession i n a subj ect 's visual fiel d , the subj ect n o t only reported a movement from the fi rst position to the second, but also a smoot h t ransformation of the c ircle i nto the square during the movemen t . If the two figures were of d i fferent sizes , t hen t he subject reported t h at the first figure grew or s h r u n k smoothly as i t moved t o t h e second posit ion . If a barrier ( i n t h e for m o f a l i ne ) was i mposed between the posi t i on s of the first and the second fl ashes , t hen the figure moved from t he pos i t i on of t he first flash to the barrier, t hen moved forward ( i n the t h i rd d i mension ) to cross the barrier, back to the same p l ane, and t hen moved to the posit ion of the secon d flas h , w i t h all percei ved m ovement being smooth and conti nuous. When t he flashes consisted of groups of figures, i nstead of si ngle figures, even more i nteres t i n g phenomena were observed . Some examples of the pairs of figures used by Kolers in this st udy are shown in Figure 4 . 2 . I n each case, the grou p of figu res i n 4 . 2 ( a ) was flashed first , followed by the group of figures in 4 . 2 ( b ) . In the fi rst exam ple, when the group of figures shown in 4 . 2 [i ] ( a ) was flashed fol lowed b y t h e group o f figures i n 4 . 2 [i ] ( b ) , t h e t h ree right figures in ( a ) moved as one u n i t , w h i le the left most ci rcle i n ( a ) moved around to become t h e right most circle in ( b ) . If a dot was flashed followed by fou r dots in fou r d i fferent d i rect ions ( 4 . 2 [i i ] ) , the subj ect saw the center dot 'explode' and move in fou r outward d i rect ions simultaneously. A remarkable t h i ng was t hat u nder no ci rcu mstances d i d Kolers find t h at the apparent motion paths of d i fferent figures cross. For i nstance, when the group of figures i n 4 . 2 [i i i ] ( a ) was flashed fol lowed b y the group of figures i n 4 . 2 [ i i i ] ( b ) , t hen t h e t o p ci rcle in ( a ) moved to the right to become the top square in ( b ) , and the bot tom s q u are in ( a ) moved to become the bottom circle in ( b ) . Kolers' experi ments w i t h colored figures yielded t h e most surpris i ng re sults . When a red dot was fl ashed fol l owed by a green one, the subject saw a c o n t i n u o u s m ot i on al l right . B u t as far as t h e color of the dot was c o n c ern e d t h e s u b j e c t reported t h at the dot stayed red t i l l about h al fway, and t hen i t abruptly changed to green. K o l e rs and Green 's [ 1 984] later experiments with color pai rs , in w h i ch a pair of red-green dots was flashed followed by a p ai r of green- red dots ( Fi gu re 4 . 2 [i v] ) , noted that the subject saw a l i near movement of the i n i t i al pai r of dots to the posit ion of the second pai r , w i t h the colors of the dots abrupt ly changi ng from red-green to gree n r ed about halfway. ,
-
A l l t h i s evidence clearly poi nts to the fact t h at our perceptual and cog n i t i ve a p pa rat u s is not a passi ve receptor of sensory s t i m u l i , but ass er t s a
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[ii ]
[iii]
[iv]
OD O D
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(b)
D O DO 0 0 0 0
0
D
D
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® ©
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FIGURE 4 . 2 : Kolers' example s that u se apparent motion t o demon strate the complexity of the visual sy stem. In each of the examples, the group of figures in (a) is flashed on the screen in front of the subj ect, followed by the group of fi gures in (b) . The subject does not ' see ' two succesive flashes, but a smooth and continuous motion. In (i) the three right figures in (a) move to the right as one unit, while the leftmost circle moves around to become the righ tmo st circle in (b). In (ii) th e circle in (a) 'explodes' in four circles, whi c h move outwards s imu ltan eou sly to become figure (b). In (iii) the circle and the square in (a) move smoothly to the right (without crossing paths) while transformin� 1 n to the square and the circle, respectively, to become figure (b) . In (iv) the red- green p air of dots in (a) move smoothly to position (b) , while the dots abruptly change colors to green-red about halfway. (From Kolers [ 1 972] and Kolers & Green [ 1 984] .)
1 00
Part I: The Problem
form at i ve s p i r i t i n shap i n g the sense dat a t h rough its concepts. Someti mes it makes us see some even t even when the sensory s t i m u l i correspon d i n g to t hat event are not t here. A n d , at other t i mes , it m akes an object disap pear even t hough we are d i rectly receiving sense data from t h at object . In e i t her case, w h at we see in the m i nd's eye i s not what i s in front of the eye. 4.2.2
C o nc e p t s can O rganize t he Wo rld D iffe r e nt ly
The second hypothesis concern i n g i nteract ionism is t h at it is possi ble to organi ze the same environment , the same sense data., i n d i fferent conceptual ways. ( Note t h at bot h t h i s hypot hesis and i t s negation are consistent w i t h the view t h at concepts are more t h a n sense i m p ression s . ) I p resent two studies here, each of w h i ch corroborate the hypothesis i n a d i fferent way. O n e source of su pport i n g evi dence is provided by t h e semi n a.! work of Benj am i n Lee Whorf, whom T h ave already i n t roduced in the l as t chapter. In fact , his study c i ted i n the l ast chapter i s relevant to t h i s section as wel l , for i t showed how d i fferent c u l t u res can conceptual i ze t h e worl d d i fferentl y s o t hat their s i m i l arity metrics are d i fferent. I n anot her st udy, W horf [ 1 950] showed t h at even w h at we consider as t he most fu n damental concepts can be d i fferent i n d i fferent c u l t u res and can lead to rad i cal l y d i fferent world views . For i nstance, we o r g an i z e the world i n terms of space and time. We refer to spat ial d i mension s as ' here, ' ' t h ere, ' ' ah ead , ' ' b e h i n d , ' 'above, ' ' below , ' a n d s o on . We a l so h av� t h e t h ree tenses t o refer t o t h e temporal d i men sion. I n t h e Hopi l anguage , however, t here i s no concept of t i me. I nstead , Hopi people d i v i de their world i nto two grand concept s : ' mani fested ' and ' u n m ani fe s t . ' T h e ' m an i fested ' category corresponds to w h atever i s or was accessible to the sen ses . The m o unt a i n I am looki ng at now , and my r ec ol lect i o n of t h e snowstorm I saw yesterday woul d both fit i n !. h i s cal.egory. The 'unmanifest ' c a t e go r y i n c l u des e v e r y t h i n g that is not m an i fest . Thus, any t h i n g t h at h as not yet happened ( my p l an s for wh a t. I w i l l do tomor row ) , plus every t h i n g t h at i s i m agi ned ( w h a t. my daughter might be doing w hen I am a.t wor k ) wou l d fal l i n t o t h i s category. I n spite of t h i s d i fferent con ce p tual organ ization , Whorf argued : " [T] he Hopi language i s c a p a b l e of account i ng for and descri b i ng correct ly, in a pragmat i c or operat ional sense, all observable phenomena of the u n i verse . " [ Whorf 1 950, p . 58.] A not her study by a psychologist A lexander Romanovi ch Luria supports d i fferent way t h e h y p o t h e s i s t h at there m igh t be al ternate ways of orga n i z i ng sense d a t a . Notice t hat t h e experi ments of ges t a l t ps y ch o l o gy, as wel l as m any other phenomena of visual i l l u s i o n t h at h ave been i nves t i gated since
in
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t hen , suggest that we d o not al ways 'see' w h at i s i n front o f the eye, b u t fab ricate the objects of perception an d cogn i t ion , at least part ial ly. G i ven that , one wonders i f people w i t h different cul t u r a l backgrounds fabri cate d i ffer ently. For if so, t hen t h i s wou l d agai n suggest t h at one can concep t u al i ze t he same sense data, same wor l d , i n al tern ate ways. T h i s i s exactly what Luria. demonstrated by studyi ng the effects of c u l t u ral backgro u n d on i nd i v i d u al perception and cogn i t ion i n Uzbekistan , the heart of w h at was Soviet U n ion then . ( See Luri a. [ 1 976] . Tho u gh t h i s st u dy was carried out i n 1 93 1 -32 , it was only p u b l i shed in 1 9 76. )
Most of L u r i a's experi mental subjects l i ved i n remote v i l l ages of Uz b ek istan. At the t i me t he study was cond u c t e d , L u ria. notes, " [T] hes e reg i ons of the Soviet U nion were u ndergoing es p eci ally p ro fou n d socioeconom i c and c u l t u ral c hanges . The period we observed i n c l uded the begi n n i ngs of col l ec t i v i zation and other rad i cal socioeconom ic changes as wel l as the eman c ipation of women . Because the period stud ied was one of t ransi tion , we were able to make our study to some exte n t comparati ve. Thus we co u l d observe b o t h u nderdevel oped i l l i terate groups ( l i v i n g i n v i l l ages ) and groups already i nvolved in modern l i fe, ex p erie n c i n g t h e fi rs t i n fl u e n ces of t h e so c i al realign ment . " [ L ur i a. 1 9 76, p. 1 4 ] . There were fi ve groups of subjects: " ( 1 ) lchkari women l i v i n g in remote v i l l ages who were i l l i terate and n ot in volved in any modern soci al acti v i t ies. ( 2 ) Peasants in remote v i l l ages , who cont i nued to mai ntai n an i n d i vidualistic economy, to rem ai n i l l i terate, and to i nvol ve t hemsel ves in n o way w i t h social i zed l abor. ( 3 ) Women who attended short - term courses in the teach ing of k i n dergart ners. As a rule, they s t i l l h ad no form a l educat ion and al most no l i teracy trai n i ng. ( 4 ) A c t i ve ' co llecti ve farm ' workers a n d you ng p eo p l e who h ave t aken short courses . ( 5 ) Wome n s t udents a dm i t t e d to a. t eachers' s c h ool after two or t h ree years of study. Their e d u c at i o n al q u a l i fi c a.t i o n s , h o wev e r , were s t i l l fai r l y l ow . " [ L u r i a 1 976, p . 1 5] . W i t h t h ese groups of s u b j e c t s , L u r i a. ch arted t h e i r p e r forman ce for a w ho l e range of p e r c e p t u a l il.n d cogn i t i ve p rocesses , such as color perception , visual i l l u sion , abstract ion , deduct ion , and s o o n . 1 re v i e w o n l y t wo sets of experiments here. The fi r s t set of experi ments concerned t h e perce p t i o n o f color hues . The subjects were p resented w i t h 27 d i ffe r e nt h ues in t h e form of skeins of wool , and were t hen asked to n ame the colors. The res u l t s were i n teresting because 5 9 . 5 % of t he Ichkari w o m e n came u p with object-category n ame s- t h at i s , n a m es t hat referred to the color b y u s i n g a c o n c ret e obj ect o f t h at color ( s u c h as i r i s , l iver, s p o i led cot t o n , e t c . ) rat her t h an s o m e a b s t rac t c o l o r name ( s uch as b l u e , green , e t c . ) - a s op posed to o n l y 1 6 . 3 % of th<' women at teachers ' school . Even more i n t e r e s t i n g was the case w h e n t h e subjects were asked t o
1 02
Part I: The Problem
group the colors accordi n g to whatever colors t hey t hought were ' s i m i l ar . ' Whereas t h e l ast fou r groups gave what m i ght b e consi dered more o r less ' normal ' response, Ichkari women , who rou t i nely engaged in embroidery, and w ho chose objects to name hues, " [ P ] resented u s with an enti rely different system . As a rule, the i n s t ruction to d i vide t he colors into groups created complete con fusion and called forth responses such as , ' I t can ' t be done , ' ' None of them are the same, you can 't put them toget her , ' ' T hey're not at al l al i ke , ' or 'This i s l i ke cal f 's-dung, and this i s l i ke peach . ' The women usual ly began by putting d i fferent skei ns together, t hen attempted to explai n their color groups but shook t hei r heads i n perplexi ty an d fai led t o complete t he t ask . " [Luria 1 9 76, p . 2 7 . ] I n the forced classi fi cation p a r t of the experimen t , 70% of t he Ichkari women refused . A l l t h i s led Luria to con clude, " [T] he p rocess by w h i ch [ Ichka.ri women] grou p and c l assify colors differs markedly from t h at of assigning t hem to distinct categories as descri bed in t he standard l iteratu re on the psychology of color perception and encod i ng ." [p. 30]. The second set of Luria's experiments concerned the perception of optical i l l usions. He tested the suscept i b i l i ty of the subj ects i n each of the fi ve groups to certai n optical i l l usions. Two of the i l lusions used i n Luria's study are shown i n Figure 4. 3 , and Table 4. 1 shows the percentage of subj ects from each of t he fi ve groups who percei ved t hese opti cal i l l usions. One can see fro m the t a b l e that there i s a. strong correlation between the social background o f the subjects a n d thei r abi l i ty to percei ve optical i ll usions: significantly fewer Ichka.ri women and peasants were able to see the i l l usions t h an collective-farm a.cti vists and women at teachers ' schoo l . W h i l e a.ck nowledging the somewhat tentat i ve status of t hese fi nd i ngs ,
si nce such experi ments can not be easily rep l i cated , L u r i a nevertheless argued t h at it "clearly shows t h at o p t i c a l i l l u s i o n s are l i n ked to com p l ex psychologi c al processes that vary i n a.ccorda.nce w i t h socio- h istori cal development" and
"percept ual processes h i t herto regarded as p u rely phy s i ological (and t h u s u n i versal ) are i n fl uenced b y socioh i storic development . " [ L u r i a 1 976, p p . 4345] . It m ay be of i nterest to note here t h at Kolers , in his st udy of apparent motion, also fou n d t h at some su bjects were u n able to see appare n t motion at all . W h i l e h e did not system atically i nvestigate any correla t i on between t h e c u l t u ral backgro u n d of the s u b je c ts and t hei r i nabil i ty to see appare n t m otion, he , nevertheless, noted that most of t hose who were unable to see apparent mot i o n were engi neers and physicians [Kolers 1 9 7 2 , p . 1 60] . ( See
Chapt er
4:
Cognition as In t eract ion
1 03
(a)
T
(b)
U
v
FIGURE 4 . 3 : Optical illusions used in the study by Luria. I n figure (a) the circles marked X and Y are of equal size, but X seems bigger than Y. In figure (b) , the angles marked R S and T U are of equal size, but the angle RS appears bigger. (From Luria [197 6] .)
No. of S u bj ects
Group
Ichkari women
9
Peasant s
Fig.
Fig. 4 . 3 ( b )
O p t i cal I l l u s i o n
4.3(a)
33.3%
25
20 . 8 %
25.0%
25
64 .0%
36 0%
40
85.0%
7 7 . 5%
38
92. 1 %
7 1 . 0%
11.1%
Women i n
preschool courses
Collective-farm act i v i s t s
Women at
teachers ' school Tab le
4. 1 :
Perce p t i on of
O p t i c a l I l l usions by Luria's S u b j ec t s . Percen t age
fi g ures show t he n u m ber of subj ects in each
sponding o p t i c a l
group who
i l l usion . ( From Tabl e 6, p. 4 4 ,
in Luria.
percei ved t h e
[ 1 976] . )
corre
Part I: The Problem
1 04
also Segal l , Campbell & Herskov i ts [ 1 966] ; and Deregowski [ 1 980] for more studi es of the effect of c u l t u ral backgrou n d on visual percepti on . ) T h u s , we see t h at w h i l e concepts can go beyond what i s g i ven t o t h e senses i n organ i z i ng the worl d , they do s o i n d ifferent ways, s o t h at d i fferent people can see the world in d i fferent ways. 4.2.3
C o nc e p t s C annot O rgani z e t he World A r b it rarily
A d m i t t i n g t h at concepts can organ i ze the worl d d i fferently for d i fferent peo p l e , the next i ssue t h at natu ral l y suggests i tself is whether t h i s organ i zat ion i s const rai ned i n any way. Can concepts organi ze reali ty i n any arbi t rary way? The answer, a vehement "No! ," m ight seem obvious to most peopl e . S t i l l , i t wou l d b e u sefu l t o consi der some empirical facts su pport i n g t h i s con c lusion . A nyone who h as worked on a project i nvol v i n g assembly of physical components-b u il d i ng a model gl i der or a book-shelf; sew i ng a shirt ; k n i t t i ng a sweater; or even hangi ng a p i c t u re on the wal l-knows t h at i t i s all too easy to m ake m i s t akes . W h at ch aracteri zes a ' m i st ake' is the fact t h at car ryi n g out cert ai n operat ions t h at one t hought woul d lead to a certai n state of affairs, results in a d i fferent state altoget her. The g l i der does not fly. The p i ct u re fal l s dow n . A n d so on . Somet i mes we can look back and reali ze what we did wrong . But at other t i mes, we go over the i nstructions carefu l ly agai n and agai n , b u t cannot find any p l ace we m i ght have made a m i s t ake. A n d , yet , t h e g l i der does n o t fly. T h i s feel i n g i s q u i t e com mon when t r y i n g one's fi rst p roject i n vo l v i n g a new sk i l l . Reali ty does not care whether one fol l owed t he i ns t r u c t ions carefu l ly or n o t .
Or, consi der the s i t ua t i on w h ere you are lost i n an u n fam i l i ar tow n . I f c on c e p t u a l organ i zation i s as good as any o t h e r t h e n you ought to be , a bl e to get t o w here y o u w a n t to be by go i n g in any d i rect io n , or even by n o t goi n g anywhere at al l . I f you r concept s can organ ize the world i n any way, why can you not o r g a n i ze them so t h at far away p l aces come closer at w i l l , w i t h only the effort of reconceptualizat ion r e q u i r e d . The poi n t here i s very si mple: cert ai n actions l ead to the desi red state of affa i rs and m any others do not , in spite of our best efforts and intent ions . any
The prehi story of flight prov i d e s another rich source of e x a m pl e s w here reali ty refu s e d to accept m any conceptual org a n i z at i on s imposed on i t , wi t h a fe w com i c but most ly t r agi c consequences . In h i s t horough s t u d y, H art [ 1 985] provi des a detai led look at t he conce pt u a l and t h eor e t i cal backgrou n d
Chap t er
4:
Cogn i tion a.s In teraction
1 05
of t he h u m an attempts at m an ned fl i gh t , covering a period u p to the end of the eighteen t h century. He notes t hat the designs of the pre- fl ight flying m a chines were far from arbitrary. Rather they took into account metaphysi cal , theological , and cosmologi cal arguments about t h e nature of ai r, empi ri cal observations of the flight of birds, and various other logical and rat ional points of views. Yet , none of t hese at tempts resulted i n a su ccessful flight . For i n stance, i n 1 772, A b be P ierre Desforges of Fran ce designed an el aborate contraption and j um ped from the top of Tou r G u i nette in Etampes. H i s design was q u i t e sophisti cated a n d took i n t o account em pi rical observations of the flight of swallows. Desforges made provisions for h i s m ach ine to be able to carry a 1 50 l b p i l ot and an add i t i onal l uggage of 1 5 lb. H e est i m ated , based on comparisons w i t h the fl ight of swal lows and w i t h rowing a boat , t h at h i s m ach i n e would be able to cover 30 leagues an hour i n favorable w i n d . In spite of the elaborate design and const ruction , attention to the det ai l s , n u merous cal c u l ations and empirical facts t h at were taken i nto ac coun t , Desforges ' contraption fel l to the grou n d from the l 00 ft tower. It was m i raculous t h at Desforges escaped from t he fall w i t h o n ly a bruised elbow . ( See H art [ 1 985] , p p . 1 59- 1 63 . ) Thus, we see t hat real i ty i s not a passive receptor of our con ceptual organ i zations, but ferociously asserts i tself. It does not care whether we are fol low i ng a certai n set of i n st ructions to t he tee, or t h at we h ave spent years of i n tellectu al , emotional and physical energy in form u l ating some el aborate t heory or constructing a soph i s t i cated m ach ine. It does not even care how rat i onal , logical , or coherent with empiri cal observat ions are our t heories. The t heory and t he dreams of flying are easily shattered by the d i spassionate and u ncari n g reali ty as the sophisti cated flying m ach i n e p l u m mets to t h e grou n d l i ke a dead b i r d . Real i ty deci des i n i t s ow n mysterious way whet her to accept or r ej e ct our concep t ual organ i zation . 4_2.4
' U niversals ' and t he P hysiological B as is of Cognition
The fact that re al i ty i m p oses i t s own co nst rai n t s on o n e ' s concep t u al or gani zation suggests an i ntriguing hypothesis: Cou l d it be t hat all d i fferent conceptual organizations h ave a c o m m on den om i n at o r ? I n d eed , t h i s hy pothesis has been purs ued vigorously by many scholars, who sought to fi n d the common denom i n ator u n derly ing all c o n c e p t u a l orga1 1 i z a t i o n s . As t h i s hypothesis contradicts t h e i n terac t ion v i e w o f cogn i t ion-i f t h e common de n om i n n.tor ex i s t s , o n e cannot s ay t h at it i s crea t ed-i t is i m portant to review
1 06
Part I: The Problem
the empirical evi dence support ing i t . B roadly speak ing, t here are two verstons o f t he common denomi n ator hypothesis t h at h ave been i n vestigated . In one version , the obj ec t i ve is to demonstrate t h at reality h as a m i n d - i n dependent ontology and structure, and all concept u al organizations can be redu ced to i t . The origin of t h i s ' reductionist' approach to the world c a n be t raced back to Descartes ' i dea t h at the world is a machine t hat operates accordi n g to a certain fi xed set of laws�an i dea t h at recei ved a strong i m petus from Newtonian mechan i cs . However , w i t h t h e advent of quantum mechanics, i t h as lost some of i t s appeal i n t h i s centu ry. Though most physical scientists s t i l l work u n der t he assumption t h at t here are laws out there i n the wor l d , and i t i s the objecti ve of science to disco ver what t hey are, several scholars h ave put forth strong and con v i n c i ng arguments to show t h at the laws and t he t heories of p hysical sciences are not as m i n d - i ndependent as it m ay seem , but are partly creations of t he scient i fi c com m u n i ty. ( See Gerhart & R ussell [ 1 984] , Jones [ 1 982] , and Tur b ayne [ 1 962] . ) The second version of t he common denomi n ator hypot hesi s argues t h at a l l conceptual organizations share some i n variant structures, w h i ch are often referred to as ' u n i versals . ' It i s preci sely for t h i s reason t h at ant h ropologists, l i nguists and psychologi sts h ave repeatedly sought to demonstrate the exis tence of u n i versals across different languages and cultures . Then , i n recent years , a new twist h as been added to this version of the common denomi nator hypothesis. It i s argued that u n iversals , ass u m i ng t h at t hey exist , are rooted in the physiological structur e of the cog n i t i ve agent 's body and brai n . This hypothesis i s bolstered b y t h e phenomenal leap t h at our k nowledge of neurophysiology has t aken in t h i s century. I t h as been demonstrated t h at i n animals w i t h sim ple brai n structures , such as horseshoe crabs and frogs, t he processi ng of sensory i nformation starts ri ght at the receptors , and t h at t h i s p rocessing i s goal-oriented . ( See Hartli ne [ 1 967] ; and Let t v i n e l a l . [ 1 959] . ) For i ns t ance, certai n cells i n the frog's ret i n a are spec i al i zed to detect bugs, w h i l e cer t a i n ot hers are speciali zed to detect p redators .
T hu s , at least for
frogs , their uni versals of ' b ugs ' an d ' p redators , ' if we may call t hem u n i
versals, can be seen to a r i s e from t h e i r neurophysiology. The goal-oriented nature of perception h as even been demonstrated for animal s w i t h more com plex brains [ R u bel 1 988] . For i n stance, the v isual system of cats , monkeys an d h u m an s has evol ved so that it looks for s t r aig h t edges .
In sp i t e of all t h i s , t h e attempts to demons trate the existence of uni versals for ani m al s w i t h c o m p l e x brai n s , such as us h u m an s , and p rov ide a neurophysiological basis for t h e m , has not yet been fruitfu l . I demonst rate
Chapt er
4:
Cognition as In teraction
107
t h i s point i n t h i s sect ion b y consi dering t h e u n i versals for color terms , which h ave been i ntensi vely i n vestigated . In 1 969, Berli n and K ay published a study demonstrat i ng the exi stence of u n i versals i n naming color categories . T hey stud ied 20 l anguages experimen t al ly, and consi dered the existing relevant l i terat u re on 78 other languages , to show , " F i rst , t here exist u n i versal ly for hu mans eleven basic percept u al color categories , w h i ch serve as the psychophysi cal referents of the eleven or fewer b asic color terms i n any language. Second, i n the h istory of a gi ven language, encoding of perceptual categories i nto b asic color terms fol lows a fi xed part i al order. The two possi ble tem poral orders are: white b l ac k·
w hite b l ac k ·
]
-->
red --> green
-->
yel low
--> b l ue -->
brow n
] --> red --> yellow --> green --> blue --> brown
-->
-->
[ [
purple pink orange grey
purple pi n k orange g rey
T h i r d , the overal l temporal order is properly consi dered an evo l u tionary one; color lexi cons w i t h few terms tend to occur in as sociation with rel at i vely sim ple cultures and s i m p l e technologies, w h i l e color lexi cons w i t h many terms tend to o c c u r i n association with complex c u l t u r e s and com plex te c h n o l og i es ( to the extent t h at com p l e x i ty of c u l t u re a n d techn ology can be assessed ob j ec t i ve l y ) " [Ber l i n & K ay 1 969, p. 1 04] A com p rehens i ve effort to prov i de a neurophysiological b as i s for Berl i n and K ay's color uni versals has been made by F loyd Rat l i ff [ 1 976] . R at l i ff started by r e v i e wing t h e ex i s t i n g research o n the neurophy s i o l ogy o f color v i sion , w h i ch recon ci les t h e oppos i t i o n of t h e You n g- Hel m ho l t z t h eor y of t ri c h ro
m at i c addi t i ve color and t h e Heri ng t heory of tet rachromat i c opponent c o l ors .
A ccord i ng to t h e You ng - Hel m h o l t z t h eo ry,
a.l l
r i ved from s u i table com b i n at i o n s of t h ree ' pr i m ar y '
blue. This t h e o r y
i s s u p p o r t ed by t h e
fact t h a t
s e n s at i o n s a.re de colors : red , green , and
color
i n o u r ret i n a , t h ere are t h ree
10
Pa. rt
I: The Problem
kinds of cones ( t he cell s pri m arily responsi ble for color vision ) t hat are most sensi t i ve to the wavelengt hs corresponding to the colors red , green , and blue, respecti vely. The Hering theory, seemi ngly on t he cont rary, suggests t h at al l color sensat ion results from comb i n ations of t wo antagon i s t i c pairs of colors: red-green and yellow- blue. This t heory is supported by the fact t h at t here are fou r psychological ly basic colors-red , green, yellow, and b l ue-and , fur t her, sensat ions of red and green suppress each other, and so do the sensations of yellow and b l ue. Thus, for i n st ance, we can h ave a color sensat ion of reddish yellow ( orange ) , or reddish blue ( purple ) , or green ish yel low ( chartreuse ) , or green ish blue ( t urquoise ) , but not of reddish green or yellowish blue. I n reconc i l i ng t hese t wo theories , Rat l i ff brought i n the studies of De Val ois and h i s colleagues on the visual system of t he macaque monkey, w h i ch happens to be very si m i lar to t h at of humans. ( See De Valoi s , A b ramov , & J acobs [ 1 966] ; and De Valois & J acobs [ 1 968] . ) De Valois e t a l. mon i tored the response o f single cel ls lead i ng from the lateral gen iculate n u c leus to the visual cortex of the mon key. They fou nd t he p resence of fou r types of spect ral ly opponent neu ron s . These spect rally opponent neurons are exci ted by light from one part of the spectrum and i n h i b i ted by l ight from anot her part of the spect ru m . The fou r types of neurons are: red-excit atory and green - i n h i b i tory, green -excitatory and r e d - i n h i b i t ory, yel low-exc i t atory and b l u e- i n h i b i tory, and bl ue-exci t atory and yellow- i n h i b i tory. The p resence of t hese fou r types of neurons clearly provi des a neurophysiological fou ndation to the Hering tet rachromatic opponent color t h eo ry. Moreover , Rat l i ff bri ngs i n A bramov and Levi ne's model to explai n how the t h ree k i nds of cones i n t h e ret i n a m ight b e connected to t h e cel l s i n t he l ateral gen i c u l ate nucleus so as to prod uce a response concurring with De Valois e t al. 's observat ions. Thus, the two t heories are "no longer r eg a r d e d as c on t ra d i c to r y, but as com p lement ary . Each refers princi pally to a d i fferent level of the v i sual system . " [ Rat l i ff 1 9 76 , p . 3 1 7] .
Tak i n g all these fi n d i ngs i nto ac co u nt , Rat l i ff t hen went o n t o provide grou n d s-i n terms of neurophysiologi cal , psychophysical , and psychological evi dence-for the partial order of the color terms found i n Berli n an d K ay ' s studies. For i nstance, the grounds offered for the l ater posi tion of blue ( com pared to red , green and yel low ) in the order of development are: the weak and narrow sens i t i v i ty of t he p i gm e n t in t h e ' b l u e ' cones ( c o m p ared to ' red ' and ' gr ee n ' c o n es ) ; the fact that according to Abramov and Levi ne's model the response of ' blue' cones from the ret i n a does not interact w i t h t h at of the other cones u n t i l relat i vely late i n the i ntegrat ive process; the fact that t he center of the fovea ( t h e central part of ret i n a ) i s b l ue- b l i n d ; an d the fact that th e lens and the macular pigment in the eye absorb b l u e l i gh t . S i m i l arly, the
Chap t er
4:
Cogni tion
as
In t eraction
1 09
reasons suggested for t he early appearance of ' red ' in Berl i n & K ay's partial order are: t he pigment in the ' red ' cones i s the most sen s i t i ve of the three; the response of ' red ' cones from the ret i n a is i n corporated early on in t he i ntegrat i ve process t h at p rod u ces opponent response and , moreover , t hese are the only type of cones that m ake a contribut ion to each and every one of the fou r types of opponent response cel ls; the center of the fovea is most sen s i t i ve to red ; the chromat i c aberrat ion caused by absorption by lens and macular p igment i n the eye favors the red ; etc. A l l the argu ments advan ced by Rat l i ff to explai n t he part i al order of B er l i n and K ay ' s color u n i versals constit ute what m ight be considered a very weak case of circum stantial evi dence. I shou ld emp hasize here that the issue at stake i s not the color pe1·ception, b u t the n a m es fo r· colo rs . You m ay recal l Luria's study here w h i ch showed t hat I c h kari wom en on no acco u n t showed any deficiency of color perception. On the cont rary, they refused to group d i fferent h ues u n der one l abel , arguing t h at each of t hem i s a d i fferent color altoget her. Rat l i ff h i m self mentions the study by H eider an d O l i vier [ 1 972] t h at demonst rated t hat Dani speakers , who h ave only two color terms i n t heir language m ala for ' w h i te-war m ' hues an d m ili for ' dark-cool' hues, are ful l y capable of distinguishing different hues, even though t h e y are gi ven the same name. The i ssue at stake i s the emergence of l i n g u i s t i c categories t h at group various h ues toget her. A n d i t i s in this regard t hat R at l i ff ' s arguments fall short . For i nstance, given a l l t h e fac t s suggesting dom i n an c e of red over blue, if one were to u se them to show that our perception of the color red i s b etter than t h a t of b l u e , or t h at w e are capab l e of m a k i n g fi n e r disti n ctions of hue in the red region of t he spectrum t han i n t he blue reg ion t hen t here wou l d b e a reason a.bl e argu ment su b j e ct to em p i r i ca l con fi r m ation . B u t to argue from t hose facts that a cult ure wou l d deve l o p the t e r m for red before the term for b l ue const i t utes a long leap fro m ne u r o p hy s i o l og i c a l structures to l i nguistic st r u c t u re s w i t ho u t any sati sfactory acco u n t of the p rocesses or ,
s t r u c t u res t h at medi ate t h i s t r an s i t i on .
to fi l l the gap between n e u rophysi ological s t r u c t u res and struct u res for the color terms was m ade by K ay and M c D a n i el [ 1 978] . Starting from De Va lo i s e t al. 's fou r types of opponent response cel ls, An
at t e m p t
l i ngui st i c
a n d h i s co l l e agu e s
an d posi t i n g t h at t h e t w o other types of non-opponent s t u d i e d by De Va l o i s
e n co de
response cel l s
the l u m i n os i ty
-
also
i n fo r m a t i o n ,
t he responses of all these cel ls can be combi ned by using fuzzy set - theore t i c operat i on s of un ion and i n t e rsec t i o n to p ro d u c e various other color terms. For i n s t a n ce, t h e t e r m -rm:Ji i n D an i for d a r k -cool
t h ey went on to s h ow how
-
Part I: The Problem
l lO
h ues can be represented as ' b l ack OR green OR blue,' where by OR we mean the fuzzy set-un ion operat ion. S i m i l ar ly, the color orange is represented as ' red + yellow , ' where + i s a slightly modified version of fuzzy set- i ntersection operat ion. Thus, the fuzzy set - u n ion and fuzzy set - intersection operations are seen to mediate the transition from neurophysiological structures to linguistic ones . These operat ions themselves , however, are not grounded i n the neuro physiological structure of the brai n , at least in as far as we know. Thus, the question still remai n s : Why, when fi fty-seven composite categories can be formed by applying the fuzzy set- u nion operation to two or more of the six fu n d amental neural response categories ( black , white, red , green, yellow, and b l ue ) , do only three of them exist as u n i versals? Even i f we rule out t hose composi tes t h at i nclude both ca.tegories of an opponent pair-that i s , we do not want to consi der those composi tes t h at i n clude both black and white, or both red and green-t here are still twenty possi ble composites. Why are only th ree of t hem u n i versal ? Why is ' red OR blue' not a color u n i versal? U n l ess t hese questions can be sati sfactorily answered , the u n i versals for color terms must remain essen t i a l l y an emp i r ical finding. G i ven that, i t i s perhaps n o t surprising that l ater research h as cast doubts o n Berl i n and K ay's hypothes i s . MacLau ry [ 1 987] ci tes t he case of the ' yellow- w i t h-gree n ' category i n S huswap t hat i s n o t i ncl uded i n Berli n a n d K ay ' s sequence o f color u n i versal s . M o s s [ 1 989] uses the case of p u r p l e i n Russ i an to argue agai nst t he Berl i n - K ay hypothes i s . To sum u p t he d iscussion o f t h i s sect ion , t here are t w o key poi nts. The first rat her obvious point i s t h at the structure of our brai ns and bodies does affect cogn i t ion , for t he processes of perception and cogni tion t ake place i n th e brai n . The second point i s that t hough one coul d argue, i n principle, t hat physi ological structures m i ght be a source of u n i ve r s a l s , the evi dence for t h i s can only be seen in a n i m a l s w i t h a r e l a t i ve l y s i m p l e nervous s y stem . T h e s t ru c t u re of t h e h u m an b r a i n is m u c h too complex, and our know ledge of i t i s much too fragment ary, to t ry to look for a di rect connection be tween u n i versals, i f t hei r existence can be demonst rated c o n v i n c i n gl y, and the physiologi cal organ i zat ion of the brai n . Wife
Both t hese points are perhaps best demonstrated i n a series o f touchi ng t a le s of h i s pat i e n t s by D r . O l i ver S acks i n Th e Ma n Who Mistook His
for
aberrat ion , b u t what i s more i n t e re st i ng is the variety of ways i n w h ich the rest of t he brai n compensates for t hese ab errat ions w h i l e preservi n g the i d e n t i ty of t h e person as a whole. This, if noth ing else, definitely p o i n t s away a Ha t .
Physical dam age t o t h e brai n d oes i n deed res u l t i n cogn i t i ve
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1 11
from a s i mple- m i n ded i dentificat ion of cogni t i ve struct u res w i t h physiological struct u res . 4.2.5
S u m mary
The research reviewed in t h i s section clearly shows t h at the world we see i n o u r m i nd ' s eye i s a worl d that i s not 'given' b u t i s constructed by o u r cogn i t i ve apparatu s . Yet , t h i s construct ion i s not arbi t rary but i s const rai ned by real i ty. One m i ght say that the concep tual organ ization of the world is brought about by an i nteraction between the cogn i t i ve agent and the envi ronmen t , a process i n w h i ch each parti c ipant is act i vely i nvol ved . The problem i s i n explai n i ng the role of the envi ron ment i n t h i s i nterac tion . If we assume t h at it h as a p reconceptual ( m i n d - i n dependent ) ontology and structure, then we need to show how ( an d why ) d i fferent conceptual organizations are created from it. If we assume that i t does not have a pre concep tual ontology and struct u re, then we need to show how it can rej ect arbi trary concep t u al organ i zat ions. So the problem remai n s . I now exam i ne three d i fferent approaches to cogni ti o n t h at are i nteractionist in spi ri t , and analyze h ow far t h i s problem is addressed in e a ch of t hem .
4.3
From Kant to Goodman : Worldmaking
Nelson Goodman put forth a comprehens i ve framework of cogn i t i on in h i s beautifully written books Languages of A 1'l [ 1 9 76) a n d Wa ys of World making [1 978) . That he is a vehement supporter of t he i nteraction view i s rather o b v i o u s l y reflected i n the t i l les o f h i s wor k s : ' R eal i ty R e m ad e , ' ' T h e Fabrication o f Fac t s , ' an d , o f course, ' Ways o f Worl d m ak i n g ' S i n ce Good man's fr a m e wo r k i s the cul m i n at i on of a t h e m e t h at was s t ar t e d by K ant and n u r t u red by Cassirer, it wou l d be u sefu l to take a b r i ef look at K ant 's and Cassirer ' s approaches to interac t i o n i s m b e fo r e d e l v i n g i n to G o o d m an .
two
I t i s i n Immanuel Kant's c el eb r a t e d Critique of Pm'e Reason that we fi n d t he roots o f a const ruct i v i s t approach to cogn i t ion that i s the hall m ark of i nteractionis m. K a nt t o o k h i s p o i n t of depart u re from the earl ier t radi tions w here knowledge was con si dered to be knowledge of the o b j e c t s i n t he wor l d . Instead , h e focused on the process of c o gn i t i on w h i c h fo rces objects i nto t h e ,
s t r u c t u re o f conce p t s .
Kant a c k n ow le dged the metaphysi cal p ro b l e m
o n e fa c e s i n s u p p o s i n g
1 12
Part I: Th e Problem
that our conceptual organi zation , and our knowledge, conform s to some p re exi sting structure in the world , namely t h at t hen one must be able to specify this struct u re at l east i n some respects , so that t hese specifications can d i s t i nguish between genuine knowledge and heresy. Not i n g the fai l ure of various p h i losophers before him to address this problem , Kant argued t hat a better approach m i ght be to reverse the s u p posi tion, so that the objects in the world are seen to conform to the struct u re of our concepts. K an t ' s concepts, w h i ch he referred to as ca t egories, are s u bject i ve i n that t hey h i gh light the subj ect 's role i n cogn i t ion-t hey are a priori and exist i n dependent l y of experience. Yet , categories are objecti ve i n t h at t hey do not vary from consciousness to consciousness . The relationships between cate gories are not u n i que for my con sciousness, but are true in all consciousness. It was necessary to t ake this posit ion to explai n the obj ecti ve n at ur e of t he natural sciences, which are essentially cat egorical i n Kant 's account. A s far as the external world i s concerned , K ant made a d i s t i n ction between the noumenal world, a world of th ings in t h e mselves, and a p henomenal wor l d , a world o f appeara n ces. The world o f appearances i s the world t h at i s gi ven to us by our senses , which we are in a position to k now . The noumenal world, however, i s not knowable, but one can think about it. It was necessary to posit a noumenal world t h at one can t h i n k abou t , s i n ce otherwise i t woul d lead us t o conclude that t h e world o f appearances i s made out o f not h i ng . T h e n K ant introd uced sch e m as to med i ate between categories a n d the world of appearances. The d i s t i n ct ion between t hese t h ree key concepts of Kant's account of cogn i t ion can be better apprec i ated with an exam p le . W h e n w e say that the sum of the t h ree a n gles of a triangle equals t w o right angles , we are r e ferri n g to the category triangle, w h i ch is the abst ract no tion of a triangle. Being abstrac t , however, i t cannot be i m agi ned ( you can imagine a parti cular triangle, b u t not the abstract co n c e p t t r i angle ) , an d t herefore, c annot be appl i ed to fi g u res t h at we see . lt i s t h e schema of t r i a ngl e t h at allows u s to i m ag i n e fi g ure s t h at a r e t ri angles , and it i s through the s c h e m a of t r i a n gl e t h at the concept of t r i angle becomes applicable to the world of appe aran c e s , wh ich c o n t a i n s part i c ul ar t r i a n gu l a r objects. Thus, our categories organ ize o u r wor l d of a p pearan ces t h rough their respective schemas . These are the key fea t u r e s o f K an t ' s a p p roach t o cogn i t i on . While he en the subject ' s role in cogni t i o n , he i s q u i te s i l e n t abo u t h ow the world of t h i n g s i n t h e m sel ves co n s t r ai n s the possible ways in w h i ch the world of appearances can be organ i zed by our c at egori e s . However, we shou l d t ake note of K rausser's [ 1 974] arguments that t h e r e are two p os t u l at e s t h u s i as t i c a l l y e n d o r se d
Chap t er
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1 13
i mplied i n K an t ' s p h i losophy. The first pos t u l ate is t h at i n order to h ave an e m p i r i cal structure i n the sciences, we must be able to i nteract w i t h and experience the world of t h i ngs in t hemselves . Second ly, this world of t h ings i n t hemselves must have some order and struct u re, even t hough t h i s order or structure is not knowable. The metaphysical revolu t ion that J< ant started-regard i ng only the pro cess of cogni t ion as accessi ble and knowab le but not the world of thi ngs i n t hem sel ves-achieved i t s fu l l i ntensi ty i n t h e p h i l osophy of Ernst C assirer. H e focused on Kant's schem a, developed it i nto a t h eory of symboli c forms, and then p roceeded to apply i t to various human act i v i t ies such as language, mathemat i c s , natu ral sciences , myths an d rel igion , et c . I n t h i s t ask Cassi rer great l y benefited from certai n developments in mathemat i cs an d the n at u ral sciences s i n ce K an t , such as non- Euc l i dean geometries and t he t heory of rel ati v i ty, as well as the avai l ab i l i ty of a great deal of research in anthropology, l i nguistics, mythology, rel igion, and an i m al cogn i t i on . ( Cass i rer's theory i s outli ned i n h i s monumental Th e Ph ilosophy of Sym bolic F01·ms [ 1 955] , a sum m ary of w h i ch can be fou n d i n his An Essay o n Ma n [ 1 944] . For some of t he app l i cations of h i s t heory see Language a n d Myth [ 1 946] and Th e Problem of Knowledge [ 1 950] . See al so Susanne Langer 's Ph ilosophy in a Ne w Key [ 1 942] and Feeling and Fo rm [ 1 953] for fu rther el aborat i o n of Cassirer's t h eo r y and i t s app l ication to the p h i l osophy of art . ) ,
The creat ion of symbols, for Cassirer, i s the pri m ary fu nction of human consciousness . He saw cogni t ion merely as one of the act i v i t ies t h at man i fests the symbo l i c fun c t i on ; notable among ot hers bei ng art and religion . The symboli c act i v i ty was properly cal led creat i o n si nce it i s only in the making of symbols t hat the kaleidoscopi c fl u x of i m p ress ions i s h al t e d an d gi ven a for m t h at can be com p rehended . The m u l t i pl i city of sy mbol i c forms, as wel l as their creative a s p e c t s is summed up n ic e l y i n the fol l ow i n g passa g e : " E very aut hent i c fu n c t i on
of the h u m an spirit h as this d ec i s i ve common w i t h cogn i t i on : i t does n o t merely copy but rather embodies an or i g i n al fo r m at i ve power. ll does not e x p r ess pass i v e l y the mere fact t h at somet h i n g i s presen t but con tai ns an i n dependent energy of the h u m an s p i r i t t h rough w h ich t h e s i m p l e p res e nce of the p h e n o m e non ass u mes a d e fi n i t e ' mean i ng,' a p articu l ar i deational content. T h i s i s as t r u e of art as it is of cog n i t io n ; it i s as t rue of my t h as of rel i g i on . A l l l i ve i n part icular i m age- worl ds, which d o not merely refl ect t h e e m p i r i cally gi ven , b u t w h i c h rather prod uce i t i n accordance w i t h an i n dependent p r i n c i ple. Each of t h ese fu n c t i o n s c reates i t s own charac t e r i s t i c in
,
Part I: The Problem
1 14
symboli c forms which, if not s i m i l ar to the i ntellectual symbols, enj oy equal rank as prod ucts of the human spi r i t . None of these forms can simply be reduced to, or derived from , the others ; each of them design ates a particular approach , in w h i ch and t h rough which i t const itutes its own aspect of ' reali ty. "' [Cassirer 1 955, vol . 1 , p . 78] . Here we see t h at the i ntersubj ect i v i ty of K ant 's categories i s t urned i nto a multiplici ty of symbol i c worlds by C assi rer. Moreover, t hese m u l t i ple worlds are consi dered i rred ucible to one another. Thus, Cassi rer's account expli c i t ly endorses the view that reali ty can be conceptualized i n alternate ways. C assi rer elaborated at quite some length on what exactly i s a symbol . He d raws a disti nction between signs and symbols. [ C assi rer 1 94 4 , Chaps. II and I I I ; Langer 1 942, Chaps. II and I I I . ] S igns are the basis of ani mal cognition. They are d i rect l i nks between the sensory and effectory organs of an an i m al . For i n stance, we can train a dog to associate the soun d of a bell to avai labi l i ty of food . The dog comes running to a p reappoi nted place expect ing food every t i me she hears the sound of the bel l . It m ay even start some physiological reactions i n the dog, such as sal i vat i on . In t h i s case, the ringing of the bell acts as a sign for the dog. I t i s closely tied to the p hysical wor l d . The dog cannot ' t h i n k ' about it in the absence of the sign. Even when the sign i s presented , i t i nvariably results in some action . Symbols , on the other hand, are taken to be the foun d at i on of h um an intel l i gence: " Between t he receptor system and the effector system, w h i ch are to be found i n al l an i m al species , we find i n man a t h i rd l i n k which we m ay descri be as the symbolic sys t e m . " [Cassi rer 1 944 , p . 24. ] Symbols can be looked upon as signs t hat have become independent and free-floati n g in that t hey are no longer d irect ly
connected to the sensory or the effectory organs.
Thus, w e may think of food in our idle moments , w i t hout b e i n g h u n g r y , or the word ' food ' b e i n g mentioned at a l l . M or e ove r , even w h e n a s y m b o l is explicitly me n t i on e d , we can m a n i p u l a t e i t , t a l k a b o u t i t , w i t h o u t at once get t i n g ac t i v e l y i n v ol ve d . Symbols themselves are divided i nto three types: m im et i c , an alogi cal , and discursive, in the order of their developmen t . [Cassi rer 1 955, vol . 1 , pp. 1 861 9 7 ; Langer 1 94 2 , C h a p . I V . ] T h a t i s , m i m e t i c s y m b o l s are s u p p o s e d to be the fi r s t ones t h at a culture develops, fo l l o w e d by a n alog i c al ones, ulti m ately lead i n g to d i s cursi ve symbol s . M i me t i c symbols consist i n re p l i c at i n g the sense i m p ress i o n c a u sed by the obj ect that i s being designated . For i nstance, t hunder might be designated by a thu nder-l i ke sou n d . I n the second type, t e r me d 'analogical ' or ' p resentational ' symbol s , the symbol i s some kind of
Chapt er
4:
Cogni t ion as In t eract ion
H5
structural model of the object designated . A l l kinds of picture l anguage fall s i n t h i s category. Finally, d i scursive symbols are those i n which t here is no d i rect relationship between the symbol and the object designated . For i nstance, the Engli s h word ' cat ' does not bear any resemb l an ce with the ani m al species i t designates . Despite t hese elaborations of what a symbol i s , it is not clear i n Cas sirer's account how the symbol i c worlds are prevented from being arb i t rary. If K ant 's version of i nteract ionism is seen as lean i n g too far in the d i rection of i ntersubjec t i v i ty by posit i ng t ranscendental categories , then Cassi rer's i nter actionism seems to bend too far in exact ly the opposite d i rection by making t he symbol all powerful creator of form , and red u c i ng the role of the env i ronment to a passi ve recipien t . I t i s i n Nelson Goodman's approach that w e find j ust t he right balan ce between t hese t wo extremes . He embraces Cassi rer in mai ntai n i ng t hat t here are d i fferent modes of cogni t i o n , and each creates i t s own ' world . ' But he also argues t hat every ' worl d ' h as its own cri teria of rightness t hat are obj ect i ve , so that the j udgment whether something i s a fact or a fal lacy w i t h i n a gi ven ' world ' no longer depends on the w h i m of the subject . For instan ce, we can fi x our frame of reference so t hat the earth is motionless. But then the r i ght n e ss of the statement "the sun revolves arou n d t h e eart h " i s a m a t t er of obj ecti ve verification, and cannot be deci ded arbi trari ly. Thus , the role of t he subj ect , in Goodman 's worldmaking view, i s seen in estab l i s h i n g the frame of reference, and t he role of the env i ronment i s viewed i n obj ect i fying the facts relat i ve to t he frame of reference. Goodm an also emphasizes t he need for hav i ng a frame of reference, using an analogy w i t h the map [ Good man 1 978, p . 1 1 4] . In order to use a map, we must first locate ou rselves on i t . A n d once we locate o u rsel ves on i t , the frame of reference gets fi xed , a n d t h e ' worl d ' ac q u i res a fixed ontology and stru c t u re . N o w i n order to g e t to t h e t rai n s t a.t i o n , c e r t a i n s e t s of d i rec t i o n s a r t> correct .
and ot hers are wrong, and this correctness i s
a m at ter of object ivity.
T h i s account , however , w h i le i t comes close to reso l v i ng of i nteract ioni s m , does not q ui t e do so.
The problem
is
the paradox
to exp l a i n how
reali ty ob j ectifies the ' world . ' Not i ce t hat in the map analogy, it d oes so by virtue of a frameless structure. A map has certain fixed struct u re even b efore we lo cate ou rsel ves on i t . Moreove r , t h i s s t ru c t u r e is k n o w a b l e w i t h o u t l o cating ou rselves o n i t . 1 And all frames of r efere n c es c a n b e deri ved from 1 F i l m d i rector A l fred H i tchcock rem i n isced t h at before co m i n g to t h e U n i tes S t ates , he was so fascin ated by New York City t h at he had memori zed i ts m a p . He knew the locations of the stores and theaters , the sched u l e of trains, and so on . When he wou l d
Part T: The Problem
116
t h i s u n i versal frameless structur e , so its knowledge is usefu l . I n fact , t h e map analogy i s not very apt here, because one o f Goodman 's points, a point t h at he argues rat her well , i s that i t i s not al ways possi ble to resol ve conflicts between d i fferent worlds by red ucing t hem to some frameless wor l d . [Goodman 1 978, V I I , pp. 1 09- 1 40 . ] B u t , i f it i s not some frameless worl d t hat is obj ecti fying the rel a t i ve ' wor l d s , ' t hen what is? In answering this question lies the key to t he paradox of i n teractionism .
4.4
P iaget ' s C o n s t r u c t i v i s m
T h e pioneering work o f Jean P i aget , t he biologi s t , the p h i losopher and , most of al l , the psychologi st, prov i des another com prehens i ve framework of i nter actionism. Th roughout his p ro l i fi c career, P i aget was a staunch supporter of t he view that real i ty does not h ave a p re-existing struct ure, but i s acti vely const r ucted by the cogn i t i ve agent. This t heme echoes i n all of P i aget 's writ ings. His nu merous i n genious and meticulously executed experi ments showed how various concepts-such as obj ect permanence, t i me durat ion , temporal succession , speed ; geo m et r i c al concepts l i ke l en gt h , angle, curvature, area, and vol ume; logical concepts l i ke class i nclusion, ' a l l ' and ' s o m e ; ' m u l t i p l i ca t i ve classification , seri at ion; nu meri cal concepts; and so on-are grad u al l y constructed b y the child t h rough i ncreasi ngly com plex i nteractions w i t h t h e env i ronment . ( See I n helder & P i aget [ 1 959] ; P i aget [ 1 936, 1 93 7 , 1 94 5 , 1 946, 1 946a, 1 98 1 , 1 983] ; P i aget & In helder [ 1 948] ; P i aget , l nhelder & Szemi n ska [ 1 948] ; and P i aget & Szem inska [ 1 94 1 ] . For an overview see P i aget & Tnhelder [ 1 966] and P i aget [ 1 970] . ) For i n st an ce, t ake the notion o f obj ect permanence i t self. Piaget ' s ex p e r i m e n ts show that the w o r l d is not al read y cut u p i n t o n u merous object s , but a ch i l d , rts s h e grows an d d e ve l o ps cognitively, arri ves a t t h e idea o f an ' o b j e ct ' t h rough s uccessi ve con s t ructions [ P i aget 1 93 7 , Chap. 1 ] . Early on , t he ch i l d ' s co n ce p t of obj ect is i n separable from her actions. Somet h i n g i s an obj ect as long as i t c a n b e gras p e d , or sucked . A t this p oi n t , if t h e obj ect is taken away from the ch i l d , she merely repeats her act i ons an t i c i p a t i n g the reappearance of the obj ect : the chi l d wou l d continue to m ake the sucking motions or the m o t i on s of open i n g and clench i ng her fists. Later on , the ch i l d begi ns to assoc i ate d i fferent sensory stimuli res u l t i ng meet A mericans at parties, t h e y wou l d invariably ask h i m w h e n he was l ast in New Yor k . To w h i ch H i tch cock , t o t h e i r u t te r am azement , wou l d reply t h at he h a d never been there. (Truffaut 1 98 4 , p . 1 25.]
Chap ter
4:
117
Cogni tion as In teraction
from the same objec t : she w i l l sh ake a rattle i n order to make the sou n d , or turn her head towards the sound i n order to see t he object making the soun d , e t c . B u t the chi l d h as no notion of object permanence yet . I f somet h i ng i s not p resent to t he senses d i rectly, t hen i t is simply not t here. For i n stance, i f o n e h i des a toy w i t h w h i ch t h e ch i l d h as been p l ay i n g u n der a h and kerch ief, the chi l d w i l l show no i nterest in recovering i t , even if t h e act of h i d i ng was carried out in fu l l view of the ch i l d , and the ch i l d h as the motor abi l i ty to remove the hand kerc h i ef. S t i l l l ater in her cogni t i ve developmen t , the c h i l d begi n s to acti vely search for object s . H owever , t here is an i nteresting seq uen ce of developments. At one point , t he chi l d w i l l ret rieve a toy t h at is h i d den beh i n d a screen by remov i n g the screen , as long as the act of h i d i n g is carried out in front of the ch i l d . But after the toy is h i dden and retrieved from beh i n d screen A several t i mes, if the toy is h i d den beh i n d screen B, again in fu l l view of the chi l d , the chi l d sti l l looks beh i n d screen A t o ret rieve i t . O n l y l ater i n t he course of her development does the chi l d m ake a more adequate association between the sequence of events w i t nessed and the location of the toy. At t h i s stage, invisible d i s p l acements sti l l con fuse the ch i l d . If a toy i s put i n a box , a n d the b o x i s taken beh i n d the screen , where the toy i s taken out so t h at the ch i l d can not see i t , an d the em pty box i s brought out agai n , t hen t h e chi l d does not k now w here to look for t h e toy. Event u al ly, when t he chi l d does m ake the connection , she tempora r i l y regresses to the earl ier behavior so t h at she searches for t h e toy, h i dden beh i n d screen B , by l i fting screen A, from where the toy was ret rieved the l ast few t i mes. Thus, we see t h at the concept of object permanence is not a s i m p le and pri m i t i ve concept after al l , but requ i res an elaborate intellectual const ruction . It i s construction i n the sense that the concept is embedded i n t h e d i fferent
ways in which the child can act upon an objec t . the c h i ld grows , t h e o b jed h oo d co n c e p t becomes
As
the act i on repertoire of
i n c reas i n g l y c om p l e x , u n l i l
t h e ad u l t version of t h e concept em erges t h rough abs t r act i o n . T h i s l ast poi n t ca.n be ern p h a.s i zed b y con s i d e r i n g t h e n o t i o n of i d en t i ty. A d u l t s can see an object p reser v i n g i t s i d en t i ty t h rough v11.rious tra.n sform a t ions of orientat i on , p os i t i on , fo r m , shape, and s i ze . For i n stance, a piece of
string is the same string whether i t is arranged in the s h ape of a c i rcle or a s quare . H owever, a c h il d , until a
c e rt a i n
s t age or h e r cogn i t i ve d e velopment,
would insist t h at t hey are d i fferent t h i n g s , for t h e c h i l d h as not yet learned t h at i n t ra n s fo rm i n g an object in various ways , somet h i ng is conserved , and it is t h i s conservat i o n t h at i s at the heart of t h e concept of i d e n t i ty. T h i s difference between t h e adul t ' s a n d the ch i l d ' s concepts of i d e n t i t y reveals
Part I: Th e Problem
1 18
itself in an i nterest ing way i n the phenomenon of apparent motion. Recall that i n Kolers ' experiments, when a circle and a square were flashed i n quick succession near each other i n the visual field of an adul t , the adu l t reported a u n i form movement of the c i rcle to t he position of the square, during w h i ch the circle was smoothly t ransformed i nto a square. C h i l dren , on t he other han d , report t hat t he circle remai ns a circle u n t i l it i s near t he posit ion of t he square, where i t abrup t l y changes into another obj ect , a square. ( See P iaget [ 1 970] , pp. 54-5 7 . ) ( T h i s is remi n i scent of t he adu l t 's experience when t he color, rat her t h an the shape, of the flash was varied i n Kolers' experiments. See also Goodman 's [ 1 978, V , 6 , p p . 85-89] exp l anations . ) Based on many such studies, P i aget arti c u l ated h i s act ion-oriented ap proach , according to which, to know an obj ect is to act upon it and to transform it, so that " K nowing real i ty means const ructing systems of trans form ations t h at correspon d , more or less adequately, to reali ty. " [ P i aget 1 9 70, p. 1 5 . ] Moreover, the process of know i ng i tsel f works by t ransfor m i ng reali ty, " [K] nowledge results from cont i n uous construction, s i n ce i n each act of understan d i ng, some degree of i nvent ion is i nvolved ; in developmen t , t he passage from one stage to the next i s always characterized by t he formation of new struct ures w h i ch d i d not exist before, either in the external wor l d or in t he subject's m i n d . " [ P i aget 1 9 70, p. 77.] P i aget , of course, el aborated i n quite some detail h i s action-oriented ap p roach . The key concept in his elaborat ion is t h at of an equ i l i br i u m b etween t he comp lementary processes of ass i m i l at ion and accommodat ion . This con cept was borrowed from biological systems, which shoul d not be surprising gi ven t h at P i aget started h i s career as a biologis t . The analogy i s exp li c i t l y laid o u t i n o n e of P i aget 's ear lier works : organ ism is a cycle o f physiochemi cal and k i neti c processes i n constant relat i on to the environment, are engendered by each other. Let a , b, c , e t c . , be t he elements of this organ i zed total i ty and x, y, z, e t c . , the correspondi ng elements of the sur r ound i ng env i ronmen t . The schema of org anization is t herefore t h e following: " T he
whi ch ,
1.
a
2.
b+y
3.
c
+
+
x -----+
b;
----+
c;
z -----+
a;
et c .
The p rocesses ( 1 ) , ( 2 ) , e t c . , may consist eit her
a c t i ons ( when t he organ ism i ngests s u b s t a n c e s
of x
ch e m
i c a l re
w h i ch it w i l l
Chap t er
1 19
Cogni t ion as In teraction
4:
t ransform into a substance b com prising part of i t s structure ) , or of any physi cal tran sformations whatsoever, or fi n ally, in part i cu lar, of sensory- motor behavior ( when a cycle of bod i l y movements a , com b i ned with external movements x , res u l t i n b w h i ch itself enters the cycle of organization ) . The rel at i onsh i p w h i ch u n i tes the organi zed elements x, y, z, et c . , is therefore a rel ation s h i p of assim ilation, that i s to say, t he funct i on i n g of the organ ism does not dest roy i t but conserves the cycle of organ ization and coordi n ates the gi ven data of the envi ronment in such a way as to i ncorporate t hem in t h at cycle. Let us therefore suppose that , i n t he envi ronment , a variation i s produced w h i ch transforms x into ' x . E i t her the organi s m does not adapt and the cycle ruptures , or else adaptat ion takes place, w h i ch means that the organ ized cycle has been mod i fied by closing up on itsel f:
1.
a +
2 . b' 3. c
x
'
+ y +
b' ;
----> ---->
z ---->
c; a;
etc.
I f we call this result of the p ressu res exerted by the en v i ronment acco m m odation ( transformation of b i nto b' ) , we can accord ingly say that adaptation i s a n equ ilib1·ium between assim ilation a n d a cco m m odatio n .
This defi n i t ion applies t o i ntel l i gence a s wel l . Intel l i gence is as similation to t he extent that it i n corporates all the given data of e x p e r ience w i t h i n its framework . . . . [M ] ental l i fe is also a cco m modation to the environ men t . Assi m i l ation can never be p u re because by i ncorporat i n g n e w e l e m e n t s i n t o i t s earl i e r s c h e m at a the i n t e l l i gen c e c o n s t an t l y m o d i fies t h e I aUer i n order to adj ust t h e m to n e w element s . Conversely, t h i n gs are never k n ow n by t hemselves, s i n ce t h i s wor k of accom modation is o n ly poss i b l e as a fu n ct i o n of the i n verse process of ass i m i l at i on . We s h a J I t h u s
see h o w the very concept of the object i s far from being i n n ate and necessi t ates a const ruction w h i ch i s simultaneously ass i m i la tory and accommodat ing." ( Piaget [ 1 936) , p p . 1 7-1 9, e m p h as i s P i aget ' s . )
I
i n cluded this long quotation because to u n d e r st an d the
co g n i t i ve mech
a n i sms of ass i m ilat i o n and accom modat ion-an d t hey are goi ng to play a
m ajor role i n my account of c o gn i tion laid out i n the next ch ap te r
-
it
is
Pa.rt
1 20
[:
Th e Problem
helpfu l to see t hei r biological roots . The analogy between biologi cal systems and cogn i t i ve systems resu rfaced in P i aget 's later works [ 1 967, 1 974] , t hough he used it i n the reverse d i rect ion this t i me by app lying his i nsights from psychological stud ies of cogn i t ion to b iological systems . Some more recent stud ies h ave carried t h i s an alogy quite far by proposing elaborate t heories that ex plai n know ledge and cogn i t ion on a biological basi s . [ M at u rana & Varel a 1 98 7 ; B arham 1 990.] I n any case, my i nterest being i n cogn i t i ve ass i m i l ation and accom mo dation , it wou l d be useful to eluci date t hese mechan i sms fu rt her w i t h some exam ples. Assi m i lation i s the process by w h i ch a cogn i t i ve agent sees every s i t u at ion, every environmen t , t h rough the struct u re of its pre-ex i st i n g con cepts, or sch emas. For i nstance, an i n fant may attempt to suck at any object pressed to her l i p s , thereby ass i m i l at i n g the object to her 'sucking schema . ' As far a s t h i s schema i s concerned , every obj ect i s a n object to be s ucked . A rich source of examples of ass i m i l at ion are chi l d ren 's playfu l act i v i t ies, especially those i n vol ving ' p retend sit uations. ' A child playing with a doll house is essentially ass i m i l at i ng the dol l house and the dolls to her schema of domest i c l i fe. Assi m i l ation m ay lead to diffe re n t iation, as t he object being assi m i l ated may produce an unex pected , or otherwise i nterest i ng, response. For i n stance, a ch i l d who has developed the schema of ' grasp an object and bring i t to the mouth to suck on it' may find the object visually interesting as well .
However, assi m i l ation alone produces only a p l ayful behavior and not an ' i ntel l igen t ' one. The unexpected ness of response i s lost u nless it is integra t e d i nto t he conceptual organi zation by suitably modifying i t . P recisely t h i s tas k i s accompli shed b y the process of a cco m m odation. In accom modation
t h e cogni t i ve agent reorgani zes i t s schemas
by
taking
account o f t h e env i ronment a l d i fferences so as t o preserve an overall u n i ty. The overall u n i ty comes from the fac t t h at the cogn i t i ve
agent , i n ass i m i i t s schemas , h as 'expectat i o n s ' t h at are fulfilled by t h e enviro n ment . When t h i s overall u n i ty i s d i s t u r b e d either t h e cogn i t i ve agen t does not survive ( as t h e t ragi c fai l u res of several heavier- t h an-ai r flight attempts before t h e Wright b rothers tes t ifies ) , o r else i t reorgani zes i t s schemas so a s to m a i n t a i n t h e overal l u n i ty. lat i n g t h e e n v i ro n m e n t t o
,
I t i s the accom modat ion t h at g i v e s the cogn i t i ve agen t a capac i t y to
· Jearn . ' However, every act of accommodation p r e s u pp os e s a prior s t ep of ass i m i l ation. A l so, it is t h e i n t erplay of assi m i l at i on and accommodation, i n c onj u nct io n w i t h generalization, t h at i s respons i b l e for ge n er ati n g new schemas via d i fferentiat i o n . I n the exam ple of the c h i l d who, in act i ng o u t
Ch apt er
4:
Cogni tion
as
In teraction
121
the schema o f ' grasp objects and bring them t o l i ps t o suck , ' finds the ob ject v isually i nteresting also, i ntegrat i n g t h i s observation i nto her network of schemas m i gh t result in a new schema of ' grasp t h a t object and bring it to the v isual fiel d , ' w h i ch can t hen be general ized i nto ' grasp a n y object and bring i t to the v i s u al field to look at i t . ' Various schemas t h at a cogn i t i ve agent m ay possess are not all i sol ated , but are i n terconnected as a network. For example, both the schemas j ust mentioned m ake use of, and are connected w i t h , the schema of ' grasp objects . ' M any of the key con cepts of P i aget 's con st ruc tiv ism have been gi ven pre cise characterizations using logi cal and algeb rai c tool s . [ P i aget 1 953; Wermus 1 9 7 1 2 ] Two of t hese concepts play an i m portant role in my framework . The first i s the notion of an operation, which i s an i ntern alized action . P i aget requ i res an operat ion to h ave the fol lowing fou r characteristics:
1 . "[A]n operat ion i s an act ion t h at can be i n ternal i zed ; t h at i s , i t can be carried out in thought as wel l as executed material ly." ( Pi aget [ 1 9 70) , p. 21.) 2 . " [I ] t i s a reversi ble act ion; t h at i s , i t can t ake p l ace i n one d i rect ion or in the opposite direction . This is not true of all a c t i o n . I f 1 smoke my pipe t h rough to the end , I cannot reverse t h i s action and h ave it back agai n fi l led u p w i t h the same tobacco . . . On the other hand, ad d i t ion is an example of an operat ion. I can add one to one and get two, and I can subt ract one from two and get one agai n . " ( P i aget [ 1 970] , pp. 2 1 -22. ) 3 . " [A n operation] always supposes some conservat ion , some i n vari an t . I t i s of course a. t ransformation , s i n ce i t i s a n act ion , but i t i s a. t ransfor mation t h at does not t ransform every t h i ng at once, or else there wou l d be no possibility o f revers i b i l i ty. Fo r i n s t a.ncc, i n t h e cnse o f a r i t h me t i cal ad d i t ion we ca n t ran sfor m t h e way we gro11 p t h e parts togd . h e r. 'vVe can say 5 + ] , or 4 + 2 , or 3 + 3 , b u t t h e i n va r i a n t i s t h <" sum -" ( P i n.get [ 1 970] , p . 22)
4 . " [ ] o operat ion exists alone. Every operat ion i s related to a . system of operations, or to a. total structure as we cal l i t . " ( P i a.get [ 1 970] , p . 22. See also Pia.get [ 1 967] , p p . 208-2 1 2 . ) The s l r u c l u re t h a t
the
P i ageL refers t o above i s a n abstract sch e m a . H e a.H r i b u tes
follow i ng c h a r a c t e r i s t i cs
to
s t r u c t u res :
21 arn gr atefu l Lo Ugo B u y for lransl a l i n g l h i s paper from French .
1 22
Part 1: The Problem
1 . " [ A ] structure is a total i ty ; t h at i s , it is a system governed by laws t h at apply to the system as such , and not only to one or another element of lhe system . " ( P i aget [ 1 9 70] , p . 22. See also P i aget 1 96 7 , p . 1 39 . ) 2 . " [These l aws] are l aws o f t ran sformat ion; t hey are not stat i c character i s t i c s . " ( P i aget [ 1 970] , p. 2 3 . )
3 . " [A] struct u re i s self- regulating ; t h at i s , i n order to carry out t hese l aws of t ransformation , we need not go outside the system to find some external element . S i m i l arly, once a l aw of t ransformation h as b een applied , the res u l t does not end u p outside t he system . " ( Pi aget [ 1 970] , p . 2 3 . ) T h i s property is referred to as closu 1·e . 4 . Structures m ay relate to each other, and elements of a structure can themsel ves be structures as a whole. ( P i aget [ 1 967] , p. 1 4 0 ; P i aget [ 1 970] , p. 2 3 . ) 5 . S t r u ct u res, while maintai n i ng closure, m ight s t i l l be open to exch a nges with the e n viro n m e n t . ( P i aget [ 1 967] , pp. 1 54- 1 58 . ) It i s t h i s l ast character i s t i c that allows t h e structures t o b e appl i ed t o the envi ron ment , thereby mak i ng t hem m e a n ingful.
P i aget 's i nteract ionism also expl icitly took i nto account the role of the envi ronment i n r u l i n g out arb i t rary const ructions. P i aget 's v i ews on this m atter are best art iculated i n h i s l ast and most fasci n at i n g work t h at was on ly p u b l i shed posthumously [ P i aget 1 98 1 ; 1 983] . It focuses on how chi l d ren come to develop the concepts of possi b i l i ty and necessi ty, a n d h o w i t relates to their cogni t i ve development i n o t h e r respects, such a s emergence of operational structures from si m p l e sensory- motor act ion schemas . The term ' poss i b i l i ty ' here refers to t he cogni t i ve age n t ' s choi ces of act i o n s or operations, a n d ' n e c ess i t y ' to the const rai nts i m po s e d by t he e n v i r onm e nt . P i aget ' s s t u d i e s , i n co l l abo rat i o n w i t h se v e r al ot her psychologists, led h i m to conclude t hat poss i b i l i t i es develop through successive d iffere n tiati on s . A s t he child's repertoi re of schemas grows, and her organi zat ion b ecomes more complex, she sees newer ways of i nteracti ng w i t h the environment , and t herei n l ies the sou rce of her p o ss i b i li t i es . For i nstance, in one exper iment [Pi ageL 1 98 1 , Chap. 7, p p . 70-77] , ch i l d ren were gi ven a n u m ber of objects , s u c h as a p i ece of woo d , a candle, t h ree lead weights, a sponge, etc . , and a cy l i n d r i c al aqu ar i u m par t i ally fi l led w i t h wate r . T hey were t h e n asked lo use the obje c t s to raise the water level i n t h e aqu ar i u m as h i gh as they can . Younger children were unable to d i fferent i ate between their own ac t i on s
Ch apt er
4:
Cogni tion as In teraction
1 23
and the i nteractions between the objects. Some of them wou l d start p u t t i n g objects i n the water i n random order. O n e of t hem , w h e n she needed more obj ects , merely took some objects out of the aquar i u m and put them back , as i f t h at wou l d m ake a d i fference. Some ch ildren noti ced t h at some objects, l i ke a sponge, float , and t ried to u se t heir hands to forci b l y submerge t hem , expec t i ng t hem to stay submerged . O l der ch i ld ren, learn to use the heavier objects to keep the l i ghter objects submerged . Thus, we see that the act ion of p u t t i n g objects in water to raise the level leads, by observing t h at it h as d i fferent effects on d i fferent obj ects , to the discovery of the act ion to use heavier objects to keep floati n g objects submerged . Necessi ty, w h i le seen to be t h e const rai nt i m posed by the environment , pertai n s , nonetheless, "to t he compositions carried out by t he subject and is not an observable datum i nherent i n obj ects." [ P i aget 1 983, p . 1 35]. I n t h i s respec t , the source of necessi ty l ies i n t h e organization of the ch i l d 's schemas, and it reflects the environmental constrai nt in as much as the organi zat ion of the chi l d ' s schemas h as i ntegrated t h e resu l t s of t he past i n t eractions with t he environment . The point here i s simply that the environment responds in a certain way to the cogni t i ve agent's act ions, and this response i s not al ways predi ctable. When t he cogni t i ve agent 's .predi ct ions are not met , then it must r eo r g an i z e its schemas to i ntegrate t h i s observat i o n . Thus, it i s through acco m modation t h at t he envi ronment prevents a schema from h aving an arbit rary structure. B u t since it is the cogni t i ve agent who deci des w h i ch act i ons to carry out on which objects and w h i ch parts of the envi ron ment , the necessary constrai nts i n the environment are still seen in terms of relat i on s h i ps between t he cog n i t i ve agent 's act ions and schemas. This observation i mp l i c i tly resolves the p aradox of i nteract ionism . For one coul d argue now t h at a cogni t i ve agent can act i n an environ ment i n a variety o f way s . W h i ch act i o n s are ac t u a l l y carried out depe n d s o n t h e cogn i t i ve agent . B ut the re su l t s of t h e s e act ions are determ i ned by real i ty, and are not controlled by t he cogni t i ve age n t ( t hough it m ay h ave foreseen the res u l t s , and rnay even h ave initiated the ac t i o ns expressly to achieve t hose res u l t s ) . A n d since these resu l t s affect the organ ization of the cog n i t i ve agent 's schernas, we see that the cogni t i ve agent's conceptual organ i zation i s determ ined i n part b y the cogni t i ve agen t and i n part b y the environ ment .
Part I: The Problem
1 24
4.5
Lakoff- J ohnson : T he Bodily B asis of Cognition
ln the l ast chapter, 1 d i scussed the Lakoffian approach to the creation of s i m i l ari ty, and pointed out t hat i t explains the p henomenon by rooti ng i t i n a cogni t i ve mechanism that i s responsible for creat i ng at tributes o f an obj ect (or even t , or s i t u at i on ) . Though we saw t here t h at the L akoffian approach does not real ly resol ve the paradox of the c reat ion of s i m i l arity, t h i s conclusion was arri ved at w i t hout consi dering the Lakoffi an approach to cogn i tion . Now t h at we are exam i n i ng the i nteract ionist views of cogni t i o n , i t wou l d be i n teresting to see w h at add i t i onal l i ght , i f any, does the Lakoffian app roach to cogn i t i on shed on e i t her the paradox of the creat ion of s i m i l ari ty, or t he paradox of i nteractionism in cogn i t ion. ( T he Lakoffian approach to cogn i t ion is briefly ou t l i ned in Lakoff & Joh nson [ 1 980] , and el aborated i n Johnson [ 1 987] an d Lakoff [ 1 987] . )
The i ntent o f the Lakoffian app roach i s t o strike a balance between the obj ecti v i st view, accord i n g to w h i ch t here i s some object i ve pre-exi s t i n g on tology and s t ru c t ur e of the wor l d , and our concepts reflect t h i s ontology and structure; and the subject i v i s t view, according to w h i ch t here i s no external constraint on mean i n g and experience, and concepts can arb i t rari ly organize one's experience. I t wou ld l i ke to argue t h at real i ty can be conceptual i zed in altern ate ways, and yet rule out arb i t rariness. It wants to maintain t hat "there are real t h i ngs, ex i s t i n g i n dependently of us, w h i ch const rai n both how we i nteract w i t h t hem and how we comp rehend them . " [Lakoff & Jo h n son 1 980, p. 226 . ] A t the same t i me, it woul d also l i ke to hold t h at "mean ing is always mean i ng t o a. person . . . [and] w i l l not depend on [her] rational k n ow ledge alone b u t on [ her ] p a s t experiences , val ues , fee l i n g s , and i n t u i t i ve i n s ight s . " [ Lakoff & J o h n son 1 98 0 , p . 227.] T here a r e t w o aspects of Lakoff and Johnson ' s work t h at m u s t be dis
t h e need to fi nd a. b ala n c e bet ween t h e two ext remes of objec t i vism and subj ect i v i s m . T h i s i s their forte; s i n ce the evi dence gat hered by Lakoff and his colleagues is, i n deed , quite i m p ress i ve. The other aspect h as to do w i t h act ually striking t h e b a l ance bet ween object ivism a n d subjectivism i n some r eas on ab l e way. It is t h i s secon d aspect of the L akoffi an approach t h at is of con ce r n to u s here, a.s we are i n terested in seeing what l i gh t it can shed on the paradox o f i nteract ion i s m . t i n g u i s hed here. O n e i s t h e i r a m as s i n g of e m p i r i cal l i n gu i s t i c data t o s how
To ach i eve al l objecti ves , Lakoff a n d J o h n son developed a. n e.xp e. ri e. n l i a l view of cogn i t i on . A ccord i n g to t h i s view, "con ceptual s t r u c t u re i s mean-
Ch apt er
4:
Cogni tion as In teract ion
1 25
i ngful because i t i s e m bodied, t h at i s , i t ari ses from , a n d i s t ied to our pre concept ual bod i l y experiences . " [ Lakoff 1 98 7 , p. 26 7 . ) It is fu rther suggested t hat certai n experiences t h at we h ave are preconcept ual in t h at they are d i rectly meaningfu l . For i n st ance, our experience of u p- dow n orientation i s d i rectly mean i ngful because of our h avi ng bodies of a certa i n sor t . M oreover, t hese precon cepts h ave their own struct u re, or i nternal logi c , t h at i s d i rect ly accessi ble to us. For i nstance, the part-whole preconcept i n c l udes in its basic l ogi c : " I f A i s a . part of B, t hen B i s not a. part of A." [ Lakoff 1 987, p . 273.] A n d the link preconcep t , the bodily basis of which i s t raced to the u m b i l ical cord , i n c l u des as its b asic logic : " I f A i s l i n ked to B , t hen B i s l i n ked to A . " [ Lakoff 1 987, p . 2 74 . ] O t h er abstract concepts are m ade mean i ngfu l i n d i rectly b y t h e structures of d i rectly mean i ngfu l preconcepts. Two mechan isms that can render i n d i rect concepts mean i ngfu l are metaphor a n d metonymy. For i n stance, t h e abstract experience of marriage i s made mean i ngfu l metaphorical l y b y t h e part-whole preconcept : marriage is con si dered the creat ion of a w h o l e w i t h t he spou ses being the parts. A metaphor, i n t h i s process, works b y map p i n g the precon cept structure i nto the abstract domai n i n such a way t h at t h e b as i c logic of the p reconcept struct ure is p reserved . W h i l e i n a. general way the Lakoffia.n approach to cognition is quite ap peali ng-i ts i ntentions are certai n l y quite ap peal i n g-i t does not stand up to close scruti ny. I h ave already pointed out one m aj or problem with this approach i n the l ast chapter. We saw t h at the La. k offi an approach cannot explai n h ow an abst ract concep t , the t arget of a metaphor, resi sts arb i t rary struct uring u n l ess one posi ts t h at the target al ready h as a preconceptual structure. For metaphors to map preconcepts i nto abst ract domai n s , the ab stract dom ai n m u st h ave s om e t h i n g t h at can be m a p p e d i nto; it m u s t h a.ve
an onto l ogy. A n d i n o r d � r for t h e con d i t i o n l h a.t l h e m Ap p i n g preser ve t h e b as i c l ogi c o f t h e p r e c o n c e p t to b e s i g n i fi c a n t , i t m u st be poss i ble for t h�
abstract dom ai n to someti meR not, p reserve t h i s basic l ogi c . B u t the a.b stract domai n can do that, o n l y if i t al ready h as i t s ow n l ogi c , i t s own s t r u ct u re . T h u s , t he abst ract domai n m u s t h ave i t s ow n p reco n cep t u al ontology and
st ructure. But t hen a cou p l e of other q u es t i on s i m med i at el y arise: W hy is it t h at t h i s p reconcept u al struct u re can not be u n derstood d i rect ly and non metaphori cal l y ?
I s t h i s preco n cep t u al s t r u ct u re t h e same for
ev
e ryo n e '?
If
t h i s second ques t i o n i s ans wered affi rmati vely, t hen i t i s on ly o n e s t e p away from p o s i t i n g a
u n i ve r sal , o b j e c t i v e r e al i t y . B u t
if it is an s wered n egati vely,
t hen one wants t o know w h at it i s t h at s t r u c t u res the same dom ai n d i f
feren t l y for d i fferent people bejo 1·e the domai n is con ce p t u al i ze d . M ac
Cormac [ 1 985] , p . 68 . )
( See
a l so
1 26
Pari I: Th e Problem
A s i m i lar problem , i n fac t , exists w i t h the p reconcepts as welL T hey are considered to have a gestalt struct u re t hat is di rectly u n derstood . B u t if the preconcepts are al ready structu red , t hen this struct u r i n g should be the same for everyone. A d m i t t i ng that the structures are dependent on our bodies, p reconcepts should be the same across human bei ngs . B u t then that wou l d make t hem ' u n i versal s ' i n the sense t h at t h e st ruct u re o f t hese p reconcepts shoul d be constant across d i fferent c u l t u res-a posit ion t h at L akoff e t al. do not seem to want to take, for t h ey oppose i t vehemently at several p l aces . Of cou rse, Lakoff and Johnson explici tly menti on that the body i s not the only t h i ng t hat structures our con cepts, b u t "a vast backgroun d of c u l t u ral presuppos i t i ons" is i n vol ved as wel L [ Lakoff & Johnson 1 980, p. 5 7 . ] B u t t hen , one needs some explanation o f how c u l t u ral p resuppos i t ions enter the part-whole, up- down , or l i n k preconcepts, w h i ch are so fun d ament aL There i s also the probl em w i t h respect to the genesis of p reconcepts. Tak i n g them as pri m i t i ves com pletely overlooks their developmen t . P i aget 's numerous studies clearly show that al l the bas i c l evel p reconcepts of L akoff and Johnson are a result of i n tellectual construction. For i nstance, chi ld ren do not at once u n derstand the not i on of const rai nt or symmetry t h at i s the basic logic of Lakoff ' s l i n k preconcept . [ P i aget 1 9 3 6 , p p . 323-33 1 .] O f course, Lakoff m i gh t argue t h at he i s making precisely the same poi n t , for the genesi s o f t hese preconcepts i s t h e evi dence t h at t hey are rooted i n experience. B u t then i t seems quite arbi t rary to disti nguish them as preconcepts, since t hey can be analyzed i n terms of other more pri m i t i ve concepts ( P i aget 's schemas ) ; and a case can be made for the abstract concepts that i f their stru c t u r i n g i n terms o f the p recon cepts i s quite often used i n a c u l t ure, and forms the basis of experien cing t hose concept s , as i n ' more i s u p and less i s dow n , ' t hen w hy shoul d we not regard t hem as preconcepts as wel L
To s u m u p , t h e Lakoffian experient i al account a r·t iculates the empirical phenomen a, b u t does n o t exp l a i n t h e m . T hat many of t he convent ional metaph o rs in l anguage h ave p h y s i c a l domai ns as their sou rce i s an em p i r i cal fact . C al l i n g t hem preconcepts m e r e l y captu res t h i s fact . T h at preconcepts arc u n derstood d i re ct l y , i s agai n an em p i r i cal fact ( i gnori n g their genesis ) , as t h ey are not u nderstood as a n yt h i ng else. That abst ract domai ns are u n derstood metaphorically by preconcepts is another empirical fact . T h at an abst ract domai n can be struct ured in d ifferent ways by d i fferent preconcep t s , but n o t arbitrar i ly, i s yet a n o t he r e m p i r i ca l fac t . So far a.l l these features of t he e x p e r i e n t i al account are statements of emp i r ic a l fact . The r e a l problem i s i n explai n i ng how t h i s rest ructuring of abst ract dom a i n s i s possi b l e , w i t hout b e i n g arb i t rary. And why t he abstract domains cannot be u n derstood as such, l i ke preconcepts. T h i s is w here the experient i al approach is si lent .
Chap ter
4:
Cogni tion as In teract ion
1 27
A nywhere L akoff and Johnson come c lose to deal i n g w i t h t h i s p roblem , t hey vehemently assert t h at i t is so-alternati ve con cept ual izations are possible and t hey are not ar b i t rary-bu t say not h i n g w hatsoever to i l l u m i nate how and why it is so. In part i c u lar, their experiential acco u n t is not much help i n resol ving the paradox of i nteraction ism.
Conclusions
4.6
The m a i n obj ecti ve of t h i s chapter h as been to shed light on the problem of the c reat ion of attributes and structures that occurs as a cogn i t i ve agent concep t uali zes its env i ronment . The problem i s in ex p l ai n i ng the apparent paradox t h at comes from mai n t ai n i ng, on one han d , that the attribu tes and structures can be created , an d hence do not reflect some p re-existing ones , and , on the other hand , t h at t h i s c reat ion i s not arb i t rary, b u t is somehow constrai ned by the envi ronment ( wh i c h , n everthel ess, does not h ave a pre exist i n g structure ) . I n resolving t h i s paradox l ies the key to ex p l ai n i ng the p henomenon of the c reation of si m i l ari ty, as we s a w at the end of the last c h ap t e r
I started w i t h a brief review of some e m p i r i cal evi dence s u p p o r t in g both parts of the paradox . We saw that our mi nds do, i n deed , c reate attributes and structures i n the envi ron ment-attributes and struct ures t hat are ' seen ' even when the corresponding s t i m u l i are not present i n the environ ment . Moreover, d i fferent people create d i fferent at tribu tes and structures, and i n d i fferent ways. A s a result , t h e same environment can b e concept ual i zed i n rad i cally d i fferent fashions-as i n the European A m eri can view vs . the N at i ve A meri can views of the u n i verse. B u t t h i s c reation can not be arbi t rary, as the prehi story of flight c l e a r l y a t t e s t s . We also saw that t hough the physiology .
of o u r body a n d hmin does affect cognition , it does not provide set of cond i t ions to
rule out arbitrary
a
su fficient
creat ion of at t r i b u tes an d s t r u c t u r e s .
Then I presented , in some detai l , t h ree d i fferent el abor;,.t i o n s o f t h e i n ter acti o n view , and discussed what each of them h as to say a b o u t its p aradox .
We saw t h at the development of interactionism i n t h e p h i l osop h i cal vei n , K a n t a n d c u l m i n at i n g i n G oo d m an , p ro v i des t h e i l l u m i n at i ng i n sig h t t h at t h e co g n i t i ve a ge n t asserts i t s role i n establ i s h i n g t h e fran<e of referen ce , and then the envi ron ment object ifies t he t r u t h s and fal sehoods with respect to t h at frame of reference. W h i l e t h i s ex p l an at i o n comes c l ose to resolving t h e paradox , it does not do so for t he fo l l ow i n g reason s . Whe11 d i ffe r e n t frames of reference can be u n i fied in a fram el e ss ' wo rl d , ' as in "The Ear t h m o v e s relat i ve to the S u n " t h at u n i fies "The Earth stands s t i l l an d ori ginat ing i n
12
Part I:
Th e Pro blem
the S u n m oves a round i t " an d "The S u n stands st i l l and the Earth moves aroun d i t , " t hen Goodman 's account does not prov i d e a sat i sfactory answer to why one must h ave a frame of referen ce, an d why one cannot k now the envi ronment in a frameless way. T h i s i ssue i s i m portant because if one coul d know t h e env i ronment w i t hout estab l i s h i ng a frame o f reference, t hen t hat woul d become the u n i versal object i ve k n ow ledge of the env i ronmen t , and all questions, with respect to any frame of reference, c a n be answered by con s u l t i n g i t , thereby leav i ng no room for creat ion of any k i n d . And when two frames of reference can not b e red u ced to one another, and Goodm an pro v i des several exam ples of them , it i s not c lear what objec t ifies them, for one cannot say t h at it i s the autonomous struct u re of t he frameless ' worl d , ' as i n the previous case . Fol lowi ng that, I d i scussed P i aget 's construct i v i s m at some lengt h , s i n ce many of i t s i deas h ave played a cent ral role i n t h e development of my ap proach. Though P i aget d i d not expl i c i t l y add ress the paradox of i nteraction ism , his accou nt i m p l i es a clear reso l u t i o n of i t . A subject can act o n an object in a variety of ways, b u t h ow the object responds to any of t h e act ions depends on the obj ect , and i s t h u s determ i ned by t h e env i ronmen t . The equ i l i br i u m of i nteract ion between t h e subject and t he environment ( t h at makes i t so t h at the env i ron ment meets t he expectat ions of t h e subject ) can be ruptured by the e n v i ronmen t , w i t h poss i b ly d i sastrous consequen ces for the subject u n l ess an appropriate accom modation takes p l ace. T h i s i s the key insight of P i aget t h at h as been i n corporated in my framework . F i nally, T p resented the experien t i al v iew of cogni t io n , bei ng developed by Lakoff and Johnson , t hat emphasi zes t he bod i ly basis of cogni t i o n . Acknowl edging the m ass of em p i r i cal data from l i ng u i st i cs t h at Lakoff and his col l eag ues h ave gat hered to strengthen the view t hat our concepts do not reflect some p re-ex i s t i n g m i n cl - i n d cp c n clent s t r u c t u re in t h e env i ronme n t , w h i ch is a H e r c u l e a n t as k in i t sel f, we see, n ever t h el e s s , t h at the experi e u t i <�l a c c o u 11 t
is q u i t e vague, n. n d s o m e t i m e s even con t r n.d i do ry, on how t h e en v i ro n m e n t objec t i fies o u r c o n cc pt u n l s t r u c t u res (to p revent t hem from b ei n g arb i t rary )
without hav i ng a pre-ex ist i ng and m i n d - i n dependent st ruct u re i t self. Thi s i s the problem I t ack le, u s i n g t h e i n s i g h t s o f G o o d m a n a.n d P i a.g et , i n the next chapter .
P art I I A Theory
C hapt e r 5 A n Int eract ionist A p p roach t o C ognit ion : Infor mal O verview
5.1
I ntrod uction
We saw i n the l ast chapter that t here is a p aradox i m pl i c i t i n the i n teraction view of cog n i t i o n . The paradox is in ass i g n i n g rea l i ty the role of c on s t r a i n i ng our conceptual organ i zations, but denying i t a m i nd-i ndependen t , p reconcep t u al ontology and structure. ( If real i ty i s g i ven a preconcept ual ontology and structure , then t h i s becomes the ' un i versal ' k nowledge structure, an i dea that i s expressly rej ected by the i nteraction view. ) We also saw that the theories of Goodman , P i aget and Lakoff & Johnson , each of whom approached i nter act ion ism by a different route, fai l to resolve this p aradox ex p l i c i t ly, t hough some of them come quite close to doing so. You might also recal l , f ro m C h ap
ter 3 , t hat resol v i n g t h i s pL!.radox i s necessary to gi ve a. satisfactory account of si m i l ar i ty- c reat i n g m e t ap h ors , and t o ad d ress an analogous paradox raised by the phenomenon of
c reat i on
of
s i m i l ari ty.
In t h i s ch apter an d t h e nex t , T l a.y out a formal fra m ework fo r the i n terac t i o n view of cogn i t i o n t h at i s specific al l y art i c u l ated to deal w i t h its i m p l i c i t p a r adox. This chapter i s concerned w i th i nt r o d u c i n g all t h e k e y con cepts o f my a p p r o a c h i n fo rmal l y an d i n t u i t i vely, and a precise mat hemat i c al t reat ment is t aken up in t h e next ch apt er . It i s h oped t h a t the d i scussion of this ch ap ter will mot i vate y o u to pres� on through the form a l detai l s o f the next chapte r , and will m ake them easier to d i gest . To el ab orate t he exact n a t u re
down i t s two com ponents . O n
of i nteraction , one
one s i d e of interaction
m u s t begi n by p i n n i n g
are t he
i nternal repre-
Pari II: A Theory
1 32
sentat ions of t he cog n i t i ve agent , w h i ch I refer to as concept n elw01·ks . Now t here is no problem i n art i c u l at i ng precisely what the concept networks are . T hey have been variously characterized as sch emas by P i aget , as n e t wo rk models by Hesse [ 1 974, Chap. 2] , as cogn itive doma ins by Scott et al. [ 1 979] , as fonn by B ateson [ 1 979] , as m e n tal spaces by Faucon nier [ 1 985] , as m e ntal m odels by Hol l an d el al. [ 1 986] , an d as idealized cognitive models by Lakoff [ 1 987] , to mention a few . For my p urpose here, com b i n i ng P i aget 's schemas and C assi rer's symbol s , I ch oose a somewhat general characterization of them as symbol i c systems h aving an operational st ructure, w h i ch correspond to al gebras . O n the other side of interaction is real i ty, w h i ch i s a d i fferent c u p of tea. h ave al ready emphas i zed the paradoxi cal posi tion t h at the i nteraction view creates w i t h respect to the ontology an d struct u re of real i ty. To resol ve this paradox , I first i nt ro d u ce the s e ns o ri m o t o r d a t a set, w h i ch i s reality that i s made avai I a b l e for conceptuali zat ion t h rough the sensorimotor apparatus o f the cog n i t i ve agent . T h e n I argue that w h i l e the ontology o f the sensori motor data set i s deter m i ned by the cogn i t i ve agent ' s percept ual an d motor apparat u s , i t s s t r u c t u re ( as seen from t h i s ontology ) i s determ i ned by real i ty. The sensori motor data set m ay not be cogn i t i vely visi ble to the cog n i t i ve agent ; we cannot ' see' the i m age on our ret ina, even t h ou gh it form s the raw data for our visual system . Fol lowing P i aget 's action-oriented approach , the sensorimotor data set i s also for m a l i zed as an algebra. I
Then I i nt rodu ce the concept of cognitive 1·elations, w h i ch are l i n ks t hat connect concepts i n the concept networks w i t h parts of the sensori motor data set . S i nce the sen sori motor data set i s rooted in reali ty, cogni t i ve relat ions become the l i nks between the i nternal concepts of the cog n i t i ve agen t a n d real i ty. Moreover, fo l l o w i ng C assi r e r , T m a i n t a i n t h at i t i s o n l y by fo r m i n g a cogn i t i ve rel at i o n - by i n s t an t i at i ng concepts ( s y m b o l s ) of a. con cept network-t h a t real i t y acqui res an experient i al ont ology for t h e cog n i t i ve a g e n t . I refer to this experien t i al ontology as the e n v im n m e n t . Thus , it is a cogn i t i ve relat i on t h at m akes a concept network ·m e a n ingful and i t i s a cog n i t i ve relat ion that bri ngs real ity w i t h i n the cog n i t i ve grasp of the c o g n i t i v e agent i n t h e form of an env i ron ment . A
cogn i t i ve relat ion i s formed by the cogn i t i ve agent.
And
si nce
it
is a
cog n i t i ve rel ation t h at g i ves an experient i al ontology to t he e n v i ro n ment , i t
fol l ows
ontology of
envi ronment i s determ i ned
by the
cogn i t i ve
agent . H owever, the struct u re of the en v i ronment w i t h respect to t h i s ontol t h at t h e
the
ogy i s deter m i ned by real i ty ( w h i ch act s t hrough t he autonomous structure of the sensori motor data set s ) , and is external to t he cognitive agen t . In this
Chap ter
5:
Cogni tion : Informal O verview
1 33
observat ion lies the key to resol ving the paradox of i nteraction i s m . A concept network i nstant i ated by a cogn i t i ve relation i s referred to a s I n a cogn i t i ve model , two autonomous structures can be d i s t i ngui shed . One is t he structure of the concept network ( determi ned by the cogni t i ve agent ) , and the other i s t he structure of the e n v i ronment ( determi ned by reali ty ) as seen from the experiential ontology created by the cogni t i ve relation . Ideal ly, one wou l d l i ke t he two structures to be the same. A t least t h i s i s the goal t hat the cogni t i ve agent must strive for , if i t wi shes to use the cogn i t i ve model to m ake useful pred i ctions about the envi ron ment . I refer to the struct ure p reserving characteristic of some cogn i t i ve m odels ( and cogni t i ve relat i o n s ) as coh e re ncy. a
cogn itive m odel.
H ow can the cogni t i ve agen t m ai nt ai n the coherency of i ts cogn i t i ve mod els? I t cannot change the struct u re of the env i ronment with respect to any gi ven ontology. The only parameters u n der i t s cont rol are the structure of t he con cept networks and the ontology of the env i ronment ( how the net works are i nstanti ated v i a cogni t i ve rel at ions ) . Correspondingly, l i n t roduce two mechanisms t he cogni t i ve agent might use, i n d i v i d ually or i n concert , to keep its cogni t i ve models coherent . One m e c h a n i s m , cal led a cco m m odation, work s by changi ng the structure of t h e concept network , w h i l e keepi n g the cogni t i ve relation ( and the experiential o n t o logy of the environ ment ) fixed . The other mechan i s m , called p mjection, works by keepi ng the structure of the concept network i nvariant, but modifying the cogni t i ve relation , thereby changing the experiential ontology of the envi ronment , so t h at i t s struct ure ( wh i c h is determ ined by reali t y ) can become coheren t w i t h the structur e of the concept networ k . For i nstance, m a p p i n g a terrai n i s a n accommodati ng process. T h e mean Lween
' water' are kep t fixed , b u t t h e relat ions bo
concepts a r c altered t o reflect the s t at e of affai rs in the Pnviron· mont . Notice, however , t h at i t i s t h e cog n i t i ve age n t who d el e r m i nes w h at ' land ' and ' water ' mean . L i nes of l at i t u de an d longi t u de , o n the other h an d , are exam ples o f projection. T h e s t r u c t u re o f t h e concept n et wo r k i s fixed and the environment i s g i ve n an o n t o l o gy accordi ngly. Reali ty, howeve r , con strains the possible ontologies . That is, s i n ce it is real i ty t h at determines the structur e of t he environment w i t h r e s p e c t to a.ny given ont o l o g y , if the co g n i t i ve agent wishes to see a certain s t r u c t u r e i n t h e en v i ron men t , :several possible ontolo g ies are r u l e d out by real i ty, for t h ey do not resu l t in the req u i s i te structure. The lines of lat i t u de and longi tude c a n be i n st a n t i ated in more than one way, but the autonomous s t ru c t ure of r e a l i t y r u les o u t m an y p o s si b i l i t i es . For i nstance, New York C i t y, C o p e n hagen and Tokyo cannot
ings of concepts l i ke ' l an d ' and t heBe
Pa. r i II: A Theory
1 34
be all assigned the same l at i t ude. Moreover , once the system of reference i s put i n place, whether t w o gi ven p l aces h ave the same l at i t ude or n o t i s no longer a matter of arbi t rary deci sion by the cog n i t i ve agent , b u t i s a m atter of object i ve veri fication . Thus, accom modation is the p rocess by w h i ch t he environment affects ( ac t i n g t h rough the sensori motor data set ) the structu res of the cogni t i ve agen t ' s concept networ k . A n d proj ect ion i s the process by w h i ch the cogn i t i ve agent affects t he struct u re seen i n t he environment . I am deliberately using the word ' affects' and not ' deter m ines' here because in each of the t wo processes , both the cogni t i ve agent and the environment p l ay a role i n determ i n i n g the structure t h at results from the p rocess. The d i fference l ies only from the perspecti ve of an outside observer , whereby p roj ection can b e viewed ' as i f ' the cog n i t i ve agent i s the origi n ator of the perturbations a n d the envi ronment t h e reci pient ; an d vice versa for accom modat ion . C learly, my p roj ection corresponds to P i aget 's assi m i l ation . Why, then , am I coi n i ng a new term ? The reason is t h at P i aget 's ass i m i l ation h as been gi ven a very wide i n terpretat ion. A s I pointed out in the last chapter, P i aget h i mself uses i t i n at least t wo d i fferent ways: biological assi m i l ation , a mechan i sm by w h i ch an organ ism absorbs energy from i t s envi ron ment and t ransforms it to a form t h at i t can use, a fam i l i ar example being i ngestion ; and behavioral , or cogn i t i ve ass i m i l ati on, w h i ch is closer to my proj ection mechan i s m . Moreover, cogni t i ve ass i m i lation i t self i s given a b road scope: for i n s t ance, P i aget argues t h at i t i s pri m ar i ly responsible for t he formation of memory. ( See Pi aget [ 1 9 76] , p . 1 4 1 . ) Though I do not necessari l y rej ect the i dea t h at the very same mech an ism can in fact u n derlie such seemi ngly d i ve r se processes , I do not wish to see my p r oj e c t i o n w h i c h i s g i ven a very -
prec i s e
m ean i n g i n my app roach t o i n terac t i o n i s m-bu rdened by having to
al l . course, t h i s i s o n l y a b road overv i e w , and i n t h e rest o f t h i s c h apter I elaborate my i nterac t i o n view o f cogn i t i o n by mea.n s of exam ples, d efi n i t ions, a n d depi ctions. I fi r s t present a s i mple, yet surprisingly r i c h example to i l l ustrate al l t h e k e y concepts of my framework i n Sec t i on 2 . I n the s u b
ex p l a i n t h em Of
se q u e n t t h ree sec t i o n s J e l aborate u p o n conce p t n e t work s , envi ronments a n d sensori motor d a t a sets , and c og n i t i ve relat ion s . I n Section 6 , T examine the mec h an i s m s of p rojection and accommodation i n more dept h . In Sec t i on 7, I p resen t some feat u res of cogn i t i ve models, such as ' groupi ngs ' i nduced on the environment , and i n t roduce some useful terms. I n Sec t i o n 8 , I i n t r o d u c e t h e concept of a ' l ayered c o g n i t i v e system , ' and point out h ow multiple ' worl d s , ' i n the sense of Goodman , c a n be created. Finally, i n S ec t i o n 9, I s u mmarize
Ch ap t er
5:
sensory vector:
Cogn i t ion : In form al O verview
v
v
11111
00100
1 35
/ v 1 1 100
FIGURE 5 . 1 : Sen sory organ of Spinner. The ' eye ' consists of five cells that work i n an on-off fashion. The off cells are shown as darkened. A line (or any other object) in front of the eye forms an image on it by casting a shadow and turning off certain cells. The ' state s ' of the eye are represented by sen sory vectors. The three examples here show the image cast on the eye by l ine s in different orien t ation s , and the corresponding sen sory vectors.
t he mai n t heses embodied in my framework of i nteract ion i s m .
5.2
A n Example
To start w i t h I i n t ro d u ce a s o m e w h at art i fi c i al , b u t n o n e t h eless i n teres t i n g and r i c h e x amp l e to i n t ro d u ce al l t h e va r i o u s features of my fr a m e w o r k of i n terac t i o n i s m . Let u s t ransport ourselves to the two d i m e n s i o n al w o r l d of Edwin Abbot t 's Fla tla n d . We fi n d o u r se l v es i n an area o f Pia / la n d t h at i s i n h ab i ted by s e v e r a l strai g h t- l i nes and a, c o g n i t i v e agent named S p i n n e r . ,
w i t h i ts w or l d The sens o ry organ consists of five l i g h t sen s i t i ve cel l s , c l o s e l y packed t ogeth e r a n d arranged i n a row , as shown i n Figure 5 . 1 . Eac h cel l works i n an on- off fas h i o n mean i ng that w h e n t h e l ight i m p i ng i n g on i t exceeds a cer t ai n t hreshold t h e n t h e cell t u rn s 'on , ' r e m a i n i n g ' o ff ' o t h e r w i s e . The cel l s respond i n s t an t l y : t h a.t i s , a s s o o n as the l i ght i m p i n g i n g u p on a cell exceeds its threshol d , the cell t urns o n , and w h e n t h e l i g h t l evel fal l s below i t s t h resho l d , t h e cell t u r n s o ff i m medi ately.
S p i n ner h as very s i mple sensory and effectory organs that ena b l e i t to i n teract .
,
U n i form d i ffu s e d
l i g h t p e r vades a.l l Fla tla n d .
W h e n a s t raight - l i ne is in
1 36
Part II: A Theory
fron t of S p i n ner's 'eye, ' i t casts a shadow on the eye and turns some cells ofT. Obviously, w h i c h cel ls get t u rned off depends on t he length of the l i ne as well as its posi tion and orientation w i t h respect to t he eye. A few s i t uations are shown in F i g u re 5 . 1. We can ignore t he effect of the di stance between t he eye and the l i n e . A l so, i t is assumed t h at all the l i nes h ave a small t h i ck ness, and the cells in the eye are closely packed toget her, so t hat w hen a l i ne is perpen d i c u l ar to t h e eye, exactly one cel l in the eye is t u rned off. I represent the i m age formed on the eye at any t i m e by a fi ve bit b i n ary string. The b i t s , from left to righ t , correspond to the cells of the eye, also from left to right w i t h t he eye facing u p . A 0 in any b i t position means t h at t here i s no i m age formed on the correspon d i ng cel l ( i t i s t u rned on ) and a 1 i n any b i t posi tion mean s t h at an i m age i s formed on t he corresponding cel l (i t h as been t u rned off ) . I refer to a n y such binary string as a s en s o 1·y vector. Thus, t h e sen sory vector represents t he output of the fi ve cells i n S p i n ner 's eye i n any gi ven s i t u at ion . I n Figure 5. 1 , the sensory vectors are shown below t h e correspondi ng i m ages .
The five cel ls i n S p i n ner's eye also consti tute i t s e ffectory organ . S p i n ner can emit a smal l jet-stream of ai r from any one ( b ut not more t h an one) of t hese cel l s at any time. This st ream can only be em i t ted i n short bursts, but the i ntensity of a b u rst can be va ried somewhat by S p i n ner. The jet-stream can cause t he line facing the eye, if t h ere is one, to be rotated or p ushed back , as shown in Figure 5 . 2 . A s for the sensory organ, act i vat ion of t h e effectory organ a t any t i m e i s represented by means o f a n effecto ry vector. A n effectory vector also h as fi ve positions correspon d i n g to t h e fi ve cel ls, and the val ue i n each position i n d i cates t h e input to the correspond i n g cel l t hat determi nes the i ntensi ty of t h e b u rst em i t ted by t h at cel l . However, i n s t e a d of a l l ow i n g only 0 or 1 i n any p osi t i o n , I allow any n u m ber from 0 t.o 3 . As o n e m i g h t exp�d , ll. 0 i n any p os i t i o n mea.n s t. b ll.t t h e correspo n d i ng cel l i s i n ac t i ve as an cffectory o r g a n . A non-ze ro n u m b e r in a pos i t ion means t hat t he corresponding cell is act i ve , where the magn i t u de of the number approx imately represents the i n t e n s i t y of t h e b u rst . I say ' a ppr o x i m a t e l y ' because w hereas a 2- b u rst i s st ronger t h an a 1 - bursl a n d weaker t h an a 3 - b u r s t , i t i s not n ecessari l y t w i ce as s t ron g as a 1 - b u rs t . I leave i t at t h at because to m ake t h i ngs any more precise wou l d r e q u i r e a com p r e h e n s i v el y worked out physi cs o f motion for Fla tla nd, w h i c h m ay be an i nteres t i n g t ask in i t self b u t an u n necessary and d i s tra.cti n g one for this e x am p l e . Val i d effectory vectors are only t h ose t h at h ave zeros i n at least fou r position s . Effectory vectors for the acti vat ion patterns in F i g u r e 5.2 are shown next to them .
Ch ap t er 5: Cognition : Inform al O verview
1 37 transformed state
initial state
t
effectory vector:
v
effectory vector:
/ t u
(1)
(2)
>
00002
>
03000
" u
'-------,>
(3) effectory vector:
- ,
00 1 00
-
FIGURE 5 . 2 : Effe c tory Organ of Spinner. The cells in the eye double as effectory organs by emitting a j e t s tre am (shown by an arro w) of air. The jet s tream emitted in bursts, may cause the line fac ing the eye to rotate. S pinner can emit a burst from only one of the cells at any one time, but the burst can be emi tted in three possible s trength s. Here, three examples are shown to demonstrate how Spin ner may use its effect ory organ to transform its world .
Part II: A Theory
1 38
Not i ce t hat the sensory and the effectory organs of S p i n ner restrict i t s world v i e w consi derably. The sensory organ allows for o n l y t h i rty t w o d i f ferent states , and whatever world Spi n ner h appens to be i n , i t i s red uced to one of these states . S i m i l arly, the effectory organ of S p i n ner allows fi fteen possi ble act i ons that it can take in any s i t uation at any t i me . Thus, the sensori motor apparat us m akes every world m an i fest to S p i nner in a certai n way. I refer to t h i s m an i festation as the s e ns o rim o t o r da t a s e t . A sensori motor data set h as a n o n t o logy, w h i ch i ncludes t he sensory states a n d the actions of S p i n ner, and a struclU1·e, w h i ch shows how the sensory states are affected by t he actions. Note here t h at t hough the ontology of any sensori motor dat a set is com pletely determ i ned by the sensory and effectory organ s of S p i n ner, its structure i s extern a l to S p i n ner, and i s completely deter m ined by real i ty. For i n stance, giv e n t hat the i m age on the eye of S p i n ner at some t i me is 1 11 1 1 and it act i vates its effectory organ as 00002, the i m age t h at is subsequently formed on S p i n ner's eye is determi ned by the external reali ty. T h ree exa m ples are shown in Figure 5 . 3 . In each case it is the n at u re of the object facing S p i n ner t h at determi nes the outcome of t h i s action . Though the correspondence between t he sensory st ates and t he t h i ngs i n i t s world i s ri g i d ly fi xed i n t h e c ase o f S p i n ner, a cogn i t i ve agent m i ght be able to ch a nge it by alteri ng the b i as of its sensorimotor apparat us. But even t hen , the struct u re of the sensori motor data set resul t i ng from any gi ven b i as of the sensori motor apparat u s is deter m i ned by reali ty. I elaborate t h i s point later i n Section 8. Now assume t h at t he world of S p i n ner consists of various zones in the form of u n i form p a rallel strips, as shown i n Figure 5 . 4 . The w i d t h of each zone exactly equals the length of S p i n ner's eye, and t he boundaries between zones run perpen d i c u l ar to the axi s of the eye. S p i n ner can occupy any one zone at a t i m e , and h as the fu l l view of the part of the zone faci ng t he eye. I t cannot c h a n ge i t s orientat i on w i t h respect to t h e i n t e r z o n e boundaries , but i t can hop from one zone to anot her. This hop is, h o we v e r , a d i s c reet event so t h at S p i n ne r can never have a view of more than one zone at any time. -
Each zone i s i n h ab i ted by exad l y one s t raig h t l i n e and t he length of each line is equal to the w i d t h of i t s zone. S i nce all zones are of t he same w i d t h , i t means t h at a l l l i nes are of t he same length a l s o T h u s w h e n S p i n n e r is i n a zone, and the l i n e occupy i ng that zone i s faci n g i t and i s parallel to its eye, t h e i m age of t he l i ne covers all fi ve cel l s ; t hat is, t he sensory vector is 1 1 1 1 1 . The l i nes can move around i n their respecti ve zones . A l i ne can turn around i t s m i ddle poi nt to any degree and i n a ny d i rect i o n , and can move horizontal ly and vert i cally, as long as none of t he mo ve m en t s cause any part -
,
.
,
Chapt er
5:
Cogn i t ion : Inform al Overview
1 39 transformed state
initial state
t
(1) effectory vector:
v 00002
L::J t
(2) effectory vector:
v 00002
Q
(3 ) effectory vector:
v 00002
0 v
FIG URE 5 . 3 : The three examples s hown here demons trate that the ' s tructure ' of the sensorimotor data set is rooted in the external world. In all three cases, t h e initial state of the eye and the activation of the effectory organ are the same . Yet, the transformed state, which depends on the nature of the object facing the eye, i s ctifferen t i n each case.
Part II: A Theory
140
/
�
:\_/: I
FIGURE 5 . 4 : The Environment of Spinner. It consists of zones in the fom1 of paral lel strips. Each zone is inhabited by a line. The lines can tum around the i r middle point a n d move vertically a n d horizontally, as l o n g as t h e movements keep them completely inside their respective zones. Spin ner can hop from one zone to another, but t h a t h ap pen s as a discreet ev e nt . Thus, Spinner can never view more than o n e zone simultaneou sly.
Chapt er
5:
Cogn i tion : Informal O verview
141
of the l i n e t o ven t u re out o f its zone. The l i nes love to spin aroun d , and can often be seen dancing w i l dly. S p i n ner can also cause the l i ne in its zone, i f t here is one facing it, to spi n . I n fact , S p i n ner loves doi ng t h at , ( and s o d o t h e l i nes , ) s o m u ch s o that over the generations ' mental structures' have evol ved in Spin ner that reflect its u n derstan d i ng of t he behavior of the l i nes , as wel l as its ways of affecti ng t h i s behavior. I show some of t hese mental structures, or co ncept n etw01·ks as I refer to them from now on, i n Figure 5 . 5 . C N 1 i n 5 . 5 ( a) shows Spinner's concept network for m ak i n g the l i nes spi n ; CN2 i n 5 . 5 ( b ) is a concept network for u n derstan d i ng the l i nes ' behavior when t hey spin by t hemsel ves ; and C 3 i n 5 . 5 ( c ) i s a concept network Spi nner uses for centering a l i n e i n its zone i f i t i s off-center. A concept network i s essentially a struct u red set of concepts. I m ake a d i s t i n ction between symbols ( obj ect-concep t s ) and operators ( fu n ctional concep ts ) . I n the concept network CNl, for example, ' v l i ne' and ' h l i ne' are symbols, whereas ' qt ur n' and 'e- l t u r n ' are operators . An operator speci fies how a symbol can be derived from other symbols. Thus , the operators of a concept network connect the s y m b o l s i n specific ways, t hereby i m parting the concept network with a si1·u c t u re . A l l concept networks are ful l y i nternal to the c ogn i t i ve agent i n t h at i t c a n access a n d m an i p ulate t hem a s n ecessary. Concept networks are best seen as p o t e n tial re p res e n t a tions. That i s , a s shown i n Figure 5 . 5 , the concept networks do n o t yet mean anyt h i n g or refer to anyt hing. ( Though , since l mentioned the i ntended p u rpose of these concept networks above, you m ay have guessed what the ' convent ional ' r e fe r e n t s of the conc<"pt.R of Figure 5 . 5 m ight be. lf not , i t w i l l become clear s h or
t l y. )
of i n t e rp reting t hese concept networks. A c o n c e p t network can b e i n terp reted in a wor l d by asso c i at i n g i t s con ce p t s w i t h parts of the wor l d . Of course, s i n c e Spinner does not h ave d i rect e p i s t e m i c access t o the wor l d , t h i s process i s necessari ly medi ated by the senso r i m otor data s e t . T h i s m u ch u n d erstoo d , J now come t o t h e p rocess
w
I n F i g ure 5 . 6 , I show how the concept n et w o r k C N 1 corres ponds to t h e o r l d o f S pi nne r via i t s sensorimotor data set . Object- concepts of the concept
correspond to various l i n es in the wor l d t h rough th e sensory organ . Operators correspond to the actions, via the e ffe c t o r y organ t h at can change the p os i t ion of a l i ne, thereby altering the sensory vector. The correspondence between the concept n e t w o rk and the wor l d of S p i n ner is referred to as a cogn itive 1·ela t ion a n d the i nterpreted concept network i s rderred to as a network
142
Part II: A Theory
(a) Concept Network CN l : For makin g the lines spin .
0 :;j
r4 - line
l- t
h-
lin
'� �
r- t�ur
(b)
r - turn
..:;:
/ - turn
- r3 -line
..:;:
r- turn
/- turn
r- tur n
� � /(,��:ne
:;: r2 -lin
r- turn
�
- turn
1 - turn
/ - turn / - turn
/- turn
r- turn
r- turn
14-line ..:;: E---)o - 13 -line E..:;:--- 12-line
Concept Network CN2 :
For understanding
- tL
w h e n lines spin by t h emselves.
2line h l - t u rn > 3 1ine h2 - turn > 4line hZ - tu rn > hline
(c) Concept Network CN3 : For
c
e n t eri n g
the lines.
FIGURE 5 . 5 : Concept Networks of Spinner. All operators are shown as arro w s a n d t ake o n e argument. The result of applying an operator is t o generate the symbol at the tip of the arro w from the s ymbo l at its base.
Chap t er
5:
Cogni Uon : Informal Overview
11111
/
143
\
/
01 1 10
.......
01 1 10 00100
v
v
Ct:J
v
hline
r-tline
1-tline
vline
1' 00020
t 00030
03000t
v
v\_ )V
e - rturn
qturn
"\../'
020001'
v e - lturn
FIG URE 5 . 6 : An interpretation of the concept network CN l . S y mbol s of the concept n e tw ork correspond to the objects of the environment, and the operators correspond to the actions th at might change these objects. In this case, actions are caused by the effectory organ of Spinner. Sensory and effectory vectors corresponding to the image on the eye and actions of Spinner are also shown .
Pari II: A Theory
1 44 cogn itive m odel.
Two t h i ngs should be noti ced i m medi ately about t h i s i nterpretat ion . F i rst of a l l , the symbols ' 1 - t l i ne' and ' r- t l i ne' correspond to two d i fferent l i nes in the world-or what is the same, a l i ne in two d ifferent orientat i on s-vi a t h e same sensory vector 0 1 1 1 0 . Thus, t h e cogni t i ve model effect i vely allows S p i nner to disti nguish between two di fferent s i t uations i n the world t h at both form the same i m age on its eye. Obviou sly, i t i s the effectory organ of S p i n n e r t h at i s making t h i s di s t i nction possi ble. S i n ce the orientation of a l i ne i s t h u s detectable b y t h e combi ned sensory a n d effectory organs o f S pi n ner, I represent t h i s i n format ion by p u t t i ng a n appropriately t i l ted l i ne above the sensory vector when necessary. This notat ion i s shown i n Figu re 5 . 6 . Secondly, not i ce t h at the operator ' q t u rn ' corresponds to t w o d i fferent act ions of S p i n ner-those gi ven by effectory vectors 03000 and 00030. These two act i ons a re said to be gro uped by the cogn i t i ve model , si nce seen from C N l , their effects cannot be d ist i ngui shed . This phenomenon of grouping can be evidenced in m any facets of percept ion and cogn i t i o n . T h e i n t er p re t at i o n of t he concept network creates a n e x pe r i en t i a l ontology of the worl d for S p i n n e r . T h i s experient i a l ontology is called an e n viro n m e n t . The counterparts of the symbols and the operators , respecti vely, are referred to as the o bjects and t h e tmnsformations of the envi ron ment. Thus, one can v iew t he process of interpret ing a concept network as t h at of estab l i s h i n g a. correspondence between the symbols of the concept network and the objects of the envi ronment , and between the operators of the concept network and the t ransform a t i ons of the envi ronment . However, it must al ways be remembered t h at t h e objects and t h e t ra n s format i o n s in the e n vi r on m e nt come to exist o n l y t h ro u g h t h e i n t e r p r e t a t i o n of t h e concept network, and d o n o t exist i n dependently of t h e i n terpretat i on . T h i s i s n o t to say that real ity does not e x i s t p r i or to c o n c e p t u a l i z a t i on , but only to say t hat the ont ology of reality does n o t exist prio1· to co n ceptualiza tion . This aspect of my framewor k essent ially echoes t he t heme o f C assi rer. e m p h a s i z e d is that t h oug h the c o g n i t i ve <-�.g ent de t h e envi ronment by i nterpret i n g a concept n e t w o r k , t h e s t r u c t u re of t h e envi ronment w i t h respect to t h i s ont ology is determined by reali ty. This poi nt has its root in a s i m i lar observation m ade earl ier w i t h respect to t h e sensori motor d a t a set . T h e t ransformat ions o f t h e e n v i ron m e n t are grou nded in reali ty, and must be d i s t i ng u i s h e d from t h e operators i nternal to t h e cogn i t i ve agent. Even t hough the transform ations are actu ali zed by i nterpret i n g t h e operators , once brought i nto existence, t h ey affe c t objects in t heir ow n way, and need not follow the operat ional structure of
A nother t h i ng to be
t e r m i n e s the o n t o logy of
Chap ter
5:
Cognition : In form al O verview
145
/
0 1 1 10
11111
� ./
( 03000, 0003 0 }
' 01 1 10
00 1 00
�
00
FIGURE 5 . 7 : Spinner ' s ' world-view ' a s seen from the concept network CN 1 under the interpretation of Figure 5.6. The symbol s are replaced by the corresponding states of the environment, shown here as sensory vectors with tilted lines on the top to represent orientation of the lines, if relevant. The operators are replaced by corresponding transformations, which are activations of Spinner' s effectory organ, shown here as effectory vectors. Notice that the transformations 03000 and 00030 are ' grouped ' together, and are not distinguished in thi s ' world-view. '
the concept networ k . It is always up to r eality to
s t r uc t u re t h e
envi ronment .
Of course, a cognitive agent might be able to change the
ontology of
the environment by i nterprd i 11g a d i fferent co n ce p t n e t wor k , or i11ter p re t i n g the same c o n c ep t n e t w o r k d i ffe r e n t l y, t h e r eby fo r cin g real i ty to res t r u c t u re t h e envi ronment w i t h respect to t, h i s new ontology. In fac t , as I argue i n C hapter
7,
i n this res tr uc t u ri n g
l i e s the key t o metaphor.
The structure of S p i n ne r ' s e n v i ronment w i t h respect to
the o n t o l ogy
ated by t he i nterpret at ion of Figure 5 . 6 is shown in Figure 5 . 7 . T h i s struc t ure happens to be i somorphic to the struct u re of the concept network C N l
cre
[F i g ure 5 . 5 ( a)] , but t h at m i ght not necessar i l y be t h e case . W h e n t he t wo s t r u c t u re s of a cog n i t i ve model ( o r cog n i t i ve relat. i o n ) are i somorph i c , I cal l t h e model ( o r t h e r ela t i o n ) coh erent. O bviously, a cogn i t i ve model must.
b e coherent. i f t h e cogni t i ve agent i s goi ng to u s e i t to p la n i t s
actions and
Part II: A Theoq
146 s uccessfu l l y p red ict changes in the environ ment .
Thus, what the cogn i t i ve agent ' sees ' i n the worl d t h r ough a coherent cogn i t i ve model i s an i somorphic copy of the concept networ k . This is a consequence of my assum ption t h at the only way to give an ontology to t he world is by i n terpreti n g a concept network in i t . A n d on ce such an i nterpretation is made, t he ontology of t he envi ronment is fixed . Its struct ure is then also fixed by real i ty, and this i s t he environment t hat the cogni t i ve agent experien ces i n the wor l d . A n d because the cogn i t i ve model i s cohe r en t , t h i s experienced structure o f t h e worl d i s i somorphic t o t he structure o f t he concept network .
I t must be emphasized here t h at coherency, as I have defi ned i t , i s a. characteristic of cogn i t i ve models and cog n i t i ve relat ions and not of concept networks. Therefore, coherency should not be confused w i t h the i n ternal consistency of sy m bo l ic systems, as i t d i rect ly relates to t he autonomous structure of reali ty.
Coher e ncy of cogn i t i ve models , however, is not somet h i ng a cog n i t i ve agent can cogn i t i vely ve r i fy. For i n stanc e , t h e struct u re of Figure 5 . 7 is not d i rectly accessi ble to S p i n ner, except via. expe r i m e n t at ion . A n d alt hough experimentation can prove some cogn i t i ve models to be i n coherent , i t cannot prove them coherent. There i s al ways the possi b i l i ty that the envi r onment , u nbeknownst to S p i n ner, has changed so t h at i t no longer h as t he same structure w i t h respect to the ontology estab l ished by S p i n ner. In fac t , I i nt rod uce such a. poss i b i l i ty j ust a l i t t l e bit later. A
w ord
needs to be said about t ransformat ions. I n F ig u re 5 . 6 , the t rans
formations t h at the o p e r o. t o r s of CN 1 are m ade to correspond to are t he actions of t h e cogn i t i ve agent i t se l f. Ho we ve r , this m i ght uot always b e t h e case. Fo r i nst ance, in an i nterpretat i o n of C N 2 ( not sh o wn h e r e ) , t h e t ra.ns formations co rr e s pon d i n g to its operators a r e caused b y the l i n e s t h em selves. Moreover , in cert a i n situat ions t here m i ght not even be any agent causi n g ' a t ra n s for m a tion , an d i t m i g h t be m e r e ly t he c o g n i t i v e agen t s wa.y of un derst anding changes h appen i n g i n the environment . Th u s , operators of a conc e p t network ca.n represent act ions of t h e cogn i t i ve agent as wel l as ac t i ons of other ' real ' or ' h y po t h e t ic a l ' agents. This is t h e reason T chose to call the coun t e r p a r t s of the operators ' t ransformations' rather t h an ' act i on s . '
Next I i n t rod uce t he notion of c onven t i on al i nterpretat ion. I f a. concept network i s h abit ually i nte rpre ted in a certain way, t h at i n te r p ret at i on ( and t he res u l t i n g cog n i t i ve model ) i s called conventio n a l. The i nterpret ation of F igure 5 . 6 can b e d ubbed conventional, if we assume t h a t that t h e con ce p t network C N l i s usually i nt e r pr et ed t h at way by S p i n ner. A concept ne t wor k
Chapt er
5:
Cogn i t ion : Informal O verview
I 0 1 000
/
147
1 0000
1 0000
\:; \b \:; b v b v ;
h i- t urn
:
�
h2 - turn
2 l i n e ----�3 line
\ \J :
0 1 000
\b :
v :
t rn __� >3 lin e ll i n e __h_l_ : -_u
00 1 00
\1/ :
. .
�
:
: 4 line
h 2 - t urn
00 1 00
til
\j, �
�
: e > h lin
v
.
' '
h _2_-_ tu _r_n� > 4 1� ne
_ _
!
tu h_2_-_ n_-il' _r_ > h lin e
_ _
FIGURE 5 . 8 : Two different interpretations of the concept network CN3. might be genui nely ambiguous in having more t h an o n e con ven t i o n a l i n t e r pretation; j u st as a word can be ambiguous by having more t h an one l i teral
mean i ngs. For i n s t ance, c o n ce p t n e t work C 3 h as several i n t e r p retat i o n s , t w o of w h i ch a r e shown i n F i g u re
5.8. M o r eover
all of
t hese m ight well be
p referred i n t er p retat i o n s if S p i n n er i s habit uated t o all of t hem . ,
So far we h nvt" kepl S p i n n e r i n i t s n a t u r al worl d , a n d t h erefore it is n o t s urpri s i ng t h il.t a.l l t h e i n t erp r e t il. t i o n s of i t s con cP p t networks were conven
t i onal . Now let u s t r a n s p o r t it t o an al i e n worl d t h at
is
very s i m i l a r to i t s
ow n , except t h at all t h e l i nes are s l i g h t l y s m al l e r . T h e l i nes i n t h i s n e w worl d
are
s u c h t h at w h en t hey are parallel t o the eye of S p i 11 n e r , t h e i r
o n ly fou r cel l s .
li n es
.
W h at does
shadows
cover
In e ve ry other way, t h ey beh ave j u s t l i ke t h e fi ve cel l l o ng
S p i n ne r do i n t h i s new wor l d ? It s t i l l h as i t s c o n c e pt networks.
Part II: A Th eory
1 48
B u t t hey no longer h ave convent ional i nterpretat ions. lf we s t i ck to t he old i nterpretat ions, t hen t hey are no longer coherent , as t he reader can eas i ly ver i fy. I n order to keep t h em coheren t , S p i n ner i s forced e i t her to rei n t e rp re t its concept networks , thereby changi ng the ontology of t he envi ron ment ( and i t s structure ) , or to restru c t u re them . I refer to the process of reinterpreti n g ex i s t i n g concept networks a s p roject ion a n d t he process o f 1·est ructuring ex i s t i n g concept net works-of which creat i n g new concept networks is a spec i al case-as a cco m m oda t i o n . I n projection , the structure of the concept network i s kept i nvar i an t , and t h e correspondence between the parts of the network ( i ts concepts ) and parts of the envi ronment ( i ts objects and t ransform ations) i s varied u n t i l a coher ent fit is reached . A proj ecti ve i nt erpret at ion of the concept network C N l i n the new en v i ronment i s shown i n Figure 5 . 9 ( a ) . The p rocess m i ght work by first i n terpret i n g a smal l set of symbols and operators and t hen extend i ng t h i s correspon den ce coherently. For i nstance, in t h i s case, i f ' h l i ne' is i nterpreted as the sensory vector 0 1 1 1 1 and 'e- l t u r n ' as the effectory vector 00200 , t hen t he res u l t of apply i ng 'e- l t u r n ' t o ' h l i ne , ' n am e l y the symbol ' 1 - t l i n e , ' must be i nterpr e t e d as the result of a pply i n g t ransform ation 00200 to t he sensory vector 0 1 1 1 1 , w h i ch i s the sensory vector 00 1 1 0 . Obviously, i t might be necessary to go back a n d rei nterpret the i n i t i al set of symbols and operators, or choose a di fferent set to be the i n i t ial set , depen d i n g on one's object i ve. Not i ce that t he i nterpretat ion shown in Figure 5 . 9 i s very d i fferent from the conventional i nterpret ation of F igure 5 . 6 . The autonomous s t r u c t u re of the envi ronment , w i t h respect to the new ontology created by t h i s rei nterpretat ion of C N l i s shown in F igure 5 . 9 ( b ) .
m i ght n o t i ce t h a t t h e i n terp ret at i on of P i g u re 5 . 9 groups t wo d i fferent posi t ions of a l i n e , that a r e o t h e r w i s e disti ngu ishable, in one category. Thus, as viewed from the concept n e t work , these two d i fferent s t ates in t he sensori motor data set are seen as one t h i ng. You
vert i cal
ac c o m m o d a t i o n ,
O r i f t he o l d
network i s not d i scarded , w e c a n s ay t h at. a new c o n cept network is created . However , t h e new con cept network i s c reated from the ontology p rovi ded by the cogn i t i ve age n t ' s percept ual appara t u s . The p rocess works in a sort of ' bo t t om - u p ' fashion . S p i n n er p l ays w i t h the sensory an d effec tory vectors u n t i l some pattern is detected . O n e such pat tern that m i g h t result from t h i s i n teraction is shown i n Fi gure 5 . 1 0( a ) . Then t h i s pattern i s g e n e m lized to a concept networ k , a s i n Fi gure 5 . 1 0 ( b ) . O n c e gen eral i ze d , t he concept network can h ave the origi n al pattern as a conventional i n t e r p r e t a t ion , b u t i s now capable of a d m i t t i n g other i nterpretat ions as wel l . O b v i o u s l y, In
concept
t h e concept network i s res t r u c t u red .
Chapt er
5:
Cogni tion : Informal Overview
:�� �;:.�
CONCEPT NETWORK hline SYMBOLS
ENVIRONMENT 01 1 1 1
I
..'.\.,�
r-tline
1 49
00 1 1 0
\
�;
·.-.� ·:.�.
1 -t 1 m . e - - - - - - - - - - - - - - ;,; · - - - - - - - - - - - - - 00 1 1 0 ---- - �·.-.� - --- ---- - � 00 � 00 ' e .... � v1 m ��... . . - -. . . - 000 1 0
SENS ORY VECTORS
. . .
-.·
e- rturn . . . . . . . . . . . . ;�... . . . . . . . . . . . . . . . 000 20 :.·. :.� ·.-.�
e -l turn . . . . . . . . . . . . :� . . . . . . . . . . . . . . 00 200
OPERATORS
qturn
_
�.-:.
:%.-.�-�-- 00030 i; " · � - - - -- 00300
..
...
EFFECTORY VECTORS
�:
{a)
{ 00030, 00300 }
01 1 1 1
� �
200
0002
� �
(0 00300 }
'\ 00 1 1 0
( 00 1 00 , 000 1 0 }
�
00
(b) FIGURE 5.9; A projection of th e concept network CN 1 onto the new environment in which all lines are four cells long instead of five . The correspondence between the el eme n t s of the concept network and parts of the environment is shown in (a). The 'world-view ' from the concept network CN 1 with this interpretation is shown in (b).
Pa. r t 1!: A Theory
1 50
�
/ 01 1 10
I
000 1 0
010
��
00 t 1 0 0 1 \ tl "
0 1 000
00 1 00
01 1 1 1
\
10
00 1 1 1
00 1 00
> 00 1 1 0
000 1 0
0000 1
O C D\\
(a)
_3,
r fl-line ---.;» r2-line --..;. vline l
//r- turn
r- turn
c- turn
h-line
" c - tur� "'; 3 -lme c - turn > 12-line r- turn
�
vline2
(b) 5. 1 0: An example of accommodation. The pattern of i nteraction (a) reveals a structure of the environment based on the ontolog y it by S p i n ner s sen sorimotor app arams . Generali zin g this pattern
FIGURE shown i n given to
'
results in the concept network shown in (b).
Chapt er
5:
Cognition : Informal O verview
151
accommodation i n volves learning and i nductive ge n e r a l i z ati o n . The example presented i n this section was s i m p le, but i l l u strated al l the major featu res of t he theory. I now exam i ne t hese feat ures i n more depth one at a time.
5.3
Concept Networks
Concep t s , while t hey h ave a referential function in bei n g able to connect with our sense i m p ressions, nonetheless enj oy an i ndependent status that allows u s to combine t h e m i n various ways to generate non- referential conceptual struc t ures . The existence of mathematics, various forms of fiction , etc. clearly attests to this non-referent i al role of concepts. In this p ro cess , however, con cepts show an i nherent struct u re that precludes arbit rary combi nations. For i nstance, each of the concepts ' ch il d ' and ' paren t ' is the converse of the other ; and the concept of ' mother ' i s su bsumed by the concept of ' parent . ' A nother example is prov i ded by diction ary mean i ngs. A d iction ary essentially rel ates concepts to one another w i thout connecti n g them to the thi ngs i n the exter n al world . Thus, we can talk about concept n e t w o rks, which are structured sets of concepts. My concept networks correspond to t he ' s ch e m as ' of Pi aget, the 'schematas ' of Goodman [ 1 976, I I , 6 , p p . 7 1 -74 ] , and the ' ideal ized cogni t i ve models' of L akoff [ 1 987] . A concept networ k , i n my characterization , h as two components: a set of symbols and a set of operators . O perators specify how certai n symbols can be combined to generate other symbol s . I n the e x a m p l e above, all the operators we re one-place operators, but this might not always be t h e case. I allow n - p l ac e operators for any fi n i te n . Consi der some e x am p le s . The n at u ral n u m be r system can b e set"n as a concept network. The s y mbols of this concept network wo u l d be all t h e pos i t i ve i ntegers i n c l u d i ng zero . We cou l d h ave two b i n ary operators : add i tion and In ultip l i cation. The ad d i t i o n operator ' + ' wo u l d take two n u m bers (sym bols ) as arg u m e n t s an d combine them to o u t p u t a n o t h e r n u m ber ( sy m bol ) . The m u l t i p l i c a t i o n operator ' X ' woul d b e s i m i lar. A street map provi des an example of a d i ffe re n t ki nd o f co n ce p t n e t w o r k . One cou l d t ake various p l aces i n the city to be the s y m bols of t h i s network , an d d irections l i ke ' go east one block , ' and ' t urn lefl at the second i ntersec tion , ' to be the operators. N o t i ce that the o p e rat o r s can be u n ary ( ' go east one block from X ' ) , binary ( ' go one b lock from X in di rection Y ' ) , tern ary ( ' go one block from X i n d i rection Y a n d then t u rn and g o two blocks i n
1 52
Part II: A Theory
d i rect ion Z ' ) , an d so on , where X , Y, and Z are var i ables for the symbol s . H ere also, when a n operator i s ap pl ied to t h e given symbol s , another symbol resu l t s . I n t h i s second exam ple, w e see t hat w h i le a concept network i s necessar i l y i nternal to the cog n i t i ve agent , i t m ight be manifested i n some external ob j ect . Thus, the map i s an external object that man i fests the correspon d i n g concept network. T h e symbols a n d t he operators of t h i s concept network are, nevert heless, fu lly i nternal to the cogn i t i ve agent . The i dea t h at when goi n g two blocks east from t h e t rai n station, o n e e n d s u p a t the p o s t office i s an i n ternal concept ual struct u re i n t he m i n d of the cogni t i ve agent . The map, t a ken as an obj ect by i t sel f, i s only a network of colored l i nes and regi ons, and there are no sy mbols or operators t here. A not her t h i n g to emphasize i s that the action of the operators on the symbols should not be con fused w i t h the actual result of t ak i n g the corre spon d i ng act ions in real i ty. The post office may not actually be two blocks east of t he trai n station , but i f this i s what the map show s , then this i s what the operator ' go two blocks east' gi ves when appl ied to the symbol ' t rai n stat i o n ' Thus, concept networks are only potential representations of reali ty, an d do not necessari ly corres pond to anyt h i n g by t hemsel ves .
The operators p l ay many usefu l roles i n a concept networ k . F i rst of all , t hey can b e m ade t o represent actions o f the cogn i t i ve agent , as i n C N 1 above , t hereby allow i n g it to ' foresee' the results of i t s actions w i thout actu ally carrying them ou t . One can compare d i fferent routes to the airport to see w hich one might be shorter, w i thout act ual ly tak i n g t he routes. Secondly, by making the operators represent actions of other ' real ' or ' hypothetical ' age n t s cau s i n g changes i n t h e e n v i ronment o p e r a t or s make i t poss i b l e for t h e cogn i t i ve age n t to p red i c t t h e changes i n the e n v i ronment . I f you r fr i e n d t o l d you t h at s h e wi l l b e t a k i n g t h e s u bway from t h e airport goi n g towards downtow n , and get t i ng off a.t the t h i rd stop , you cou l d figure out from the map to w h i ch station you should go i n order to meet her. Bot h t hese ap p l i c a t i on s are e x t re m e l y usefu l for any k i nd of p l a n n i n g i nvol v i n g a seq u e n c e of i nterch anges w i t h the environment . T h i rdly, op er a t ors allow for a c e r t ai n e c o n o m y of represen t a t i o n , expres sion , and com m u n i cat ion . For i nstance, i n the concept network of the na.tural n u m ber system , o n e n ee d not keep the i n fi n i t e set of symbols in one's head . S i n ce any n umber can be generated from ' 0 ' and ' 1 ' by applyi n g an appro pri ate sequen ce of operators, only two symbols and two operators need be exp l i c i t ly represented . O f course, if one h as to deal w i t h large n umbers fre quentl y, then t h i s representation wou l d be far from economi cal , but t h e n
Chapter
5:
Cogn i tion : Informal O verview
1 53
some other fi n i t ary representation might be chosen . l n the map concept net wor k , i t i s not necessary to remember the location of every place on the m ap . If you k now where t h e t rai n station i s , t h e locat ion o f any other p l ace can be fixed giving d i rect ions for how to get t here from the t rain station . The operators of a concept network also endow i t s symbols w i t h struc An operator, we h ave seen , combi nes symbols to generate another symbol . The p rocess , however, can also be v iewed in reverse: that is, an operator can be seen as decomposing a symbol i nto other sy mbol s . Some or all of t hese symbols can then be further decomposed i nto other symbols, and so on . Any such decomposit ion of a symbol i nto other symbols is cal led a descript i o n of i t . For i n st ance, the d i rections for goi n g to the post office from the t rain station coul d be called a descri p tion of the symbol ' post office . ' ( The symbol ' post office' i n t h e m a p i s really ' t h e locat ion of t h e post office , ' and not ' the post office b u i l d i n g . ' ) tures.
O bviously, a symbol can typically have m any descriptions. There m ight be more t han one way to get to the post office from the t rai n station , t hough some of them m i ght i n volve longer detours. I n Figure 5 . 1 1 , I show some descr i p tions of the symbols '3' and ' v l i ne' in the concept networks natural n umber system and C N 1 respectively. The descri ptions are depicted as l a beled ordered t rees , w here every leaf of a t ree i s l abeled w i t h a symbol of the concept network and every i ntermedi ate node h av i n g n chi l d ren i s l abeled w i t h an n-ary operator of the concept network . For a given description of a symbol , the symbols t h at res u l t from the cor respond i n g decomposit ion process are called the compo n e n ts of the original symbol ; and the sequence of operators i s called the structU1 ·e of the symbol (based on the g i ve n d e scr i pt i o n ) . T h u s , d i ffe r e n t d e s c r i p t i o n s o f a symbol ' see ' i t as m ade up of different componen t s and hav i n g d i fferent s t r u c t u re s . O n e thing to notice here is t hat every symbol i s a descri ption of i tself: t h e descri ption t h a t sees the symbol as an i n d i visible whole.
that of gen e ra t io n . G i ven it mig h t be possi ble to generate other symbols fr o m t hem by applying ap propr i a t e sequences of op e r a. l o r s . The set of all symbols t h a t can be so generated , al o 11 g wi t h the operntors of A
11
concept c l o se l y
set of sy mbols of
a
re l ated to decom pos i t ion i s
c o n ce p t network ,
the concept network , i s called t h e s u b n etwork generated by t he gi ven set of symbols . If t h i s subnetwork i ncludes all t he s y m bo l s of t h e concept network , t hen we say t hat the i n i t ial set of s ymb o l s i s a g e n e ra t ing s r t of the concept networ k . For i nstance, i n t h e n at u ral n u mber system concept networ k , t he set { 0 , 1 } i s a generat i n g set of the concept network, whereas the set { 0 , 2 } gener a t e s a subnetwork contai n i ng all the even numbers . l n C N l , any of
Pari II: A Theoq
1 54
X
+
+
�
A
�
X
A
2
+
A
(a) Three differen t 'descriptions ' of the symbol
e- rturn
""'
e - rturn
I
Wine
3
'3'. e - rturn
e- lturn
/ �
qtu
r-tline
r-tline
(b) Three different ' descriptions ' of the symbol ' vline ' in the concept network
CN l .
FIGURE 5 . 1 1 : Two example s to illustrate that a symbol i n may typically have many 'descriptions'.
a
concept network
Ch ap t er
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Cognition : Informal O verview
1 55
the symbols except ' v l i ne' can generate the ent i re concept network. I n the map concept network , all the p l aces that can be reached from the train stat i on ( according to the map ) for m the subnetwork generated by the set { ' t rai n stat i on ' } . A small i sland t hat is i n the m i ddle of the l ake woul d not be i ncl uded in this subnetwork , u n l ess the map concept network contai ns operators l i ke ' s w i m ' or ' t ake a boat . ' A nother way o f look i ng a t t h i s process o f generation m ight b e helpfu l . A g i ven set of symbols can be v iewed as a set of ' p r i m i t i ves . ' The subnetwork generated by t h i s set is t h at part of the concept network that can be descri bed by using t hese p r im i t i ves. Not i ce that every symbol in the subnetwork h as a descrip t i on w i t h all i t s components i nc luded i n the gi ven set of pri m i t i ves , i mp l y i n g t hat every symbol i n the subnetwork can be descri bed i n terms of t hese prim i t i ves . A generati n g set of the concept network , from t h i s view, i s essent i al l y a set of p r i m i t i ves , i n terms o f which the whole concept network can be described . A generat i n g set of a concept network i s sai d to be minimal i f no symbol i n t h i s set can be generated from the remai n i n g ones . Thus, a m i n i mal generati n g set contai ns the m i n i mu m n u mber of pri m i t i ves t hat are necessary to describe t he concept networ k . For the natural n u mber system concept networ k , a m i n i mu m generati ng set is { 0 , l } ; whereas for CN 1 any of the sets { h l i ne } , { r- t l i ne} , and { 1- t l i ne } is a m i n i mal generat i n g set . Thus, s i nce a concept network does not h ave to have a u n i que m i n i mal generat i ng set , i t can be descri bed in a variety of ways, and in terms of d i fferent pri m i t i ves . This i s a key factor in exp l ai n i n g various characteristics of cogn i t i o n , i n c l u d i ng metaphor. Speak i ng of req u i rements brings me to the c o n s t r a i n t s the concept net work s must. sat i s fy i n my framework : so far, I !l ave onl y sai d t h at a concept network consists of symbols and operators . The symbols and operators , i n order t o c o n s t i t u t e a concept n e twork, must meet the fo l l o w i n g t h ree cri teria: l.
The set. of operators must. be finite.
2 . Every operator must be
physically realizable . In
ot her word s , for every
operator t here must exist some physical system t h at i m plement s i t . 3.
The con cept network m u s t b e fi n i t ely genera t ed: at least one fi n i t e gen erat i n g s e t .
t h at i s , i t must h ave
T hese t hree req u irements o n concept networks ensure thei r fi n i te b i l i ty, t hereby addressing t he i ssues raised i n Partee [ 1 9 79] .
representa
Part II: A Theory
1 56
I t i s eas i l y veri fied that all the concept networks I i nt roduced so far sat i s fy these t h ree const rai nts. N o t i ce that the set of symbols of a concept network can be fi n i te or i n fi n i te . A concept network i s said to be finite if its set of symbols is fi n i te and infinite otherwise. Natu ral number system i s a n i n fi n i te concept network , w hereas C N l i s a fi n i t e one.
A t this poi n t I wou l d l i ke to m ake some remarks relati n g my concept networks to some s i m i l ar not ions t h at h ave been proposed elsewhere. I n doi ng s o I m u s t em p h asize t h at m i ne i s a preci se a n d formal characterizat i o n , whereas the ones mention ed below, though based on e m p i r i cal evi dence, are nevertheless vaguely speci fied at best . For t h i s reason I believe t h at much can be acco m p l i shed by bridging t he gap between t he two approaches : t he emp i r i cal concept networks can be gi ven a formal bas i s , and the u sefu lness and scope of t h i fra m ework can be w idened con s i derably. •
A concept network can h ave m any operators that change a g i ven set of symbols i nto anot her symbol . For i nstance , in the ' fami ly ' con cept network , each of the operators 'gives b i rth t o , ' ' n u r t u res , ' and ' contri bu tes genet i c m ateri a l to' can change the symbol ' mother' i nto ' ch i l d . ' M o reove r , i n i n s t a n t i a t i ng the concept network , it i s not nec essary to i nstan t i ate every operator. Thus, t he concepts ' mother' and ' ch i l d ' C
radi al
system t h at L a koff
u ses
to demo n s t rate t h e s t r u c t ure of
catego r i e s , in the concept n e t w or k correspon d i n g
to
B a l an , w h i ch
i n c l udes women , fi r e , and d a.ngero u s t h i ngs , t he s y m b o l ' wo m e n ' c a n
p rototype ( t here m i ght be ot her prototypes a� wel l ) . wou l d b e c o m e a d i s t a n t sy m bo l of t h e concept ne t w o r k . This i s because the d e r i vat i o n from ' wome n ' to ' d a n gero u s t h i ngs ' i s a l o n g o n e : go i n g from ' women ' to 'sun , ' then to 'fire , ' and fi n ally arri v i n g at ' d angerous th in gs . ' [Lakoff 1 987, p. 1 00 . ] be consi dered
T h en ' d an gero u s t h i n g s ' a
Both t hese feat ures show that m y concept networks w i t h the idealized cognitive models of Lakoff.
can
be con c i l i ated
Chapt er
5:
Cognition : Inform al O verview
1 .5 7
•
I believe t hat the concept networks a s formalized here are able t o char acterize most fol k and cultural models descri bed by various l i nguists and anth ropologi sts in Hol l an d and Q u i n n [ 1 987] . There i s not h i n g in my characterization t hat requi res concept networks to be com plex. I f necessary, add i t ional constrai nts c a n be p laced to guarantee that t h e complex i ty o f any concept network does n o t exceed a certai n level . For i nstance, one coul d l i m i t the number of symbols, the number of opera tors , or the maximum arity of the operators . I n fact , one such approach is used in the theory of cogni t i ve development proposed by Halford and W i lson [ 1 980] , where t he arity of operators is related to the stage of the cogni t i ve development in the chi l d . The first stage is characterized by u n ary operators , the secon d w i t h b i n ary operators, and so on .
•
F i n al ly, my con cept networks fully capture P i a.get's ch aracterization of them as ' closed systems that are, at the same t i me, open to exchanges w i t h t he environment . ' ( See P i aget [ 1 967] , p p . 1 .54- 1 58. ) The reason i s t h at concept networks can be ci7'cu lm·. A concept network is said to contain ci rcularity i f i t h as symbol s , or sets of symbol s , X1 , . . . , Xn such t h at X1 generates X2 , X2 g e n e r a t e s X3 , . . . , Xn - l gene r a tes Xn , and Xn generates X1 . For i n stance, C N 1 is c i rcular i n an obvious way. In fact, any concept network with i nvert ible operat ions exhibits circularity. C i rcularity allows a concept network a choice of p ri m i t i ves and a. variety of organi zations depen d i n g on w h i ch symbols are d i rect ly i nterpreted i n the wor l d . This p o i n t i s very i mportant because i t shows that the same concept network can organi ze r ea l i ty i n different way d ep e n d i n g on how it is i n stantiated . In Lakoff 's exampl e o f B al a n i n Dyi rb a l t h at was mentioned above , if the sym b o l ' fire' i s con s i d er ed a pri m i t i ve an d a. prototype of the c o n c ept network, t hen ' women' becomes a d i s t a n t symbol and ' dan ge ro u s t h i ng s ' b e co m es a more central one. I nstan t i ated i n t h i s w ay , the concept network woul d s t ru c t u r e the world d iffe reJ J U y than lhe way i l does i n Dyirbal .
Finally, a maj or issue that I h ave not yet touched u pon i s : How do concept networks come about in the fi rst place? T h o u g h to fully add ress this quest ion is beyond the scope of this wor k , T recog n i ze t h ree different ways in w h i ch a c o n ce p t network m ay be formed . 1 . A concept net work m ight be lea rn ed. Th e learn i n g m i ght or might not have been gui ded by another cognitive agent such as a teacher.
Part II: A Th eory
1 58
2 . A concept network m i ght be derived from other existi n g concept net works. J ust to mention a few poss i b i l i t ies: the cogni t i ve agent m ight form a subnetwork of an ex i s t i ng concept network; extend a concept network by ad d i n g more symbols and operators to i t ; combine two or more concept networks to form a l arger u n i fied concept networ k , etc. ( See also Goodman [ 1 9 78] , pp. 7- 1 7 . ) 3 . A c oncept network might b e i n heri ted genet i cal l y. That i s , i t m i ght be i m p l icit l y man i fested in t he b iological ( or p hysical ) s t r u c t u re of t he co g n i t i ve agent . A l l t h i s means i s t h at I recogn i ze t h at cert ai n concep t n etworks m ight be present w i t hout eit her bei ng learned or bei n g deri ved from other concept n etworks.
I n closing, let me agai n u nderscore the fact that concept networks are p u rely sy n ta c t i c systems t h at are meani ngle s s u nless i nterpreted ap propriately in an en v i ronment .
5 .4
Environments and Sensorimotor D ata Sets
This bri ngs us to the second component of the i nteraction process: re ali t y. Here we are i n deep water, for to ch aract e rize r eality i n any way gi ves i t a preex isting s t ruct ure. B u t not to cha r ac t eri ze i t leaves us no way to talk about how i t m i gh t affect t h e proce s s of i nteraction . To b reak out of t h i s seem i n g l y paradox i c al s i t u at i o n , l d i s t i ng u ish between t h ree levels o f real i ty.
At o u e level is t h e real i ty t h at is not k n owable by t h e cogn i t i ve agent , for i t req u i res a G od s eye v i e w . T h i s level of real i ty corresponds lo the K ant i an world of th ings-in-the mselves an d .J ungian Ple ro m a . ( See J u n g's VI [ Serm o n es a d Mo r l u o s , t ranslated into English as Seven Sermons l o lh e Dead, i n I-loe l ler [ 1 982] , p p . 44-.5 8. ) For i n s t ance , the zomd s t r 11 d ure of S pi n ner 's envi ro n ment , v i s i b l e i n our God's eye v i ew , cannot b e k n own by S p i n ner. As far a.s S pi n n e r is con c e rn e d , the effect of a hop may well be lo ca u s e the old l i ne t o d i sappe a r and a new l i ne to a p p e a r in a random '
o r i en t a t i o n . Here, however, I i n corporate Krausser's [ 1 974] two observat i o n s . O ne is t hat t h i s level of rea l i ty i s not an u n s t r u c t u red m ass , b u t h as a mind i n d e p e n dent a u t onomous s t r u c t u re t h at c a n n ot be sp e c i fied o r known . The reason this s t ruct u re can not be spe c i fied is that no a priori ontology exists for this level of rea l i t y , and spec i fy i ng a structure presupposes an ontology.
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One m i ght quite reasonably obj ect here: How can I posit a m i n d - i n dependent structure w i thout posi t i ng a m i n d - i ndependent ontology? M y answer is t hat I can posit a m i n d - i n dependent structure w i thout need i n g a m i nd-i ndependent ontology as long as I do not h ave to specify what the structure is, for i t is only in specifying the structure that I need the ontology. Ascri bing a m i nd i ndependent struct u re to this level of real i ty i s l i ke t he existence p roofs i n mathematics, where the existence of some m at hemati cal object i s p roved w i t hout specifying what the object i s . T h e second observation o f K rausser that i s i n corporated i s that the cog n i t i ve agent can i nteract w i t h t h i s level of real ity. In fact, it is only by i nteract i n g w i t h t h i s reali ty that the cogn i t i ve agent can part i ally receive evidence of its autonomous struct u re. The second level of real i ty corresponds to the worl d of sense i m p ressions, and I refer to i t as the s e nso1·i m o t o 1· d a t a s e t . This level of reali ty is created by our sensory and motor apparatu s i nteracti ng with the worl d of t h i ngs-in themselves. That i s , i t i s our perceptual system that halts the conti nuous flux of t h i ngs- i n - t hemselves and bri ngs the fi rst level of real i ty to a manifes tation . A n d our cog n i t i ve access to t h i ngs- i n- themselves is l i m i ted to t h i s manifestat ion . A s our percept u al apparatus creates the sensori motor data set , i t neces sar i l y fol lows that the ontology of the sensorimotor data set is determi ned by our percep t u al syste m . H owever, as Eleanor Rosch [ 1 978, p. 28] astu tely noted in one of her landmark papers on the cognitive aspects of categoriza tion , t h i s world of sense i mpressions i s not u n s t r u c t u red . Rat her, r ea l i t y, as i t p resents itself to u s i n the form of sensory s t i m u l i that form the raw m a terial for con cep t u alization and categorization , i s al ready h i g h l y s t r u c t u re d : cert ai n sets of stimuli occur together, while certain o t h e r s prec l u de o n e an other. Moreover, this struct ure of the sensori motor d a t a set is d et e r m i ned b y the m i n d - i n d e p en d e n t a.u tonomous structure of the world of t h i ngs-in t hemselves . I elaborated this p o i n t i n t h e context of S p i n n e r ' s worl d , b u t let me now give a n o t h e r e x am p l e . S u p pose I am s t an d i ng in f r o n t of a t ree. It i s t h e biologi cal st ructure of my eyes t h a t determi nes what image is formed on my r e t i n a s , what contrast I see, what colors I see, e l c . (Of c o u rs e , i L also depends on t h e o b j e c t i n front of my eyes , the lighting condi tions, et c . B u t d i fferent o b j ec t s , o r t h e same object u n der different l ig ht i n g con d i t i o n s , can all be c onsi d e r ed d i fferent s t i m u l i in the sensorimotor data s e t . ) Similarly, as I walk towards the t ree, it is the structure of my motor a p pa r a t u s that deter m ines w hat possible movements I can m ake. H owever, the effect of any such movement on chan g i n g one stimulus on my ret i n a i nto another, possibly
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d i fferent , sti m ulus is deter m i ned by the structure of the external wor l d . It i s precisely i n t h i s sense t h at real i ty, w h i l e owi n g i t s for m ( as experienced by m e ) to my sensori motor apparatus, nonetheless appears as an autonomous external entity to me. Of course, this second level of real i ty i s also not always d i rectly accessi ble to u s . Neither can we ' see' the i m age on our ret i n a, nor can we acti vate every i nd i v i d u al muscle i n our body. Thus, the sensori motor data set , w h i le i t forms t he raw data t hat we recei ve from reali ty, does not reflect our con ceptual worl d view. For this reason I posit a t h i r d , concept u al level of reali ty, correspond i n g to K ant's p h e n o m e n a l world and J ung's Cre a t ed World. 1 This i s the level of reali ty t h at we experience every day. From here on , I reserve the term e n viro n m e n t to refer to t h i s level of reali ty. An envi ronment is essent i ally created by i nterpret i n g a concept network i n the sensori motor data set . Parts o f the i nterpret ation m ight b e predeter m i ned by the physi cal or b iologi cal structure of the cogn i t i ve agent , but t here m i ght be am ple room for t he cog n i t i ve agent to change the i n terpretations and create d i fferent environ ments i n the same sensori motor data set . The same observat ions m ade about t he sensori m otor data set can be made about the env i ronments with respect to their ontologies and their structures . The ontology of an env i ronment is determi ned by the cogni t i ve agent ( by i nterpret i n g a concept network ) , and t herefore i t must necessari l y m irror t he ontology of the concept network bei n g u sed for i nterpretation. For this reason , an envi ron ment , i n my form alizat i on , consists of objects and t rans formations. O bjects are counterparts of symbols, and t ransformations are cou nterparts of operators . There a.re no restrictions of a. n y k i n d p l ace d on the obj ects a.nd t ransformat ions. The set of objects m i ght b e finite or i nfi n i t e , the set of transformations m i ght be fi n i t e or i nfi n i t e , a t ransformation m ight or m i gh t not be algori t h m i c , an d the objects might or m ight not be generated by a . fi n i te su bset of them . Tt seems rea.son a.bl e not to i m p ose a.ny k i n d of requ i rements on the environment s i nce doing so wou l d amount to i m p o s i n g req ui rements on the au tonomous structure of real i ty. The s t r u c t u re of the e n v i ron ment, however , is determ i ned by t h e worl d of t h i ngs- i n - themsel ves . S i n ce t h i s point is crucial to my framework of i nterac t i o n i s m , I p rov i de some more exam ples here at the risk of bei n g red u n d an t . Fi rst , con sider a com mon o b j e c t s u c h a. s a. table. Obviously, i t s status a s a n 'object ' d i s t i nct from its s urroun d i ngs , an 'object ' that c a n be m oved from one place to anot her, bought or sol d , etc. , is solely to the fact that we i denti fy t h at chu n k of real i ty w i t h a. s y m b ol of our concept networ k . Thus, i t owes i t s 1 T his term h as also been t r a n s l ated
as
Crea t u ra b y W i nstons [J u n g 1 96 3 , A p p e n d i x
V] .
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existence as a n 'obj ect ' solely due t o our percep t u al an d cog n i t i ve apparatus. However, t he result of applying any t ransform ation on it, such as set t i n g i t on fire, h i t t i ng it hard with the palm of our han d , sel l i ng it, etc . , i s deter m i ned by t he external reali ty. Not i ce, in con nection with ' sel l i n g , ' that even t hose social and cultural i nstitut ions that are completely h uman creations-legal systems, monetary systems, marri age, come to m i n d as examples-do nev ertheless acq u i re an 'objecti ve real ity' once thei r structures, that were once created by us, are shared by a group of people and used as a b asis for their behaviors. ( See Berger & Luckmann [ 1 966] . ) A s another example, consider the l ines of l at itude and longitude. There is no doubt here t h at t hey are created by our cogni t i ve apparatus. Yet , once the ontology is created , the structu re, w h i ch determi nes whether two gi ven ' p l aces ' h ave the same lat i tude or not , i s no longer an arbi trary m atter, but i s determi ned b y the world of t h i ngs- i n - t hemselves. (The ' places ' ontology also created by our cog n i t i ve apparat us . )
5.5
Cognitive Relations and Coherency
A cogn i t i ve relation i s a . l i n k between a. concept network and real i ty. It i s a. cogni t i ve relation t h at m akes a concept network mean i ngfu l , and i t is a. cog n i t i ve rel ation that bri ngs reali ty w i t h i n the cogn i t i ve grasp of the cogn i t i ve agent . Moreover, i t i s by forming a cogn i t i ve relation that envi ronments are created out of the worl d of t h i ngs- i n - t hemsel ves (a process t h at is med i ated by t h e sensori motor data set ) . Formally, t hen , a. cogni t i ve relation becomes a correspon dence between sy m b o ls of t h e concept network and the objects of the e n v i ro n m e n t , and between the operators of the con cept- network and the t ransformat ions of t he environment . I allow a. correspondence to be one- to-one, one- to- many, many the
to-one , or many- to- m any. The corres pondence can b e total as well a.s par t i a l .
meaning that n-ary o p erators corres p ond to n-ary t ransformat ions for
However, each operator can only correspond to a t ran sformation t ype,
of t h e
same
all n . This m ay seem to be a stringent requi remen t , but i t i s a. n at ural con sequence of how environments are created . The objects and t ransformations in t h e envi ronment do n o t e x i s t i n d e p e n d e n tly of t h e cog n i t i ve age n t , b u t a re created by t h e co g n i t i v e agent b y i nstant i a t i n g a. concept network and for m i n g a cogni t i ve relation . So, i f a . symbol is i n stant i ated , the resu lti ng t h i n g i n the environment w i l l necessar i l y behave l i ke an objec t . If an n- ary operator is i n stantiated , then the correspon d i ng t h i ng in the environment w i l l n e c e ssarily be an n-ary t ransformat ion . O f course, this does n o t mean t hat
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a part of real ity can be gi ven an ontology i n only one way, s ince d i fferent concept networks can be i nstan t i ated in the same part of reali ty in d i ffer ent ways, res u l t i n g in many d i fferent ontologies ( an d crea t i ng many d ifferent environments ) . Though t h e ontology o f a n environment m i rrors t he ontology o f t he con cept network t h at created the envi ron ment , the structur e of the envi ronment i s another matter. I have al ready belabored this point i n the l ast section. So, i t i s natu ral to ask i f a cogn i t i ve rel ation i s such t h at t he autonomous struct u re of the envi ronment respects the structure of the concept n etwor k ; or, i n other words, i f t h e actions of the t ransform at ions on the objects m i rror t he act ions of t he operators on t he symbols. \11/e have already come across this p roblem when we t ransported S p i n ner to an alien env i ron men t . Let us consi der some more examples here. Consider t he concept network of natu ral nu mbers aga i n . Let the environment consist of p i les of stones . Each number-a symbol of the concept network-corresponds to all t he p i les, i f a ny, contai n i n g that many stones . O bviously, t h i s i s a one- t o-many correspondence. The operat ion of ad d i t ion c o r r e sponds to the t ransformat ion by w h i ch two p i l es are combi ned to form a n e w p ile. Now the correspondence w i l l respect the actions of operators and t ransformat ions if, and only i f, wh enever we t ake any two pi les of stones an d thei r corresp on d i n g n umbers, a n d a p p l y t h e transformation of comb i n i n g the p i les to m ake a n e w p i le, and t h e operat ion of add i t ion on the t w o n umbers, we find the res u l t i ng p i l e correspon ds to t h e res u l t i n g n u mber. To t ake another example, con s i der t h e concept network of a map. A c c o r d i n g to the map , if we go t wo blocks east from the t rain station , we should be at the post office . If t h at indeed happens when we t a k e t h e correspon d i n g action w i t h respect t o the object t h at i s t he t rai n station , then t he envi ronment preserves t h e action of the operator ' go two blocks east ' when a p p l i e d t o t h e s y mbol ' t rai n stat i on . '
To see a n exa m p le o f a correspondence t hat does not respect the actions of operators a n d t r an s form a t i o n s we o n l y need to change the envi ronment in the last exam ple t o grou ps of d o n key s an d /or carrots . Each n u m b e r now corresponds to al l the groups, i f any, contai n i n g t h at m any donkeys and /or carrots . Thus a group contai n i n g t hree donkeys a n d ten carrots corresponds t o t he n u m b e r 13. The o p e r at i o n of add i t ion still corresponds to the t rans formation by which two groups are combi ned to for m a new group . I t s h o u l d be e m p h asi z ed here t h at these groups of donkeys and/or carrot s are real i n t h e sense t h at a l l t h e members o f a g ro u p have t o b e i n close prox i m i ty. A l so t h e transformation of p u t t i ng two groups toget her i s a physical tran sforma t i o n t h a t is carried out by actually bri nging the two groups together in close
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v i ci n i ty. Obviously now , the result of t ransfor m i n g two groups i nto a new group m ight not always yield a grou p that corresponds to the ad di tion of the n um bers correspon di n g to the origi nal grou ps. For example, if a group contai n i n g ten carrots i s com b i ned with a grou p contai n i n g t h ree donkeys it might not always result in a group corresponding to t he number 13 si nce the donkeys m ight eat some carrots i f t hey are hungry. A map of a ci ty that has some errors i n it p rovides another example of a cogn i t i ve rel ation w here the struct u re of the environment does not respect the structure of the concept network . The characteristic some cogni t i ve relations have of p reservi ng the act ions of operators and t ransformations is called coh e rency. In prac t i ce, not all cog n i t i ve relat ions are coherent, as observed by Col l i n s and Gentner [ 1 987] . Moreover, a cogni t i ve relation m ight be locally coh e 1·e n t : that i s , the cogni t i ve relation restricted to a part of t he concept network and a part of the environment is coherent but t aken as a w hole i t m ight not be coherent . Local coheren cy i s a much more usefu l concept than coherency for two reasons. F i rstly, a cogni t i ve rel ation that i s to prov i de a useful basis for planning one's act ions, and to go about d ay- to- d ay l i fe , need only be local ly coherent in the appropriate parts of the concept network and the environ men t . The second reason concerns fi n i te representab i l i ty. Assum i n g that a cogni t i ve agen t can exam i n e only a fi n i te part of the concept network at any t i me, it means that the cogni t i ve agent can only estab l i sh local coherency w i t h i n fi n i t e parts of the concept network . It woul d seem that a cogn i t i ve agent can n e ver estab l i sh the c o he r en cy of a cogni t i ve relat ion between an i n fi n i t e concept network and an environment . H o w e v e r the fact t h at even i n fi n i te concept networks are req u i red to b e fi n i tely gene rated provi des t w o d i fferent ways to t i e local coherency w i t h i n fi n i t e parts to t h e co he r e n c y of cog n i t i ve relations bet ween i n fi n i t e concept n et wo r k s and environments. ,
O n e way t o con struct a fully c oh e r e n t cogn i t i ve rel ation between an i n fi n i t e concept network an d a n e n v i ronment i s a s fo l l o w s A fi n i te generat i ng set of t h e concept network i s gi ven an i n terpretation i n t h e environ ment by associ ati n g each s ymb o l in t h i s s e t w i t h an o b j e c t i n the env i ronment . .
Now the fi n i te set of operations of t he concept network i s i nterpreted by
identifying each operat i on with some t ransformation such t h at t h e resulting correspondence i s lo c a l l y coherent with respect to the ge n e r a t i n g set . This i s no problem si nce the set i s fi n i t e . N o w t h e correspondence c a n be extended
to all the symbols by associat i n g each generated symbol with the appr o p r i ately t ransformed obj ect . The correspondence does not h ave to be actual l y made-obviously i t cannot b e si n ce i t woul d req u i re that t h e i n fi n i t e set of
,
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symbols be generated . B u t as long as t h i s p rocedu re i s fol l owed to extend the correspondence to any other subset of t he symbols of the concept network , the result w i l l always be coherent . This mechanism plays a key role i n form ing a cog n i t i ve relat ion by means of p roj ection , an example of w h i ch J showed earlier when S p i n ner proj ected C N 1 onto the alien envi ron ment , t hough the concept network t here was a finite one. I n our wor l d , we u se a s i m il ar method in using mathemati cal models to p red i ct the real- world phenomena. Secondly, i t fol lows from t he defi n i t ion of coherency t h at any i n coherency in a cog n i t i ve relat i o n , even when the concept network i s i nfi n i te, i s always detectable locally w i t h i n a finite part of i t . This feat u re p l ays a key role detect i n g i n coherency when a cogn i t i ve relat ion i s being formed by acco mmodation . ln t he context of scientific t heories, which are primarily formed by accommodation , this characteristic of cog n i t i ve relation i s well know n : a scientific t heory can never be val idated, i t can only be refuted [Popper 1 959; 1 962] .
5.6
A c commodation and Projection
O bviou sly, coherency of cogn i t i ve relations i s an i deal t hat a cogni t i ve agent must strive for . For it i s the coherency of a cogni t i ve relation t h at ensures t h at a prediction arri ved at by reasoning from the concept network holds in the environment . G i ven t h at , we ask : how can a cog n i t i ve agent main tain coherency of i t s cogn i t i ve relations? Well , t here are t h ree components to a cogn i t i ve relation : the concept network, the environment , and a cor respondence between the two. Moreover, the coherency con d i t ion requ i res t h e s t r u ct u re of the con cept network and t h e s t r u c t ure of the e n v i ronment t o r esp e ct each other . So we need to ask : w h i ch of t hese parameters can be varied by the cog n i t i ve agent ?
T h e structure o f t h e environment i s rooted i n reali ty, so i t cannot be
varied by t h e cogn i t i ve age n t ( at l east not w i t ho u t changi n g t h e ontology of t h e e n v i ro n m en t ) . B u t t h a.t l eaves two parameters: t h e s t r u c t u re of t h e
concept network a n d the correspondence between the concept network and t h e e n v i ro n m e n t .
Corres p o n d i ngly, t here are two mecha n i s m s t h at can b e
u sed , i n d i v i d u a l l y or t oget her, t o mai n t a i n coherency o f cogn i t ive relat ions .
These mechan i sm s , referred to as a cco m m odation and p 1·ojection respecti vely, h ave al ready been i n t roduced in the context of S p i n ner example, and here I el aborate t hem fu rther, A ccommodation works by keepi n g the correspondence between the con-
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cepts and the environment i nvariant , and then altering the structure of t he concept network ( recall t h at 'structure' here means how the symbols are i n terrelated) whenever an i ncoherency i s detected . P roj ection works by keeping the structure of the concept network i nvariant , b u t changi ng the correspon dence between the concepts and the parts of the environmen t . I n fact , i n changi n g the correspondence, the cogni t i ve agent i s i n effect i n stanti at i ng the concept network ane w , thereby creat i n g a new envi ronment . Thus, pro jection works by i n d i rectly alteri ng the structure of the envi ron ment so that i t better fits the structure of the concept network . I say ' i nd i rectly' because what the cogni t i ve agent i s actually doing i s giving a new ontology to the environment , an d it is reali ty that is fitt i ng this ontology with a structure. The cogni t i ve agent can use both these mechan i sms i n concert to mai n tain coherency o f a cogni t i ve rel ation: t here m i g h t be some vary i n g o f the correspondence, and some restructur i ng of the concept network . H owever, i t i s p ossible to study each mechani s m separately b y hol d i n g t he effect o f the other mechani s m fixed. I n other words, we can study the effects of accom mo dation by keeping the correspondence between the concepts of the concept network and the parts of the envi ronment fixed , and then not i cing how the structure of the concept network changes so as to mai ntai n coherency. A cogni t i ve relation formed i n this fashion is referred to as a cco m m odating or e n viro n m e n t d1·iven. S i m i l arly, we can keep the structure of the concept network i n variant and then maintai n coherency solely by varyi ng correspon dences between the concepts of the concept network and the parts of the environment . A cog n i t i ve relation arri ved at by this p rocess i s referred to as p rojective or concept driven. L e t us first consider accomm o da t io n . A s menti oned before , i n forming ac commodating relations, the corresponden ce bet ween p a r ts of the t>nv i ro n men t and t h e concep t s of t h e concept network is kept fi xed . T h e correspondence might h ave been fixed by a p r i or step of project ion, or might have been hard-wi red i nt o t h e percep t u al apparatus of the cognitive agent . The s t r u c t u re of t h e concept network i s ad ap t ed to t h e s t r u c t u re of the e n v i ronment s o as to maintain coherency of the cogn i t i ve relation . I n other words , it i s t he environment , acti n g t h rough t h e fixed co r re sp o n d e nce that structu res the c on cept network . This is the reason for n am i ng the re s u l t i ng relation ,
'environment driven . '
Some examples will p er h ap s be helpful here. I m i t a t i o n comes t o mind immediately as a typical acti v i ty t h at gi ves rise to accommodating re l at i o n s ( See P i aget [ 1 945] , P ar t I , p p . 5-86 , for a fas c i n a t i n g study of t h e role p l ayed by i m i t at i o n i n the ear l y cogni ti ve development of t he ch ild . ) When one .
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Part II: A Theory
i m i t ates an act ion , a sou n d , or a view, one is copying the envi ronment i n a sense. Not i ce here t h at any i m i tation i s an i m i t at ion o n ly in cert a i n respects. If you were i m i tat i n g my act of touchi n g my n ose w i t h my left h an d , you wou l d h ave to decide whether your touch i n g my nose or your nose woul d amount to a n i m i tation . You wou l d also h ave to decide i f t h e nose should b e touched w i t h m y h an d or yours a n d i f i t shou ld be t he left or the right h an d , not to ment ion dec i d i n g whet her to i m i t ate t h e place where I was standing or s i t t i ng, the d i rection I was facing, the clothes I was weari ng at t he t i me I touched my nose, etc. A l l t h i s must be decided by a prior step of proj ection . ( See also Goodman [ 1 976] , I , 2 , p p . 6- 1 0 ; and Hofstadter [ 1 98 1 -85] , p p . 563565 . ) However, once the relevant aspects are decided , the correspondence i s estab l i shed between t h e concept network and t h e envi ronment ; o r , i n other words , the ontology of the environment h as been deter m i ned . The environ ment t akes over from t here and the cog n i t i ve agent adapts the structure of its concept network ( t h e necessary sequence of act i ons t h at woul d result i n the i m i tat i on ) t o conform t o the struct u re o f the envi ronment ( the act being i m i tated ) . There are m any other exam ples o f accommodation . I n draw i n g a geo grap h i cal map, one is essentially carrying out a process of accommodation . The ontology of the terrai n i n terms of w h i ch its structure i s to be m apped r i vers , l a kes, l an d , ocean , etc.-is deci ded beforehand. The terrain t akes over from t here and the geographer must m ake the s t ruct u re of the m a p corre spond to the structure of the terrai n . In determi n i ng the n umber of days i n a. year, one i s agai n carrying out a p rocess o f accom modat ion, for the on tologies of day and year are a l read y g r ou n ded in external phenomena, and i t i s the autonomous s t r u ct u re of the worl d that determi nes how t hese t wo p h eno m e n a are rela.ted . It d al.
m ay be of some i n ter e s t to note here that the Q-morphisms of Holland [ 1 987, C h . 2] co r r e s p o n d to what 1 h ave been cal l i ng accom modat i ng
cogn i t i ve relat i o n s here.
In
t h e i r model of cogn i t i on , t h e e n v i ron m e n t
is
ass u m e d to act o n the cogn i t i ve age n t v i a a set
of featu re detectors. These feat u re detectors estab l i s h the correspondence between the objects of t he envi ronment and the con cepts of the concept network. However, si nce the nat ure of the feature detectors i s fixed , the correspondence i s predetermined . The cogn i t i ve agen t can only m o d i fy i t s e x i s t i n g operators , or create new operators , to corres pond to the t ran sformat i on s of the envi ronment . A l l t h ese exam p les a l so h e l p to show why t h e cog n i t i ve agen t i s n ot en t i rely p assi ve in t he formation of an accom modat i ng relat ion . The p rocess of estab l i s h i n g a correspondence between t he concepts of t he concept net-
Chapt er
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Cogn i t ion : Informal Overview
1 67
work and chunks of the envi ron ment i s a prerequisite for t he format ion of an accommodat i n g relation. This choi ce is made by the cogni t i ve agent , con sciously or not . In many cases the physical and biological structu re of the agent might be such t hat the correspondence i s p redetermi ned and cannot be varied at all : t he choices are already made by evol ut ion or the system ar chi tect and the cogni t i ve agent has no conscious control over i t . However, i f t h e cogni t i ve agent does h ave some freedom i n t h i s respec t , then i t i s capable of form i n g a p roj ecti ve cogni t i ve relation, which I discuss now . A p roj ecti ve relat ion i s formed by keepi n g t he structure of the concept net work i nvar iant but changing the correspondence between the concepts of the concept network and parts of the env i ronment so as to maintain coherency. S ince the structure of the concept network is kept fi xed i n t he process , i t i s t h e struct ure o f t h e envi ronment that must conform . T h i s i s t h e reason for n am i n g the resul t i n g relat ion ' concept driven . ' Of course, the structure of the envi ronment does not act ually conform, what this means i s that the cogni t i ve agent i s asserting i t s form at i ve power in changi ng t he experien t i al ontology of the environment so as to be able to see the structure of the con cept network reflected in i t . A n d , of course, real i ty, w h i ch determi nes the structure of any experienti al ontology created by t he cogn i t i ve agent , asserts i t self by l i m i t i ng t he possible ontologies that do end u p reflecti n g t h i s struc t u re , if at all . Thus we see t h at ' concept driven ' cog n i t i ve rel ations are not completely determined by the cogni t i ve agent , j ust as 'environment driven' cogni t i ve relat ions are not completely determi ned by the env i ronment . The most classic example of proj ection i s the ret i n al i n version of i m age in our v i s u al system . We all k now t h at t he i m age formed on the ret i n a of our eye is act ually i nverted : e ve ry t h i n g is upside dow n . Ho we ve r we do not ' see' t h i n g s upside dow n . This, of course, is easily explai ned by t h e fact that o u r concept net works a l read y take t h e i n version i n to accou n t . I n other wor d s , t h e correspondence between o u r concepts a n d t h e i m ages on o u r ,
ret i n a i s such t h at the act i on s of a l l operators a r e preserve d , a.n d s i n ce ' u pside dow n ' i tself i s a concept embeddt>d i n o11r s p at i al co n cep t networ k , i t 11.c t u a l l y
co r re s po n d s t o t ho s e i m age s t h at now change t he structure of our
are ri g h t s i de u p on t h e ret i n a . S u ppose we eyes so t hat the i m ages on t h e ret i n a are
not i n verted , a t ask easily accompli shed by wearing the appropriate lenses i n
front of the eyes . Obviously, i t i m m ed i at ely m akes t he earl ier i nterpret ations of our existi n g spat i al concept networks i n coherent. T h i s experi ment was , i n fact , carried o u t by Stratton [ 1 897] a t t h e e n d o f t h e l as t cent u ry. A s one m i ght expec t , t he i n cohere n c y resulted i n vertigo and n ausea. H owever, after about a week , everything started t o appear normal . W h at m i ght h ave happened? S u rely it is too short a t i m e to ' relearn ' all t h e various s k i l l s
Part
1 68
II:
A Theory
i n w h i ch the vi s ual st i m u l i play a role, and rest ruct u re t he spat i al concept networ k . This phenomenon i s explai ned i n m y framework b y the mechani s m of project i on . In order to ' see' everything normal , w i t h the d istor t i ng glasses i n front of the eyes , all t h at was necessary was to rei nterpret the old con cept networks by changi n g the correspondence between the concepts and the ret i n al i m ages . As to be expected , S t ratton encountered a s i m il ar experience w hen he took off t he d i stort i n g glasses : i t st arted out w i t h a feel i ng of dizzi ness b u t after about a week every t h i n g was back to normal . I woul d say t hat the correspondences were back to what t hey were i n i t i al ly. This example also demonst rates t h at not al l the corresponden ces between t he concepts of our concept networks and parts of our sensori motor data set are predetermi ned for us, t hereby al low i n g us to use the mechanism of p roj ection in for m i n g cogni t i ve rel at ions. ( See also Turb ayne [ 1 962] , Chap. V I I I , Sec . 4 , for a very s i m i l ar explanation of t h i s phenomenon . ) As I show in Chapter 7, it is t h i s proj ection t h at m akes m e t a p hor possi ble, especially s i m i l ari ty-creat i ng ones. O t her exam ples of projec t i ve relat ions can be fou n d in the p l ayful act i v i t ies o f ch i l d ren . W h e n a ch i l d i dent ifies a dol l w i t h herself, s h e is essen t i al l y proj ect i ng her i m age of herself o n t o the dol l . I n any s u c h playful a c t i v i ty of c h i ldren , the i nteresti n g t h i ng is t h at the proj ection is far from arbi trary, and reveals a systemat i c struct u re t h at the chi l d is attemp tin g to p reserve. ( See P i aget [ 1 945] , Pa r t I I , p p . 8 7-2 1 2 , for a detailed study of the role played by ' pl ay ' in t he cogn i t i ve growt h of ch ildren . ) of a project i ve relat i o n , c o n s i d e r t h e l i nes of l at i t u de l o ngit u d e . Obvi o u sly, t hese l i nes do not e x i s t i n o u r envi ronment and so th e y cou l d n ot h ave been i n d u ced b y i t . I t i s a system of r e fe r e n c e t h a.t we h ave d e vel o p ed for our conveni en ce and then p r o j e ct e d onto our envi ron m en t . S i m i l arl y, our system for m easu r i ng t i m e is an i n stan ce of a m os t l y project i ve rel at i o n . N ot i ce here t h at t hough the concep ts of n igh t a.n d day a r e i n d uced b y t h e e n v i ron m e n t , t h e concep t s of h o u r, m i n u t e , and seco n d a r e p u r e l y proj e c t i ve . It i s a l s o easy t o s e e here t hat t he environment , n o t a p r i n c i pal actor in p roj ect i ve rel ations, nonetheless p l ay s a key role. I t i s true t h at we cou l d have devi sed another system in place o f l ines of l at i t u de a n d l o n g i t u d e , b u t o n ce a s y s t e m i s devi sed and proj ected , i t i s t h e envi ronment t hat deter m i nes whether two places are on the same ' lat i t ude' o r not . We cou l d h ave chosen to d i v i de t he d ay i nto 43 ' hours , ' b u t even t hen A s anot h e r e x a m p l e
and
w h e t h e r t wo eve n t s t o o k p l ace w i t h i n t h e s a m e ' ho u r ' or not i s a m atter t h at i s d e t e rm i n e d by the e nvi ronmen t .
F i n al ly, I shou l d em p h asize agai n t h at most cogn i t i ve relat ions are not
Chap ter
5:
Cognition : Informal O verview
1 69
formed by either accom modation or p roj ection act i ng alone, b u t i nstead by both mechanisms act i n g together. Perh aps the most i n terest i n g examples of t hese two mech anisms act i ng in concert are prov i ded by I m re Lakatos [ 1 976] i n h i s beaut i ful essays on the role of cou nterexamples in mathemati cal p roofs . When a counterexample to a certai n t heorem is fou n d , there are two t h ings one can do. One i s to rede fi ne the m athematical objects invol ved i n t h e proof s o a s t o excl u de the counterexample. T h i s amounts t o proj ection , because t he concepts are bei ng i nstant i ated anew. The other t h i n g one can do is to declare t he t h eorem i nvali d , and perhaps l ook for a . weaker theore m . T h i s amounts to accommodation, for t he structur e of the concept network ( man i fested in the statement of the t h eore m ) i s being altered to keep it t ru e ( coherent ) . Lakatos argues quite con v i nci ngly t h at i n most s i t u a t ions we l i ke to use a l i ttle b i t of both the mech a n i sms to keep our concept n etworks significant , mean i ngfu l , and coherent ( as far as we can asce r t ai n i t ) . ( See also the acco u n t of lea rn i ng gi ven in Pet rie [ 1 979] . In his account, the teacher works by project i n g a . concept network so a.s to reveal an i n coheren cy in the student 's cogni t i ve relat ions. The student ' learn s ' by c hangi ng the str u c t u re of her concept network-t h at i s , by accom modation . )
5.7
C ognit ive Mo dels
I refer to a concept network that h as been i n terpreted by a. cog n i t i ve relat ion an e n v i ronment a.s a . cognitive m odel. C ogn i t i ve models a r e ex p erient ial and conc e p t u al i z ed versions of real i ty, and thus t hey loos e ly correspon d to the ' worlds ' of Good man [ 1 978] . fn t h i s section I d i scuss how cogn i t i ve mod els 'group ' parts of the e n v i ro n m e n t Logel h e r . Then I p rese n t a 'gro u p i ng' pe r s p ect i ve on accom modation and proj ection . Then I d i scuss how parts of the e n v i ron m e n t arc rep resented in t he cogn i t i ve m o d e l , and how t hey acqu i re a d e sc r i p t i o n v i a the operat ional s t r u c t u re of t he concept network. Finally, I i ntroduce s om e term inology to refer to d i ffere n t c h arac ter i s t i cs o f cogni t i ve models. in
I a s sume here t h at a c o g n i t i v e model is coheren t , u n less exp l i ci t l y st ated otherwise. S i n c e coh e rency is an i deal t hat a c og n i t i ve model must ai m for , t h i s a ssump t i o n does n o t seem u n reaso n a b l e . It i s l i k e ass u m i ng t h e absence of fri ct i on i n order to d iscuss ch aracteri s t i cs of m o t i o n .
Part II: A Theory
1 70 5.7.1
G ro u p ings o n t he E nvironment
A cogn i t i ve model ' groups' t he objects and the transform at i on s i n t he envi ronment so t h at the structure i n the en v i ron ment seen with respect to these groups is i somorphic to the struct ure of the model . 1 now elaborate t h i s group i ng p henomenon w i t h some exam ples . Let us first consider gro u p i ngs on the objects of t h e environmen t . \Ve saw an example of t h i s i n Figure 5 . 9 when two different states of S p i n ner's eye, correspond i ng to the sensory vectors 000 1 0 and 0 0 1 00, were grouped together u nder one symbol ' vl i ne. ' V iewed from C N 1 , t hese two otherwise d i s t i nguishable objects of the envi ronment cannot be d i s t i ngui shed at all . A nother exam ple, from the natu ral envi ronment o f S p i nner, i s shown i n Fig u re 5 . 1 2 ( a ) and ( b ) . Here all the objects of the environment are grouped into n i ne categories. T h u s , S p i n ner's ' worl d , ' w h i ch was already s i m p l i fied by its perceptual appa rat us, is fu rther s i m p l i fied by the cog n i t i ve model . These exam p l es , of course, show grouping at a small scale, b u t i t is due to S p i n ner's h avi n g a very s i m p l e perceptual apparat us to begi n w i t h . I n our visual system , we k now t h at the i m ages on t he ret i n a. are grouped i nto various classes accord i n g to the posi tion and orientation of l i nes , edges etc. [ R ubel & \Niese! 1 9 79 . ] O f course, at the cog n i t i ve level the group i ngs are more obvious. A l l our ' words' correspond to several ' world-states . ' This suggests t h at a cogn i t i ve rel a t i o n , from the concept network to t he envi ron men t , might typi cal l y be a . o n e to m a n y affai r . One m i ght even see the whole problem of cogni t ion as t h at of grou p i n g a vast n u mber of ' world-states , ' m ade possible by t h e pe rc ep t u a l apparat u s , i n to a few categories. The e m p i r i cal research of var i o u s l i n g u i s t s a n d a n t h r o p o l o g i s t s p resen t ed i n H o l l a n d and Q u i n n [1 987] certa.i n ly supports t h i s view. -
-
T h e t ransfo r m a t i o n s c a n be grouped i n two i nteres t i n g way s . T h e first
i s t o group t h e transformations in s e q u e n ces a nd t hen relate the oper ators of the concept network w i t h t hese sequences of t ransformat i o n s . A n example o f a cogn i t i ve model that gro u p s t ransformations i n t h i s way i s shown i n Figure 5 . 1 3 ( a ) and ( b ) . T h e one operator o f t he concept network i s identified w i t h t h e sequence of t r a n s form a t ion s obtained by fi r s t ap p l y i ng the t ransformat ion 1 0000 followed by t he t ransformation 0 1 000: w h i ch m ay be written as 1 0000 o 0 1 000. way
N u merous exam ples of grou p i ng t ransformations i n sequences can also be fou n d in our percep t u al and cogni t i ve apparatu s . A s i m ple act i on such as 'j u m p ' or ' wal k ' act u al l y t ranslates i nto a sequence of m u s c l e acti vat i o n s . S i m i l ar ly, i n p l an ni n g a t r i p , w e m i ght use a concept network t h at h as a n
Chapt er
5:
Cogn i t ion : Informal O verview
±;
2-c-tilt - - - - -:�� - - -
i;:..�
171
\
I
I
\
'"
/
/
'
( 0 1 1 00, 00 1 1 0 }
2-e-tilt � ( 0 1 1 00, 00 1 1 0 }
i;:.�
3-c-tilt - - - - �. - - ..
:g
·:.·.
SYMBOLS
( 1 1 1 00 , 00 1 1 1 } '
3-e-tilt � .
( 1 1 1 00, 00 1 1 1 }
4-c-tilt �
{ 1 1 1 1 0, 0 1 1 1 1 }
.
i; ..
·:.�
..
.
:g
'-.....
/
/
.......
SENSORY VECIORS
( 1 1 1 1 0, 0 1 1 1 1 }
4-e-tilt � '.:•:, , �·. :.·.
s-line
:�� ( 1 1 1 1 1 , 0 1 1 1 0 } ... ·... :.� .. .
( 1 1 000, 000 1 1 }
o-b-line - - - -:�� - - -
��:.�
v-line �
-·���·-
( 1 0000, 0 1 000, 00 1 00, 000 1 0, 0000 1 }
·:.�
.• :. .· .'· .· :- .· :- .•:. .·:- .·.'· :.'- .· .'· .. ... .. ... .. ... ..... :.'· :.'· .. ... .· .'· .. ... .. .'· ,·
.•.
...
.'
.- .'· .- · .- _·.
�-- - ·
. .- .'· ,· .'· .- .'· .- ·. .. .'· .. .'· .. ·. .. ·. : _·. .. ·, ; _·, : ·, : ·, : ·, : ·, : _·, .- ·, : ·, : ·, : ·, : ·, _
.- _·
:..·.
OPERA TORS
c - 1 -burs t- - - -
�� ("·:.
00 1 00
EFFECTORY VECTORS
... ··.. . • ..
�; ... .. . ..
.
C O N C E PT NETW O R K
:.� ...
ENVIRONMENT
...
. •.
...
':.� '•· FIGURE 5. 1 2 (a); A n example of a cognitive model th at s h ows grouping of objects in the environment. The structure of this co gn i tive model is shown in
( b) .
1 72
--
3 -c-tilt --- 4 c tilt
2-c -tilt
Part TT: A Theo1y
�() /
4-e-tilt � 3 -e-tilt - 2-e-tilt ----;-+
v-0
FIGURE 5 . 1 2 (b) : S tructure o f the cognitive model shown i n ( a ) . Since there is only one operator ' c - 1 - burst ' all arrows refer to it.
operator ' get t o the airport , ' w h i ch a.ct ua.lly corresponds to a . se q u e n ce of actions such a.s ' walk to t he s ubway, ' ' t ake the su bway to the airport , ' ' t ake the ai rport s h u t t l e to t h e term i n a l , ' etc. ( For m i n g sequences of t ransforma tions t h at take o n l y one obj ect a.s a. n argu ment seems straightforward . To form sequen ces of n-ary t ra n s format i o n s i n genera.! , o n e composes n m- ary t ransformat ions w i t h a.n n - ary t r a n s fo r m a t i o n t o y i e l d an m - ary t ransforma tion . This i s t e c h n i c al l y c a l l e d co mpos i t i o n a n d is for m a l l y defi ned i n the ne x t cha p t e r . ) T h e secon d way t r a n sfor m a t i o n s
be grou ped i s its objects. 'vVe s a w a n o p e r ator 'qt u rn ' grouped the actions vectors 03000 and 00030. The i dea h ere
c�n
exam p l e of t h i s i n F i g u re .5 . 6 w h e n t h e
of S p i n n e r corres p o n d i n g to effectory
two or more t r a ns fo r m a t i o n s c a. u s e t h e sam e c h an g e , as seen from the concept network , t h e n t h ey appear as one. For i n s t an c e , t h ere m i g h t be several w ay s of g e t t i ng to t he a i r port , but at t h e level of abs t r ac t i o n w h e re we h av e t he operator ' get to t h e a i r p o rt , ' al l t hese ' detai l s ' ar e i rrelevant a n d
i s t h at i f
i ndisti ngu i s h able. N o t i ce t h a.t t h e s e
two ways o f group i ng the t ransformations c a n work a g ro u p i n g . A l l t h e d i fferent w ays of get t i ng t o t he
airport t h at c orr e s p o n d
t oget her t o p r o d u ce be
s e q u en c e s of
act u a l l y
be
to t h e operator 'get to t h e ai rpor t ' m i g h t. t h e m s e l ves
ac t i o n s .
real i z able
by
M o reover , each part o f any such s e q u e n c e m i ght t w o o r more ac t i o n s .
Chap t er
5:
Cognition : Informal O verview
2-1-ti1t
4-1-tilt 4 -r-tilt SYMBOLS
h -lin e
:g :�� - - -
{ 0 1 1 00, 1 1 000 }
·�
{ 0 1 1 10, 1 1 1 00, 0 1 1 1 1 }
_ _ _ _ _
3 -4-1-tilt
1 73
·.-.� �·. ...... ·:.·. �·.
l
. . . ... . . . ·:.·. ·.:::. "' · � ... �·. :.·. ·:.� - - - - -
:�:
- - - -
.. . ·.-.� ·.::.�
I
I
/ /
/
/
1 1 1 10 ........_ ""
01 1 1 1
/S ENSORY VECTORS
11111
o-b-li n e - - - - - - - · ( 00 1 1 0, 000 1 1 , 00 1 1 1 }
�
...
.•. .. . �� ...
v -line �;...� { 1 0000, 0 1 000, 00 1 00, 000 1 0 , 0000 1 } r-tilt
:�j
\ \ " , ........,__ ---- �--· ( 1 1 000, 0 1 1 00, 1 1 1 00, 0 1 1 10, 1 1 1 1 0 } .,:
·,� :.� ·:.� � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � ..... . ':_· . ... .. . �i '· · ... . EFFECTOR Y 1 -burst - - 1 0000 o 0 1 000 - - - VECTOR OPERATOR '.:,� SEQUENCE ·:.�
�
�
�:
�:
�·.
C O N C EPT NETW O R K
ENVIRONMENT
5 . 1 3 (a) : An example o f a cognitive model i n which a n operator of ' sequence ' of action s . The structure cognitive model is shown in (b).
FIGURE
of this
�� ·:.� ·:.� ... ... .• .
the concept network corresponds to a
Part II: A Theory
1 74
2-1-tilt --� 3 -4-1-tilt --� h-1ine
":0 /
4-1-ti1t --- r-tilt
O
rne �--- 4 - r-tilt
FIGURE 5. 1 3 (b) : S tructure of the cognitive model shown in (a) . All arro ws represent the operator ' 1-burst' , which is effectory vector 1 0000 followed by
0 1 000.
5.7.2
Accommo dat ion and P roj ec t i o n : A not her Perspect ive
r
W i t h t h e p h e n o m e n o n of g o u p i n g i n t h e
b a c k g ro u n d ,
we can view t h e mech
a n i s m s of accom m o d at i o n a n d proj e c t i o n from a n o t h e r p e r s p e c t i v e .
a
provides it wit h an
The p e r c e p t u al
Let us
app arat u s of t h e cog n i t i ve agen t
o n t o l o g y for t h e sensorimotor data set . T h i s ontology i s
l o o k at accom m o d at i o n fi r s t .
structured by r e l i t y, as I h av e e m p h as i zed several t i mes . Now s i n c e t h e s e n s o r i motor data set i s ava i l ab l e fo r conce p t ualization, the c o g nitiv e agent can gro u p i t s o n t o l ogy i n va.r i o u s way s , s i m p l i fyi n g i t s worl d view i n t h e p r o cess . Effect i vely, t h i s is w h at goes on w h e n a concept network i s i n te r p r et e d i n the s e n s o r i m o t o r d a t a se t . T h e s t r u c t u re of t he e nv i ronment a s seen fro m t h i s g rouped o n t o l ogy depen d s p a r t l y on t h e autonomous structure o f t h e senso
a
data set , and partl y on the w ay the g r o u p in g was carried out . T h e t i o n works by keep i n g t h e g r o u p i n g s of the sensorimo tor d at a s e t fixed , an d c h an gi n g the s t r u c t u re of the c o n cep t � e t work so t hat it reflects the structure of t h e e n v i ron ment in t e r m s of t hese grou p i ngs . T h i s process i s grap h i c a l l y demonst rated i n F i g u r e 5. 1 4 . O n e m i g h t s e e i t as t he c og n i t i ve agen t determ i n i n g w h a t goes into t h e gro u p s , and t h e e n vi r o n m e n t ri motor
p ro cess of a cc o m m od
d e t e r m i n i n g t h e s t r uc t u r e .
Chap ter
5:
Cogni tion : Informal O verview
1 75
(a)
(b)
(c)
C O G NITIVE A G ENT
E N V I R O N M E NT
FIGURE 5 . 1 4 : A perspective on accommodation. In (a) the cognitive agent gives an ontology to the environment. In (b) the environment determines the structure of this ontology. In (c) the cognitive agent adapts the strucmre of the concept network to reflect the structure of the environment.
Part II: A Theory
1 76
For project i o n , the process works i n the other d i rect i on . One al ready h as a struct u re t h at comes from the concept network being proj ected . The problem now is in comi n g u p w i t h a group i ng of the sensori motor data set t hat respects t h i s structure. S i nce the sensori motor data set has an autonomous struct u re, it l i m i ts the possi ble ways in which i t can be grouped so as to reflect the structure of the concept networ k . The cogn i t i ve agen t selects one such grouping, though this selection process m i ght also be constrai ned by the physi cal or b iologi cal struct u re of the cog n i t i ve agent . This process i s shown in F i gu re 5 . 1 5 . One m i ght see this as the cogn i t i ve agent determi n i ng the st ruct ure and the environment determ i n i ng what goes i nto the groups. This view of accommodation a n d proj ect ion better explai n s how both the cogni t i ve agent and the environ ment have a. role to play in each of the pro cesses . H owever, if we t ake the structure-determ i n i ng role to be the primary one, t hen accom modat ion can be v iewed as an envi ronment driven process and proj ection as a. concept dri ven p rocess. The result i n ei t her case i s that t he cog n i t i ve agent sees i n t he world an i somorphic copy of t he concept net wor k . 5.7.3
Represent a t i o n and D e s c r i p t i o n
Looki n g at cogn i t i ve models from another angle, we m i ght not i ce t h a.t t hey bring obj ect s a n d t ransformat ions i n the environment w i t h i n the cogni t i ve grasp of the agent . I n a cogni t i ve model , any object ( or t ransformation ) of the environment is sai d to be rep1·ese n t ed by a. symbol ( or operator ) of the concept network i f the t wo are rel ated by the cogn i t i ve relat ion. Conversely, the concept is s a i d to be a rep res e n t a t io n of the objec t . O b v ious l y, s i n ce I allow m any-to-many relat ions, an object c a n h ave m a ny representations and a c onc e p t can represent many objects . Reca l l t h at earl i e r I defi n ed the term d e s e 1·ip t i o n i n connection w i t h sym bols of a concept networ k . A descr i p t i on of a symbol i s any way of specify i ng how t h at symbol can be decomposed i nto various other symbols; or, look i n g a t i t constructi vely, how various symbols c a n be combi ned to generate the symbol being described. This termi n ology i s eas i ly exten ded to the objects in the environment via the cogn i t i ve relation of a cogni t i ve model . That i s , a descrip t i o n o f a n ob ject i n a cogn iti ve model i s a. des cri pt i on o f a n y o f i t s representations. S i n ce i t w i l l al ways be clear whether w e are talking about the environment or the concept networ k , u s i n g the same term for o b j e c ts and symbols shou ld not cause any confusion. On the contra.ry, it b r i ngs o u t a. key featu re of cogn i t i on : o bjects in the e n vi r·o n m e n t a c q u i re a descrip t i o n o n ly by
Chap t er
5:
Cogn it ion : Informal O verview
1 77
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5. 1 5 : A perspective on projection . In (a) the cognitive agent selects a concept network with an autonomous structure. In (b) the environment, based on its autonomou s structure, determines the possible groupings that respect the
FIG URE
structure of the co n cept network. In (c) the cognitive agent in instantiating a
cogni tive relation, chooses one such grouping.
1 78
Part II: A Theory
being rep1·ese n t ed in a co ncept n e t wo rk a n d via the opera t i o n a l stru c t u re of th e concept n e t wo rk.
5 . 7.4
S o me O t her M is c e l laneous Not ions
VVith group i ngs, one can define some usefu l notions related to cogni t i ve mod els. Fi rst of al l , not i ce that a grou ping can put an object (or t ransformation ) of the envi ron ment i nto more t h an one group . A ny cogni t i ve model that groups i t s envi ronment i n this way i s sai d to be a m b iguo us . For i nstance, suppose t h at in mapping a terrai n i t was deci ded to use the concepts ' wooded l an d , ' ' h i lly l an d , ' ' fl at grassy l an d , ' ' flat d ry l an d , ' ' body of water,' and ' b u ilt u p l an d . ' The map of the terrai n using t hese con cept s would be a cogni t i ve model . H owever, the model is ambiguous because an area t h at i s h il l y and a l so wooded corresponds to two d i fferent concepts ( assu m i n g t hat such an area exists in the terrai n being m apped ) . For a cogni t i ve model t h at i s being formed by accommodation , i t i s necessary t h at it be unambiguous, because otherwise the envi ronment does not p resent the cogn i t i ve agent w i t h an un ambiguous structure t h at can be used to adapt the concept networ k . I n the above exam ple, it i s not clear how a wooded h i l l i s to be represented i n the model , and how the m ap is to be structured . Secondly, when two cogni t i ve models A and B share the same environ ment , one of t hem , say A, i s sai d to be a refi n e m e nt of the other if the grouping i n d uced on the envi ronment by A is exactl y l i ke the one i n d u ced by B e xce p t that i t splits at l east one group into two or more groups. For i nst an c e , the m a. p of a terrai n using the con cepts above ( after removing t he ambi gu i t y ) wou l d be a refinement of another map that uses only t he concept s 'land' a n d ' water' ( assum ing t h at the terrai n i n c l udes some l an d with d i ffer ent fe at u r e s . ) T h u s , a refi nement m agn i fi e s the worl d - v i e w of the co g n i t i ve agent by making further d i s t i n c t i ons possible. A cogni t i ve model i s said t o c o nt a i n syn o nyms i f at l e a s t two concepts i n i t s concept network a.re related t o exactly the same group i n t he env i ronment . T h i s should be o bv i ou s . S i n ce I al low a cogn i t i ve rel ation to be parti al , t here is t h e possibility t h at not a l l the concepts of the concept network correspond t o some object in t he en v i ronm e n t . I f t hey al l do, we say that the cogni t i ve system is full. A l l t h e cognitive models of S p inner that we have seen so far are ful l . A cogn i t i ve model t hat i s conventional i s likely to be fu l l , but w hen a concept network i s i nterpreted in an unconvent ional environment , then it i s usually not ful l . Metaphori cal interpretations provide many e x am p l es of c ogni t i v e
Chapt er
5:
Cognition: Informal Overview
1 79
models t h at are not ful l , as we w i l l see i n Chapter 7. S i m i l arly, not every object or t ransformation i n the envi ronment can be represented i n the concept network . lf every object i s represented , then we say t h at the cogni t i ve model is comple t e. Some c l arification i s needed here, si nce I emphas ized earlier t h at the object an d t ransformat ions in the environment can only be created by i nstan t iating the concepts of the con cept networ k . So, i f some object or t ransformation is not represented in the concept network of a cogni t i ve model , how does i t become an object or a t ransformat ion i n the fi rst place? The answer l ies in real i z i n g that we rarely work wi t h a si ngle cogn i t i ve model i n i solation . Though a certai n cog n i t i ve model can be signi ficant at some point i n t i me, the cogni t i ve agent m i gh t be aware of other cogni t i ve models as wel l . And the envi ronment i s not j ust the envi ronment created by the concept network t hat is i n use, but m ight i n c l u de dormant i n stan t i ations of other concept networks as well. Thus, we can talk about a cogn i t i ve model bein g i n complete w i t hout creat i n g a paradox . I n the worl d of S p i n ner, the cogni t i ve models formed by the concept networks C N 1 and CN3 of Figu re 5 . 5 , along w i th their i n terpretat ions of Figures 5 . 6 and Figure 5 . 8 respecti vely, are i n complete. However, the cogni t i ve model of F i gure 5 . 1 2 i s com p lete. N umerous exam ples of com plete and i n complete cogni t i ve models can be fou n d in our wor l d . A map of Paris i s complete i f t he environment i s restri cted to the st reet l ayout o f Paris , but i n complete w i t h respect to France ( or even with respect to Paris if houses are included as part of the env i r o n me nt . ) Some formal
ch aracteristics of cognHive models with p resente d in the next chapter.
respect
to these
defined properties are
familiar with Goodman's ' n ot a.t i onn. l systems' [Good man 1976, Chap. IV], it may be instructive to note that I plac e much less stringent requirements on my cognitive models than Goodman. But then of course, Goodman's system was designed for a different p u rp o s e than the o n e t h at concerns me here.
For
5.8
those who are
Layered Cognitive System and Multiple "Worlds"
The process of establi s h i n g rirr,otor data set and the
a.
co r res p ondence bet ween the parts of the senso the con cept network seems very m u ch
concepts of
1 80
Part
II: A Theory
l i ke the p rocess by w h i ch the percept ual apparat us creates the sensori mo tor data set out of the world of t h i ngs-i n-t hemselves . For i nstance, both processes i n volve grou ping: t he perceptual apparat u s makes many d i fferent external states of real ity correspond to the same sensory state, and the cog n i t i ve apparat us makes many d i fferent sensory states correspond to the same symbol . T h i s s i m i l ar i ty suggests that it might be possible to view the pro cess of estab l i s h i n g a correspondence between the parts of the sensorimotor data set and the concept s of the concept network as if a 'cognit i ve eye' were placed between the sensori motor data set and the concept network . T h i s cogni t i ve eye woul d create another ontology from the ontology that h as been provided by the perceptual apparat u s . This, i n t urn, suggests that it m i ght be poss i ble to view the act ions of the perceptual apparat us an d t h at of the cogni t i ve apparat us of the cogn i t i ve agent in terms of the same mechan isms operat i ng at two d i fferent levels. Let us explore t h i s avenue i n the context of S p i nner's wor l d . I n the example p resented i n Section 2 , t h e sensory organ of S p i n ner was i n flexi ble and fu lly predetermi ned . T h i s made it so t hat there was a fi xed mapping from the states of the external world to the states of the eye (as represented by the sensory vector . ) I n the case of the effectory organ , S p i n ner had some degree of flex i b i l i ty in controll i n g the i ntensity of its bursts. How ever , we cou l d tacitly assume as the s i m plest case t h at the same act i vation patterns of the effectory organ-that i s , the act i vat ions correspond i ng to the same effectory vectors-always resu l ted i n the jet-stream bursts of the same i ntensi ty, it also e s t a bl i sh e d a mapping-from the transformations possi ble i n the external world t o the states of S pi nner ' s effectory organ-that was fixed once and for al l . I n fact, because of these fixed mappi ngs, it i s possible to specify all c o gn i ti ve relations shown i n Section 2 by merely associati ng t he concepts of t he c onc e pt networks with the sensory and effectory vectors . The corre sp o ndence then automatica. l ly extends to t.he l i nes and jet-streams of ai r i n t he external world via the fixed mappings created by the sensory and effe ct or y organs.
The s i t u at i o n wou l d be differen t i f Spi n n e r coul d ch ange the t h reshold of the cel ls in its eye, or if d i fferent ai r parti cle densi t i es in the external wor l d ca u se d jet-streams of d i ffer ent i ntensities to be emitted for t h e same sett i n g o f the effectory organ . To u n derstand this phenomenon, let us just consi der t he case when S p i nner can change the b i as of i ts sensory organ .
I m agi n e that , as i n Abbot t 's origi nal Flatland, t h e r e is a d e n s e fog per vad i ng the wor ld of S p i nner. The effect of t he fog is to m ake t h e i m age on the eye of S p i n ner dependent on the distance between t he eye and the object,
Chapter
5:
Cognition: Informal Overview
18 1
as shown i n Figure 5.16( a) . However, by changing the t h reshold of the cells i n i ts eye, S p i n ner can now cause d i fferent st ates of the eye-or d i fferent sen sory vectors-to correspond to the same obj ect in the worl d . Th i s i s shown i n F igure 5 . 16 ( b). But does t h i s process not seem very m uch l i ke proj ection? To make t h i s point clear, s u ppose we construct con cept networks at the percept ual level by consi dering t he states of the eye as sy mbols and the states of the effectory organ as operators. The mechan i s m s of proj ection and acco m modation can t hen be u sed to i n terpret these concept networks coherently in the external wor ld . In proj ect ion , the structur e of the concept network woul d be kept i n vari ant and t he correspon dence between the states of the percept ual organs and the objects i n the worl d wou l d be varied by chang i ng the t h reshold of the eye . In accom modation , the bias of the perceptual apparat us-t h at i s , the th reshold of the eye-wou l d be kept fixed and the structu re of t he concept network wou l d be adapted . l n fact, this i s exac t ly how t he ' concept network' of Figure 5 . 10 ( b) came about. I n Sect ion 2, by keepi ng the percep t u al apparat us fixed , we effect i vely l i m i ted Spi n ner to ac commodat i ng cogni t i ve models between the worl d of t h i ngs- i n - t hemselves and t he percept u a l level . Thus, we h ave a t h ree l ayered cogni t i ve system here: t here i s the cogn i t i ve l ayer, the perceptual l ayer, an d the external worl d layer ( Figure 5. 1 7). I f we focus on structural determi n ation , then p rojection can be seen as work i n g from the cogni t i ve l ayer to the perceptual layer, a n d from the perceptual l ayer to t he external world layer. A ccommodat ion works in the opposite d i rection : from the external worl d l ayer to t h e pe r ce p t u al layer, and from the percept ua l layer to the cognitive l aye r. Notice that th e st ruct u re of the e xter n a . l worl d l aye r is independent o f the perceptual l ay e r. The perceptual layer creates an ontology for the external world layer, by gro u p i n g the objects in various w ays , b u t not i t s structure. Si m i larly , the structure of the i n form at i on present at the perceptual layer is independent of the cognitive layer (it is d e ri ved from the autonomous st ruct u re of t h e external world l ay e r ) . Of c o u r s e , a cognitive model at the cogn i t i ve l ayer can restruct u re the 'lower- level' information present at the p ercep t ua l layer (by grouping it v ia a cogn itive relati on), but this restructuring i s far from ar b i t rar y . The autonomous structure of t h e information present at the perceptua.l l ayer resists a.nd c;w be restructured
on l y
I have e m ph as i zed time and again. The same hol ds between the p erc e p tu al layer and Lhe externa.l wor l d la.yer.
in c ert ai n ways, as
for the
i n t e r a c t ion
From h e r e , it is only a s m aJ I step fu rther to realize that a cognitive systen1 m ight well have se ver a l l aye rs , w i t h each successive l ay e r r epres en ti n g a. high er level of abs t r ac ti o n . The layers will be n u m b er e d from 0 toN, with t he l ayer
Pa.rt II: A Theory
182
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sensory vector: 11111
(a) The fog's effect on the image on Spinner's eye.
sensory vector: 10000 threshold: low
11000
11100
medium
high
(b) Spinner, by changing the threshold of the eye, can make the same obj ect correspond to the different states of the eye. FIGURE 5.16: An example to illustrate the effect of S pinner being able to chan ge the bias of its sensory organ.
Chapter
5:
Cognition: Informal Overview
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Part II:
184
Cognitive Layers
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A Theory
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0
corresponding to the external world, layer l corresponding to the immediate
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system
mi gh t require
more than one layers), and layer N corresponding to the highest level of abstraction (Figure 5.18). Each layer can contain a variety of inherited, learned, or derived concept
h
networks. The mec an isms of projection and accommodation wor k between
adjacen t layers to organize the 'lower-level' representations or 'raw-data' of the lower layer into the 'higher-order' categories or concepts of the upper layer. Since the 'lower-level' representations at the lower layer have their ow�
a ut o n o m o us structure, the process is essen t i all y interactive. Projection works
-
in a ' top cl ow n ' fashion by forc i n g the 'lower-level' r e presen t a t ions , as far
they can be forced,
other
as
fit the concepts and categories of the upper l ayer. in words, the organization of the concepts and c a te gor ies in the upper layer to
is kept fixed and it is the mapping between the two layers that is altered to maintain coherency. Accommodation works in a 'bottom-up' fashion by first grouping the 'lower-level' representations in some way, and then reorganizing
Chapter
5:
Cognition: Informal Overview
1 85
the concepts and categories-creati ng new ones, i f necessary-of the next l ayer above to reflect t he struct ure of the group i ngs . Here the correspon dence between the two layers i s kept fixed but the organ i zat ion of concepts in the upper layer is changed . A cogni t i ve rel ation between any two adj acent layers is formed by an i n terplay of these two mechan isms. G i ven any pair of adj acent layers , the flex i bil ity to proj ect a concept network in t he higher layer onto the structures in the lower layer can vary quite a b i t depen d i ng on w here the pair is located . I n certai n cases , the correspondences m i ght be hard-wi red so that the cogn i t i ve agent m i ght have no recourse but to accommodate and adapt . In some other cases , t here might be some flex i b i li ty, but certain correspondences m ight still be ' p referred' for b iological or habit ual reasons. Thus, we might still be able to refer to certain corresponden ces as 'conventional.' N ot i ce t h at a.s long a.s the ontology of the extern al world ( created by the cogni t i ve agent ) a. t a. certai n layer i n a. cogn i t i ve system i s kept the sa.me, the structure w i t h respect to t h at ontology in t h at layer can never be changed a.s a resu l t of anyt h i ng happen i n g i n the layers above i t . Of cou rse, it can be grouped d ifferent ly, and thus ' seen ' differently from a. cog n i tive model in a. h igher l ayer. B u t i t s autonomous struct u re can be changed on ly v i a. acco mmodation eman ating from any of the lower l ayers. For instance, the nature of the stimu l u s on the retin a. of the cog n i t i ve agent ex perien c i n g apparent mo tion h as i t s autonomous structur e t h at does not depend on how that s t i mu l us i s 'seen' at the conceptual l ayer. or c o ur s e t he cog n i t i ve layer might change the b i as of the ret i nal cell, but that wo u ld amount to a projection fro m the perceptual layer to the external world, a process in which the world is given a new ontology a.t the ret i n a l level . ,
Viewing
be
he l pfu l
a.
our vis ual system as
layered cognitive system might perhaps
here. The actual scene that the cognitive o.gent i s seeing would be
0. The images o n the retina would be in Layer l. Layer 2 m igh t the description of the scene in terms of lines, edges, bounda.ries, etc.
in Layer
contain
The description of the scene in terms of concepts l i ke 'table,' b ook s , etc. woul d b e contained i n Layer 3. A n d so on . T h i s v iew of the visual system is , i n fact, full y c o n si sten t with what is known about our visual system in neuro ph y si ology a.n d the br ai n theory [Hubel 1988; Pinker 1985]. For instance, in a. model of vis u a l c og n i t io n b y Ullman [1985], it h as been suggested that the process pr o c eeds in a b o tt o m u p fashion in the first few le ve l s starting from the retinal im age, and then t o p d o wn routines a.re applied to t h e resulting repr es e nt a tio n s to extract various o t her characteristics. This would s u gge s t that i n any l aye red cogni t i ve system , t he bottom few layers, referred to as '
'
-
'
'
-
'
'
Part II:
186 'perceptual layers' in Figure
A Th eory
5 . 18, might be mostly accommodating:
meaning
that the mapping between successive layers is predetermined and cannot be easily changed.
The higher 'cognitive layers,' on the other hand, might be
mostly projective: meaning that the structures of the concept networks there are not changed very often, but the 'lower-order representations' of the lower layers are grouped in various ways so as make them fit the str uct ures of the concept networks.
I
must hasten to add here that Tam by no means implying that the layers
of a cognitive system must correspond to the physiological struct ure in the cognitive agent's brain, as some layers of the visual system might; or even that it is always possible to cleanly separate any cognitive system (such as our visual system) into different layers. My point is simply that the process of integrating the autonomous str ucture of the sensorimotor data set into the structure of a concept network is best seen as happening in several stages; and at each stage, we can view the process as an interaction between two autonomous str uctures-the stru ctured 'raw data' of the 'lower' layer and the abstract conceptual structure of the 'upper' layer.
In this interaction
process, the mechanisms of projection and accommodation are used together to integrate the raw-data into abstract concepts in a way that does not violate the autonomous stru cture of either layer. Many characteristics of cognition cannot be explained without layered cognitive systems. For instance, as I discuss in Chapters
7 [§7.2]
and
8 [§8.3],
the distinction between understanding and truth can only b e explained with
cogni ti ve systems that have three or more layers and , moreover, derived s truc t ures are allowed to exist in one of the middle l ayers .
in which
Layered cognitive systems also explain why it is not necessary to carry out active ex p eriment a t ion in order to
get a new
in sigh t
or
detect s o me miscon
ception in one's beliefs. In a two layer view of cognition, any accommodation
(that i s, a ch ange
in the structure
of
a
concept network s o
herency) is necessarily and dir e ctly caused
by the
a.s to
maintain
environment. This
co
cannot
ac count for the fact that many of the adjustments in o ur concept networks including
new
insights-happen in an arm-chair.
With a lay er ed cog nit iv e
system, this is no problem since it is only accommodation between l ayers and
1
0
that require active interaction with the external world.
of l ayered cog n i ti ve systems can expl ai n how we of 'worlds '-i n the sense of Cassirer and Goodman that are not always reduc i ble to one another . A slightly differ ent grouping at a lower layer can result in an entirely different structure a few layers Final ly,
the c on ce p t
can create a multitude
above.
Though, my formalization suggests that it is theoretically possible
Chapter
5:
Cognition: Informal Overview
187
to correlate two ent i rely d i fferent ' worl ds' by bri ngi ng t hem to their lowest possible denomi n ator, t h at is the l ayer at w h i ch the groupi ngs lead ing to the t wo 'worlds' begi n to d iverge, practical l i m i t ations might prevent one from always realizing t h i s possibil i ty. The physi cal struct u re of the brain m i ght be the source of one such l i m i tation. Over t i me , certai n projections can become ' hardened ' so t hat t hey cannot be u ndone for regrou pi ng. Or certai n struct ures m ight become so rigi d t hat they can not be adapted any more. I n spite of all that , we frequently do bring two d i sparate 'worl d s ' together, creati n g a metaphor in the process, w h i ch i s the topic J d i scuss in Chapter 7. . I n closing t h i s section, let me emphasize t h at the i dea. of a layered arch i tect ure for mode l i ng perception and cognit ion is not somet h i ng rad i cally new, but h as been suggested several t i mes i n the past i n d i fferent contexts. ( See A r b i b [1972], Chap . 6; Erman et al. [1980]; H ol l an d et al. [1986]; Rumelhart e t al. [1986]; and Lippman [1987].) What i s new i n my accou n t , however, is the structural i n dependence of the layers and the mechan isms of proj ection and accommodat ion that can be used in concert to maintain the coherency of t hese i ndependent structures w i t h respect to each other.
5.9
Summary
To con clude, I p resent below the defi n i tions of the key concepts and the main theses u n d e r l y i n g the interaction view o f cognition that I outlined in t h i s chapter. •
A concept network is a set of concep ts having an a p o ten t ia l representation of reali ty.
op erational structure.
It is •
A concept network
can permit many
of concepts to act as primitves.
different and non-overla.pping sets
vVhich concepts actually
do become
primitives depends on how the concept network i� inslantia.tf'd in t he
concepts. chosen as primi t i ves, the same concept network can structure real i ty i n differen t ways.
external world. Moreover, depending on the
•
Reality i s given a n ontology b y instantiating a co nc ept network i n it, turning it into what I referred t o as an environment. This process is
mediated by t h e sensorimotor
d ata set, which is reality as apprehended percept ual apparatus of t he cognit i v e agent. Therefore, it follows that the ont o l o gy of the e nv i r o nme nt necessarily follows t h e ontology of t he concept network . by
the
1 88
Part II: A Theory •
The structure of the environment, however, is autonomous.
Reality
asserts its autonomy by imposing a structure on the ontology (created by the cognitive agent) of the environment. •
A
cognitive relation connects the elements of a concept network to the
parts of the environment.
It is through a cognitive relation that a
concept network becomes 'meaningful,' and it is through a cognitive relation that reality becomes accessible to the cognitive agent. •
Coherency refers to the property of certain cognitive relations in which the struct ure of the concept network reflects the autonomous struc ture of the environment.
Thus, coherency is a property of cognitive
relations, and not of concept networks. •
The coherency of cognitive relations cannot be determined cognitively (without having the God's eye view), though incoherency can be so determined.
•
A cognitive agent must try to keep its cognitive relations coherent as far
as it can do so. The cognitive agent uses the mechanis ms of proje ction and accommodation to maintain the coherency of its cognitive relation, whenever an incoherency is detected.
•
In projection, the str ucture of the concept network is kept invariant, while the cognitive relation is altered to maintain coherency.
•
Tn accommodation, the cognitive relation is kept invariant, while the is altered to maintain coherency.
structure of the concept network •
•
A cognitive model cognitive relation.
is
a co ncept network that is instantiated throu gh
In a co gn iti v e model, the
a
cognitive agent 'sees' an isomorphic copy of
its concept network in the environment. The isomorphism is created by grouping the objects and transformations in the environment by the cogn i t ive •
Objects
rel ation.
in
the environment of a cognitive model acquire
a.
description
only by being represented in the concept network (through the cognitive
r el a tion) and
via the operational structure
of the concept net work .
Chapter 6 An Interactionist Approach to Cognition: Formal Concepts
6.1
Introduction
I n t h i s chapter my goal i s to carry out a formal exposition of the frame work t h at was laid out i n formal ly i n t he l ast chapter. The key notions i n my framework o f i nteractionism are t hose o f ' concept networks , ' w h i ch are fi n i tely generated algebras; 'structure , ' w h i ch refers to how the operators of a concept network connect its object-concepts tog ethe r ; d escri p t ions w h i ch refer t o the ways i n w h i c h an object-concept can be decom posed i n to other object-concepts and sequences of operators; 'generating set,' which refers to how ce r tai n object-concepts can be u s ed as primitives in terms of which the w hole concept network can be descri bed ; cogn i t i ve models ,' w h i ch are r e l a ti ons from the al ge bras of lbe concept networks to the algebras of t he '
,'
'
environments; 'groupings,' an effect of the on e- l o- m a ny cognitive rel ati o n s
group a number of different sensory states into one concept u al u n i t; and co h eren cy which is the c h ar a c t er ist ic of those cogniti ve relations i n whi ch the structure of the concept network r efl ect s the autonomous struct ure of the environment. Besid e s these noti ons, there are a few other im p o rt a n t featu res such as t h e isomorphism in cogni t ive models, whereby the e n vi r o nme n t of a cognitive model is experienced by the cognitive
on the sensorimotor data sets to '
,'
agent as isomorphic to its concept network; and the finite representability of
e
coh er n cy ,
w h ereby
a cognitive agent with
a
finite brnin and without
access
to the God's eye view of the
world can maintain coherency of its cognitive re l at i o ns All these notions are g i ven a form al characterization i n this ch apter and t heir propertie are explored.
,
.
189
Part II: A Theory
190
However, i n t his p rocess I h ave t ried not to l ose sight of the aud i ence for whom t h i s book is pri marily i ntended : cognit i ve scientists not necessarily fluent in mathematics . For t h i s reason , I have, at t imes , sacrificed math emati cal elegance i n favor of easier readab i l i ty. I have also i n c l u ded many exam ples to help u nderstand the formal defi n i t ions better. Yet , I a. m sure t h at the subj ect matter of t h i s chapter would put the greatest dem ands on my not- so-m at hemat i cally-in c l i ned readers . I can only hope that the d i scus sion of the previous ch apters has provided enough of a mot i vat ion to such readers for u n dertak i n g this arduous jou rney. As one might expect , I make use of several concepts from classi cal set theory an d Un i versal A lgebra in t h i s chapter. H owever, no prior background is ass u med an d all the relevant concepts are i n t roduced fi rst with examples. A reader al ready familiar with t hese concepts m ay wish to merely skim the earlier section s , but I must cau t i on that I do make use of some non-standard con struct ions, and for this reason i t m ay be p rudent not to skip anyt h i ng al toget her. I start in Section 2 with a d i scussion of classes and group i ngs. Then, i n Section 3 , l int rod u ce rel ations between classes an d show how relations can in d u ce groupi ngs. A particular k i n d of relations called difunctional relations, w hich t u rn out to be si gnificant l ater, are i n t roduced here also. Secti o n 4 presents fu n ctions an d operators , as a prelude to i n t roducing algebras . A l ge bras are i nt rod uced in Section 5, and I sh ow how the operators of an a l gebra endow i t s objects w i t h struct u res. The term ' generating c l ass of an algebra' is defined here also. Then, in
Section 6, I
present t he concept of subalgebra. This concept is
important because one may be interested in using only
a.
part of the concept
network, and not the whole con cept network. Therefore, it would be useful to sec how the a lgebr aic stru ctu re, particularly generativity, is affected when the operators a n d/or the o bj e cts of a n a lge bra are dropped. e x ten d s
the concept of grou pi ng s ( pre v i ou sly defined with re to algebras. The te rm 'algebra of classes' is introduced here to refer to grou p i ngs wit h a.n algebraic structur e . Then , i n Section 8, the Section 7
spect to
classes )
notion o f relation s a n d function s are extended t o algebras, where they are
referred to
as
correspondences and homomorp h i s m s , respectively.
Section 9 uses al l the p re viou s ly defined concepts to formalize cognitive m o d el . The terms 'coherency' and 'local cohere ncy' are defined here, as well as some other terms l i ke ' fu l lness' and ' completeness' [§5.7.4]. Se ct i on 10 d i scusses cog n i t i ve models over the same environment, and int roduces the terms 'refinement' and 'exten sion.' Sect ion 11 characterizes projective and
Chapter
6:
]91
Cognition : Formal Concepts
accommo d at i n g cog n i t i ve models . F i nally, i n Section 1 2 , of fi n i te representab i l i ty of coheren cy.
6.2
I
d i scuss t h e i ssue
C las ses and G roupings
A class is any col lection of obj ects. It can be defined by enumerat i n g all the objects i n t he class, or by specify in g a. rule by w h i c h i t can be deci ded whether any gi ven object belongs to the class or not . An object belongi ng to a c l ass i s usually called a m ember of the class. T h u s, the col lections { 2 , 4 , 5 } , { Boston , Bombay, Sydney, Paris } , { M assachusetts, 5 , M argaret That cher } are all exam ples of classes that are spec i fied by l i s t i n g all i ts members; whereas { x such that x i s a st ate of New Englan d } , { x such that x i s an odd pos i t i ve i nteger } , { x such that x i s a rational n u mber less t h an 3 but greater t h an 3 or x i s a citizen of A ust rali a } are i n stan ces of classes t h at are defined by gi ving a rule to determine class membershi p . l t must b e emphasized that i t i s not necessary t h at t h e objects o f a class have some feat ure in common . I n other words, classes are not necessari ly defined on the basis of some preexisting property t h at al l the objects i n a class are supposed to share. I nstead , bei ng the member of a class i s i t self a property, and i n that sense, classes can crea t e com monal i ty.
If an object x i s a member of a class A, it is wri t t en as x E A . The u n i que class t h at h as no members is called the empty class and i s denoted by 0 .
Given two classes A and B , A is said to be a su bclass o f B , written as A � B , if and only i f every member of A is also a member of 1:3 . A is e q u a l to B , written as A B, i f and only i f A i s a subclass of B and also B is a subclass o f A . In o t her word s , t w o cl asses a r e e q u al t o eacb oth er i f, and =
on l y if, they have exact l y t h e same objects as
thei r members. A is
a
pmper
written as , A C B , i f and on l y i f A is a subcl ass of B but B is not a. s u b c l ass of A . Thu s the class { Boston , New York } is a s u bcl ass of the class { x such that x i s a c i ty of t h e U S } ; i n fact i t is a proper subclass. T h e class { x s u ch t h a t x i s a posi t i ve i nteger and x i s less than 5 and x is greater Lhan 3 } is e q u al to, gi ven standard ari t h met i c , t h e class { 4 } . T h e empty c l ass i s a subcla.ss of every class but i s equal only to i lsei L s u bclass
of
B,
,
A c l ass is finite if the number of d i s t i n c t objects in it is number N , and i s infinite oth erwise .
l es s
t h an som e
G i ven t wo c l ass es A and B , the union of A and B , wri tten as A U B , i s the class obtained by putting all t h e o b j e c t s i n A a n d al l t h e objects i n B t oget her . T h e i n t e rsection o f A an d B , wri t t en a s A n B , i s t h t> c l a s s of
192
Part II: A Theory
all t hose objects, and only t hose objects , t h at are members of A and also of B. Thus, if A is { French , Italian } , and B is { Engl i s h , Span i s h , French } t hen A U B i s t he class { French , Ita l ian , Engl i s h , Span i s h } ; and A n B i s the c l ass { Fren ch } . T wo classes are sai d to be disjo int i f their i ntersection i s the empty c l ass. A key concept of my framework i s gro up ing. G i ve n a class A , a gro uping of A i s a. class of subclasses of A . I n t u i t i vely, a grou ping of a class represents a classificat i on scheme for t he objects in t he c lass. F igure 6 . 1 shows some exam ples of grou p i ngs of a class. ( G roupi ngs m ay be i n d u ced by relations as explai ned below . ) G i ven a grou p i n g of a class A , i t i s said to be pai1·wise disjoint i f t h e i n tersect ion of any t wo members of the grouping i s a l ways t he empty class; and full i f the u nion of all the members of the grouping equals t h e class A i tself. In Figu re 6 . 1 , the group i n g shown in ( b ) i s fu l l but not pairwise d i sj oi n t , w hereas the one in ( c ) i s pai rw ise d isjoint but not ful l . When a group i n g i s both fu l l and pairw i se d i sjoint i t i s sai d to be a partitio n . The grou p i n g shown in 6 . 1 ( d ) i s a part i t i o n . I m u s t rem ark here that axiomat i c set theory makes a dear d i s t i n ction between sets and classes. All sets are classes but only t hose classes t hat are members of other classes are sets . The reason for mak i n g t h i s d isti nction i s t o avoid R u ssel l ' s paradox t hat comes from con s ideri n g ' t he class o f a l l such c lasses which are not a member of t hemselves. ' The axioms of set t heory deli neate precisely all those c l asses t hat are sets by defining the empty class to b e a set a n d then g i v i ng a bunch of other rules that allow new s e ts to be c reated from ex i s t i n g sets . In formaliz i ng my framework , i t m i gh t h ave been p r u dent to star t out with sets i nstead of classes. H owever, I chose cl asses so as to spare me from h a v i n g to explai n , and you from havi n g t o u n d e r s t an d , t h e a. x ioms of set theory-especi ally s i n ce t hose axi o m s are n ot cruci al t o u n derst a n d i n g my formalizat i o n . As far as Russell 's paradox is c o n c e r ne d , we can si mply rule out t hose classes t hat are members of t hemselves : t hey do not p l ay any interest i n g role in my framework any way. A reader i nterested in the axioms of set theory and know i n g further about t he hows and w hys of sets vs . c l as s e s shou l d con s u lt M ac Lane [ 1986] , Chapter X I , or Levy [ 1 979] , Chapter 1.
Chapter
6:
Cognition: Formal Concepts
(a) A class of objects.
.,. .- .. ....... . - �- .. · ----.. .._ .._ .._
("� @ � ....... ....
�:-) ..... � ...
--
-........ .... ........ . ..__ _ _ _ _ _ _ _ .. � � �
(b) A grouping over the class that is full but not pairwise disjoint.
(c) A groupin g over the class that is pairwise disjoint but not full.
(d)
A grouping over the class that is a partition .
FIGURE 6. 1 : Examples
of groupin g over a class.
193
1 94
Part II: A Theol)'
6.3
Relations
and
Induc ed G roupings
In i nstant i a t i ng a concept network , the concepts of t he network are related to the parts of the environ ment . In t h i s section I i n t roduce the concept of a relat ion formal l y. I l i m i t mysel f to relations between c lasses h ere relat ions between algebras ( wh i ch i s how cog n i t i ve relations are form al i zed ) are s aved for Section 8-u n t i l after 1 h ave i n t roduced the concept of algebra. I also s how in t h i s section how relations can i n duce groupi ngs over c l asses . I start w i t h some elementary defi n i t ions, and t hen present a few i nteres t i ng characteristics of a speci al k i n d of rel at ions called ' di fu n c tional relat ion s ' t hat i n d u ce part i t i on s over t heir c l asses . F i n a l ly, I d i scuss relations w i t h i n a c l ass. 6.3.1
Preliminary D efi nit ions
G i ven two cl asses A a n d B , the p roduct of A and B , writ ten as A x B, i s the class of al l ordered pai rs s u ch t h at the fi rst element of each pai r i s a . member of A and the second element a member of B. I f A i s { A ustral i a } an d B i s { Sy dney, Boston } then A x B i s t h e c l ass { ( A ustral ia, Sydney ) , ( A ustral i a., Boston) } . The n t h p o w e r of A , w r i t ten as A n , i s t he product of A w i t h i t self n t i mes . T h a t is, A 2 i s A x A , A3 i s A x A x A , etc. G i ven two c l asses A and B , a. rela t i o n from A to 8 i s a subclass of A x B . I n other word s , a relation assigns to each object of A zero o r more ob j ects of B. The class A is sai d to be t h e dom ain of R and c l ass B is said to be t h e codo m a i n . Exam p l es of some rel a t i o n s are shown i n Figure 6 . 2 . I f R i s a relation from A to B , t hen the i n v e rs e of R, w r i t t e n a s is the class of al l p a i rs (b, a ) , w i t h b E B and a E A , s u ch t h a t ( a , b) O bviously t h e n , R- 1 i s a relat ion from B to A . G iven a
R- 1 , E R.
from A t o B , and a no t h er relat ion S from B to C, of R and S , written as R o S , is d efi n e d to be t h e class of all p a i rs ( a , c) , with a E A an d c E C , such t hat t here i s so m e b E B w i t h (a, b) E R an d (b, c) E S . I n other words, for every object a E A , consi der all t h e ob j ec t s of B that are ass i gned t.o a by R . and t hen for e ve r y such object t a ke a l l those objects i n C t h at. are assi gned to i t by S , an d as si g n them all to a . Thus, R o S i s a relation from A to C . the
relat i o n R
co mpos i t i o n
Every relation between t.wo cl asses i n d u ces groupings o n each c l a.s s . I f R is a relation fr o m A to B , t hen for every object a E A consider t he c lass of all those o b j e c t s i n B that are assigned to a by R. This i s obviously a s u b c l a s s of B . I refer to i t as t he image of a u n der R, and w r i t e it as R(a ) . Now
Chapter
6:
Cognit ion: Formal Concepts
1 95
\
\
I
\
3 I
\ 4 \.
(a)
i
/ ;'
• , ....,._ ,;"�
CODOMAIN
DOMAIN
aa
,
\
'·..
bb
· ...
4
.1
/
(b)
FIG U R E 6.2: Three rel ations from the class
{ 1 ,2 , 3 ,4 } .
� - �
I
j /
{ a,b,ab,ba,aa,bb } to the class
Part II: A Theory
196
..
... /
/ "'--.... �..\ .
/
a
ab
f
ba
\
/
!
\
\,
i
·-� -/·
(�· ·� '. / •
.. /
b
...�.
ba
/.--. ..\ 1 I
I
\
..
..... _.. ·
\
\
/
\.•. � ....·
(a)
! t\ 2
\
ab
\ bb
\ aa /
\
�
/',
{2j
l
. )
'"
J
/
(b) FIGURE 6.3: Groupings induced by the relation of Figure 6.2(c) on (a) its domain, and (b) its codomain.
c l ass of all t h o se s u b c l asses of B t hat are i m ages of some obj ect in A i s on B. T h i s i s c a l l e d the gro u p i ng induced by R o n i t s codo m a i n . S i m i l arly, for every obj ect b E B the c l ass of a l l objects of A that are assigned to b by R i s called the p re - i m ag e of b, and i s w r i t ten as R- 1 (6) since i t i s , i n fac t , t h e s a m e a s t h e i m age o f b u n d e r t h e i nverse o f R. B y considering the p re - i m age s of a l l objects i n B u n d e r R, we get th e gmuping indu ced b y R o n i t s d o m a i n . T h e groupi ngs i n d u ced b y t h e relation o f F i g u re 6 . 2 ( c ) o n i t s domai n a n d codom a i n are s h o wn i n Figure 6 . 3 . the a
g rou p i n g
N o t i c e t h at i n
(R o S t1 6.3.2
=
s- 1 o R- 1 .
t h i s notat ional
scheme w e have R
o
S( x )
=
S ( R( x ) ) and
D ifunct ional Relat ions
A r e l a t i o n R from A to B is said to b e functional i f t he group i n g i n d u ce d by it on A is a part i t i on of A ; cofu n c l i o n a l i f the g r o u p i n g i n d u ced by t h e relation on B is a part i t ion ; and difunclional i f bot h the groupings are par t i t io n s o f
Chapter
6:
1 97
Cognjtjon: Formal Concepts
t hei r respec t i ve classes .
D ifunctional relat ions were studied by a Fren ch mathemat i c i an Riguet i n t h e l ate 1 940s . 1 ( See also M a l' cev [ 1 973] , p . 23 . ) H ere I note a few i nteres t i ng character i s t i cs of them . Before doing that , I i n t ro d u ce one more term . A r e l ation R from A to B i s sai d to be full in A , or s i m p l y full, i f the grou p i n g i n duced b y i t on i t s domai n ( A ) i s ful l . ( Recall t h at a grou p i n g is fu l l i f t he u nion of all its members equals the c l ass-A i n this case-i tsel f. ) Thu s, a relat i o n i s ful l i f every member of its domain i s related to some obj ect i n the codomai n . Now i f w e start w i t h a subclass, say X , o f A , t he n t h e image of X u n der·
R i s the class { y such that (x , y ) E R for some x i n X } . \h/e w i l l denote i t b y R(X ) . S i m i l arly, starti ng wi t h a subclass Y of B , w e c a n defi ne R- 1 (Y)
to be t he class { x s u ch that (x , y ) E R for some y i n Y } . are now easily deri ved : Fact : 6 . 1
2.
T he
fol lowing facts
Fo r a n y r·elation R fmm A lo B , the following pmper·ties h old:
Fo r all X � A, R( X ) � R( R- 1 ( R( X ) ) ) .
3. R is full if, a n d o nly if, X � R- 1 ( R( X ) ) for all X � A . P r o of: The first two remarks are i m m ediately obvious, and he re I p r e s e n t the pr o of of the t h i rd rem ark o n l y. F i rst ass u m e t h at R i s fu l l . Then for eve r y x i n A - a n d i n p ar t i c u l ar fo r every x i n X - t h e re is a y i n B such that the pair (x, y) is i n R. In other words, for every x i n X t h e r e i s some y i n R(X) such t h at ( x , y) i s i n R .
Let R(X ) be cal led Y . Now by defi n i t i o n , W 1 ( Y ) i s the class { x s uch th at ( x , y) E R for some y i n Y } . But s i n ce for every x in X, t he r e is some y i n Y s u ch that ( x , y ) i s in R, we con clude t hat e v e r y x i n X i s also i n R- 1 ( Y ) ; t hereby prov i ng half of the t h i rd remar k . To p rove the other half, assume that for every X � A w e k n o w t h at X � R- 1 ( R( X ) ) . l must now s h ow l h al R is fu l l . p rove t h i s by cont rad i c t i on . A s s u me t h at R i s I I O l ru l l . I t m e ttll S t h at least one object in A that is not related to an y t h i n g i n B by R. Cal l s u ch an object a . Now let X = { a } . Clearly, R( X ) 0 , and t h erefore R- 1 ( R ( X ) ) R- 1 ( 0 ) 0 a l s o . Therefore, i t i s not the case for X = { a } I
t h e r e i s at
=
=
1
=
I am gratefu l t o Beryl N e l so n for t r a n s l at i n g some theorems o f R i g u e t from French
into English for m e .
Part II: A Theory
198
t h at X � R - 1 ( R( X ) ) , contrad i c t i ng our ass u mption , and proving the second part of the t h i rd remark also. 0 S i nce R - 1 i s a rel ation from B to A , we can also i n fer the d u al of each remark in Fact 6 . 1 . For i nstance, the dual of remark ( 3 ) i s : R is ful l i n B i f, and only i f, Y � R(R- 1 ( Y ) ) for all Y � B . G i ven any cl ass A , a chain i n A i s a sequence o f non- decreasi n g subclasses of A: t h at i s , a sequence A0, A 1 , . . . such that A ; � A and A ; � A;+l for all i . For i n stance, i f A i s the class of all posi t i ve i ntegers, then the sequence A ; defined as : A0 = 0 , A 1 { 0 } , A 2 = { 0 , 1 } , . . . , A; = { x such that x < i } , . , i s a chai n i n A . Now gi ven a relation R from A to B , every subclass Y of B i nd u ces a chai n i n A u n der R, where the i n i t ial element of t h i s chain i s R - 1 ( Y ) , a n d t h e element fol low i n g A ; , for i 2 0 , i s R- 1 ( R( A; ) ) . R i s said t o b e disco n n ected i n A i f a l l such chai n s , for any Y � B , are constan t : mean i n g t h at Ao = A 1 = S i m i larly, every subclass X of A i n d u ces a chain i n B , with t h e i n i t i al element being R ( X ) . We say t h at R i s discon n ected in B i f al l such chain s , for any subclass X o f A , are constant . We c a n n o w p rove t h e following i n teres t i n g fact : =
·
·
.
.
· .
Fac t : 6 . 2
Given that R is a rela t i o n fm m A to B , each of t h e follo wing fo u r co nditions implies the o t h e r three: 1.
Th e grouping induced by R
on
A
is pairwise disjo int.
2.
Th e gr·o uping induced b y R o n
B
is pai1·wise disjoint.
3.
R is disco n n ected y
� B.
in
A.
Th a t
is ,
R- 1 ( Y )
=
4 - R is disco n n ected in B . fn other words, R ( X ) X � A.
R- 1 ( R( R - ' ( Y ) ) ) fo1· all
=
R( R-1 ( R( X ) ) ) for all
P r o of: I fi rst show t h at ( 1 ) implies ( 2 ) by c o nt r ad i c t i on . Assume t h at the groupi ng i n d u ced by R o n A i s pairwise d i sjoint b u t the one i n d u ced on B i s 0 n o t . T h i s m e a n s t h at for a l l y1 , y2 i n B w e e i t h e r h av e R- 1 (y, ) n R- 1 ( y2 ) or h ave R- 1 ( y 1 ) R- 1 ( y 2 ) . On t h e ot her h an d , t here exists at least one pai r of objects i n A , s ay a 1 and a2 , s u c h that R ( a 1 ) =J R(a1 ) and R(a 1 ) n R(a2 ) =J 0 . T h i s m e a n s t h a t t here i s a t l e a s t o n e obj ect , say b1 2 , that R( a ! ) and R(a2 ) =
=
h ave i n common ; and one of t hem , let us say R(at ) w i t hout loss of generality, has an o b j e c t , say b, , t hat i s not in R ( a 2 ) . This s i t uation i s depicted i n F ig u r e 6 . 4 .
Ch ap ter
6:
Cognition : Form al Con cep ts
A
1 99
B
FIG URE 6. 4 : P rop eny of rela tio n R in the proof of Face 6.2 .
Pa. r t
200
/J : A
Theory
Now consider R- 1 ( bl 2 ) and R- 1 ( b 1 ) . C learly, a 1 and a 2 are both i n R - 1 ( bt 2 ) · H owever, a 2 i s i n R - 1 ( b 1 2 ) but not i n R - 1 ( b! ) . Thus, R - 1 ( b 2 ) =/= 1 R - 1 ( b 1 ) , but R- 1 ( b 1 2 ) n R - 1 ( b ) =/= 0 . T h i s contrad i cts the assumption t hat 1 t he group i n g i n d u ced on A by R is pai rwise d i sj o i n t , and proves t h at ( 1 ) i m p lies ( 2 ) . The proof t h at ( 2 ) i m p l i es ( 1 ) can b e deri ved by duali ty-that i s , by tak i n g R- 1 to be the relat ion i n quest ion , and applying the result I j ust p roved-t hereby p roving that ( 1 ) and ( 2 ) are equi valent . I leave i t to you to com plete t he rest of t he proof. It needs to be shown th at ( 3 ) i m p l ies ( 4 )-then ( 4 ) i m p l ies ( 3 ) fol l ows from d u al i ty ; (1) i m p lies ( 3 ) ; an d ( 3 ) i m p l i es ( 1 ) . ( O f course, one cou l d fol low some other path also. ) The p roof i n each case is very s i m i lar to t he one 1 p resented here. Note that each p roof i s of the form ' M i mp lies N . ' To prove i t assume first t h at M i s true and N i s fal se. From t h i s show that the s i t uation i n Figure 6 . 4 ( o r i t s d u al ) exists. Fi nal l y, deri ve the negat ion of M from Figure 6 . 4 , thereby com plet i n g the proof by cont rad iction . 0
Facts 6 . 1 ( 3 ) and 6 . 2 together g i ve the necessary and sufficient cond i t ions for a relation to b e d i fu n ct i onal . I now show one ot her i mportant property of d i fu nctional rel at ions: Theore m : 6 . 1 Let R be a difu n ctional 1·ela tion fro m A t o B, a n d F and G be groupings induced by R o n A a n d B respectively. Th en for every X in F t h e 1·e exists a u n ique n o n - empty class Y in G , and fo1· e v e 1·y Y in G th e re exists a u n iq u e n o n - empty class X in F , s u ch th a t R( X ) Y and =
R- 1 ( Y ) = X .
P ro of: S i n ce R i s d i fu n ctional, i t i s fu l l i n bot h t h e empty c l ass 0 i s neit her i n F n o r i n G .
A a n d B . I n o t h e r word s ,
L e t u s take any X i n F . I t can not be empty, so i t must h ave at least one obj e c t i n i t , say a. A l so, by d e fi n i t i on of grouping, t here must be some object in B , s ay b , such t h at R- 1 ( b) = X . N ow for every pai r of objects x 1 , x 2 i n X , w e have b in R(xt ) a n d b i n R(x 2 ) . From t h e defi n i t i o n o f d i f u n ct i o n aJ r e l a t i on , R( x 1 ) an d R( x 2 ) must be disjoint , or equal to each o t h e r . S i nce t h ey are not di sjoint-b i s i n bot h of t hem-they m u s t be equa.l to each other. Thus,
The
R.( X )
=
R ( a ) , w h i c h is in G .
1 part , t hat R- ( R( X ) ) = X , fol lows directly from Fact 6 . 2 , i f we real ize that X i s not h i ng but R- 1 ( { b } ) . second
The proof t h at for every Y i n G t here i s a u n i que non-em pty the same propert ies i s s i m i l a r ly deri ved . o I
m ay
as wel l
r e m a r k h e r e t h at t h e above t h e o r em
X
i n F wi th
es se n tially shows
t h at
Ch ap ter 6:
Cognition: Formal Concepts
20 1
the groupi ngs i n duced by a d i fun ctional relation on i t s domain an d codomai n are bijective, t hough the term bijection i s form ally i n t roduced a l i t t le l ater.
6.3.3
Relat ions Wit hin a C lass
l now exam i ne the case when the dom ai n and codom ai n of a relation are t he same class. R is t hen said to be a rel ation over· A , m e a n i n g t h at Fl i s a subclass o f A x A . A n ambiguity i m mediately surfaces , s i n c e i n genera l t here are two di fferent groupi ngs t h at R i n d u ces on A , one by way of i m age s of objects i n A and the other from the pre- i m ages of obj ects of A . I re fe r to t h e m as th e for·wm·d group ing i n d u ced by R on A and t h e ba ckwa rd g-rouping i n d u ced by R on A , respect i vely.
I f a rel ation o ve r a class i s such that both the forward and the back ward groupi ngs i n d u ced by it are the same, we say t h at t he rel ation is symmetr·ic. O ther ways of specify i n g t he symmetry property are to say ( 1) t h a t a. rel ation R over a class A i s symmetric i f, and only i f, i t is such t h at whenever ( x , y ) E R, for some x , y E A , then ( y , x ) E R; or ( 2 ) to say t h at R is symmetric if, a. n d only if, R R-1 . Whe n a relat ion R over a cia s A i s known to be symmetric, we can talk of the gmuping i n d uced by R on A, as the m e n t i o n of forward or backward does not m ake any el i fferen ce. =
If a relation R over A is such that every object i n A i s related t o i t se l f- i n other words , for e ve ry x i n A , ( x , .r) i s i n R-t hen we say t h at R is r·eflexive . If a r el a t i o n R over a class A is such that whenever for �tny x , y , ;; E J\ i t i s t h e case t h at ( x , y ) E R a n d ( y , z ) E R t h e n (.T , z) E H , w e say t h a t R i s t ransitive. A n ot h er way o f spec i fy i n g t h e t r a n s i t i ve p roperty of a relation R i s to say R o R � R .
A r e l a t i o n over a c l ass t h at i s reflexi ve, s y m m et r i c , and s am e t i me, i s ca.l l e d a n equ ivale n ce rela t i o n . Fact : 6 . 3
If
a
th e gr·o uping on
t ra n s i t i ve ,
a.t the
R over a class A is a n equivalence r·ela lion , then induced by R i s a partition of A. In other wo nls , e v F -ry
rela tio n A
equivnle n ce r·e ln i' i o n is
difunction al.
Pro of: Assume t hat R i s an equ i valence re l at i o n over " c l ass A. Now i n t o prove t h i s fact , o n e m u s t show ( l ) t h a t t h e u n i o n o f a l l s u b c l asses in the grou ping on A i n d u ced by R is e q u al to the c l ass A, an d ( 2 ) t h at the
o rder
i n tersec tion of any t wo subclasses in t h i s g r o u p i n g i s the em pty class. I prove
both parts by cont radiction . To prove ( 1 ) , a ss u m e t h a.l i l i s nol true. S i nce every member of the gro u p i n g i s a s u b c l ass o f A , t h e u n ion of a l l t h e m e m bers can a t most equal
202
Part II: A
Theory
to A : t h at i s , it is al ways a subclass of A also. S i n ce we assumed t h at i t i s not equal t o A , i t must b e a proper subclass o f A . I n other words, there must be at least one object , say a , i n A t hat i s not i n any of the subclasses in the group i n g . T his means t hat for every x in A , a i s not i n R( x ) . In part i c u l ar , a is not i n R ( a ) , i m plying t h at R is not reflexi ve and contrad i ct i n g our i n i t i al assu m p t i o n . Hence, ( 1 ) must be true. To prove the second part , again assume i t s negat ion . That i s , t here are at least two dis ti nct subclasses of A i n the group i ng i n du ced by R such t hat their intersect ion is not t he em pty class. Let t hese be X and Y . Now s i n ce X and Y are not d i sj o i n t , they must have at least one object i n common . Call such an object a. A lso, X and Y are not equal , meani n g that one of t hem have an object t h at is not i n the other. W i thout loss of general i ty, let us say th at there is an object b that is i n X but not i n Y . Now X and Y must be the i m age u nder R of two d i fferent objects in A. Let t hese objects be x and y respecti vely. So now we h ave R ( x ) = X , R ( y ) Y, a E X , a E Y, b E X , and i t i s not the case t hat b E Y . However, t h i s means t h at ( x , a ) E R an d ( y , a ) E R . From symmetry o f R we k now that ( a , x ) i s also i n R , and from t rans i t i v i ty of R we can fu rther conclude t h at ( y , x ) is i n R. We also h ave t h at b E X i mplying that ( x , b) E R and agai n from t rans i t i v i ty of R we i n fer (y , b) E R. However, t h i s l ast fact means t hat b E Y, t hereby contrad i c t i n g our assu m p t i o n t h at X a n d Y are n o t equal . D =
The i n verse of t h i s fac t , however, i s not true. I n other words, there are d i funct ional relat ions t h at are not equi valent r e l a t i on s . As a very s i m p l e exam ple, co n s i der t h e c l ass of two o b j e c t s { a , b} and the symmetric relation { (a, b) , ( b, a ) } over it. The group i n g i n d u ced by t h i s rel a t ion i s a par t i t ion of the class, but the rel at i o n i s not reflexi ve or t r an si t i ve and i s t herefore not an equ i va l e n ce rel at ion . ,
6.4
Funct ions and O p erators
I n my framework , concept n etworks a.nd e n v i ro n m e n t s are formali zed as al gebras, and an algeb ra. is a class of objects and operators defined over t he class . C o n s eq u e ntly as a prel ude to i nt ro d u c i n g a l ge br a.s I i nt roduce t he concept of an o p e r a to r i n t h i s section . 1 do so by first discussing f u n c t i o ns , which are special k i n d s of relat ions, and then presenting operators , which are special ki nds of fu nctions. ,
,
Ch ap t er 6: Cogn i tion : Form al Con cep t s
6 .4 . 1
20:3
Funct ions
G i ven two classes A and B, a Ju nction from A t o B , i s an assignment of a u n ique member of B to each member of A . I f A were the c l ass of al l countries i n the wor l d , and B were the class of all cap i t al c i t ies of the worl d , then the assignment capital- of t h at assigns a u n i que cap i tal c i ty to each cou ntry i s a function from A to B . A fu nction i s a special k i n d of rel at i on , where, for every x E A t here i s one, and on l y one, pai r ( x , y ) , for some y E B , such t hat the pai r i s in the relation . Of the relations shown in F igu re 6.2, only the one i n ( a ) i s a fun ct ion . The relation i n 6 . 2 (b) i s not a fu nction because the objects ' ab ' and 'ba' are not assigned anyth i ng , and the rel at i on i n 6.2 ( c ) i s n o t a function because 'ab' and 'ba' are each assi gned two objects o f the cl ass B. I t simply fol lows from the defi n i tion of a fu nct ion that : Fact : 6 . 4 Eve ry function is a functional 1'ela tion. in othe1, W01'ds, t h e gmup ing induced b y a fun ction o n its domain is always a padilio n . However, the converse o f t h i s i s n o t t rue: that i s , t here are fu n ct ional relations t h at are not functions. The rel at ion is- a - city-of from the c l ass of al l cou n tries to the c lass of all cities that relates every cou ntry t o a l l the c i t i es in th at cou n t ry i s a functional relation b u t is not a fu nction .
The group i n g i nduced by a function on i t s codom ai n need not a l w ay s be a part i t i o n . However, when it i s-that is, w h e n a fu n c t i o n i s a cofu n ct i onal relation-we say t h at it i s a sm jective or onto fu nction .
S i nce every fun c t i on is a re l a t i on , we can also defi n e compos i t i on of two functions and inverse of a funct ion . Tf F i s a fu n ct ion from A to B , and G i s a fun c t ion from B to C, then the com pos i t ion of F and G, wri tten as F o G , i s a relation t h at assigns to e v e r y obj ect a i n A, the objects G ( b ) , w here b E F ( a ) . Noti ce t h at since F i s a fu nct ion , F ( a ) contains e x ac t l y one objec t , s ay b, and s i n ce G i s a fu n c t i on , G ( b ) a l s o co n t a i n s exac t l y o n e obj ect . In other words, F o G assigns e x a c t l y one object of C to e v e ry obj ect of A . T h i s leads t o the following fact :
Fact : 6 . 5
Th e co mpos itio n
of two functio ns is
H owever t h e i nverse of a fu n c t i o n , i n
a
functio n .
genera l , m ay n o t
be
a
t h e class of all posi t i ve and n egat i ve i n t egers i n c l u d i ng
fu n ct ion .
0 , call
C o n s i der
it Z, and a
function squ a ?'e fr o m Z to Z t h at ass i gns to every number its square . T he i nverse of square i s not a funct i on because some n u m bers , such as 2 and 3 , are n o t assigned any number by t he i n v er s e o f s q u a 1'e and aJso numbers such as 4 are assigned two n umbers : +2 and - 2 . A fu nction such that i t s i n verse i s also a function is sai d to be b ijective.
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II: A
Th eory
H ere agai n i t should be n oted t h at w hereas every bijecti ve fu nction i s d i fu n ctional, n o t every fu nction t hat is also a d i functional relat ion i s bijecti ve . 6.4.2
O p e rat ors
A n ope mtor over a non-empty class i s a function from some i nteger power of the class to the class i tsel f. Thus, an n-m·y opemto1· on a non-empty class A is a fu nction from An to A : a u n ary operator on A would b e a function from A to A , a b i n ary operator wou l d be a function from A 2 to A , etc. 1 f we consider the c l ass of al l pos i t i ve and negati ve i n tegers i ncluding zero, then addi t i o n , subtract i o n , and m u l t i p l i cation are al l binary operators on i t , w hereas negat ion i s a unary operator. N ot i ce t h at a n operator can b e 0-ary, in w h i ch case it does not t ake any argument but retu rns a member of the class A . G i ven any non-empty class A , t here are some spec i al operators on i t that are gi ven standard n ames . For each n > 0 , t here are n identity operators . The i t h n- m·y ident ity opemt01·, w r i t ten as J�i) ( where n 2': i > 0 ) , i s the n- ary operator such that for any a 1 , , a;, . . . , a n E A , J�i l ( a 1 , . . . , a ; , . . . , a n ) = a ; . S i m i l arly, for a n y member a E A , t h e n-ary constant operator with valu e a , w r i t ten as c�a ) ( where n 2': 0 ) , i s the n - ary operator such t h at for any a , , . . . , a n E A, CAa l ( a , , . . . , an ) = a . •
•
•
G i ven some operators over a class A , new operators can be deri ved from t hem by spec i a l i zat ion and c o m po s i t i on . If a is an n - ary o perat o r , t hen a specia liza t i o n of a i s any operator t h at i s deri ved from a by fixing one or more of its argu ments. For i n stan ce, the b i nary operator add over the class of i ntegers can be spec i al i zed as a. unary operator add3 by fixing the second argument t o be 3 , or a.s the 0- ary operator 2add5 by fixing the fi rst argument to be 2 and t h e second argument to be 5 . A s one wou l d expect , a dd3 adds 3 to the argu ment n u m b e r , a n d 2add5 a c c e p t s no arguments and al way s returns t h e n u mber 7 .
T h o u g h t he c o m p o s i t i on
of u n ary operators can be s i mply arr i ved at by funct ions, i t may not be i m me d i ately o b v i o u s how to compose operators of ari ty other t h a n l . G i ve n t h 11.t a i s an n - ary operator o ve r a non-empty class A, a n d {3 1 , . . . , fJn are 11.l l m - ary operators over A , the co m p ositio n of (/3 1 , , /3n ) w i t h a , w r i t te n as ( /31 , . . . , f3n ) o a , is the m-ary operator over A s u c h t hat for a l l a 1 , , a "' E A , ({31 , , f3n ) o a ( a 1 , , am ) = a ( fJI ( a 1 , - . - , am ) , . . . , f3n ( a 1 , . . . , a m ) ) . com p o s i ng
them
as
•
•
•
•
•
•
_
_
_
•
•
•
A n e x a m p le m ay make t h i s clearer. Consider the b i n a r y operator sub i n te ger s t h at s ubt r ac t s the second a r g u m e n t from the first argument .
over
Ch ap t er 6: Cogn i tion : Form al Con cep ts
205
Consi der also two unary operators add3 and m ult2 t h at are deri ved by spe cializing t he operators of add i t ion and m u l t i p l i cat ion respecti vely. Now the com p os i t ion of ( add3, mult2) w i t h sub i s the u n ary operator ( x + 3 ) - 2x w here x i s the argu ment number. Notice that the order i n w h i ch the oper ators are composed is very i mportant . If we compose sub w i t h m ult2, t hen we get sub o m ult2 2 ( x - y ) , w h i ch i s a b i n ary operator w i t h x being the first argument and y being t he secon d argument . =
6.5
A lgebras and Structures
In my framework, con cept networks are formali zed a s fi n i tely generated al gebras . I n t h i s section I present a general characterization of algebras , and discuss how operators of an algebra endow its objects w i t h an operat ional structure and make generat i v i ty possi ble. I start by defi n i n g w h at an alge bra is and t hen characterize the notions of descriptions and s t r u ct u res w i t h i n algebras . Follow i ng t h at , I i n t roduce the concepts o f clos u re a n d generat i n g class of an algebra. F i n ally, I i n t roduce the clos u re over operators ( polyno m i al operations ) and the computab i l i ty of operators . A lgebras
6.5.1
i s a pai r ( A , n) where A is a
n o n - e m pty c l ass of objects a n d 11 operators over A . For c o n v e n i e n c e we a.s s u m e t h at the class of operators of any algebra is alway s d i sj oi n t from its c l ass of obj ects: t h a t i s , A n n 0 for any algebr a ( A , 11 ) . W i t h each operator i n 11 w e asso c i ate i t s arity: a posit i ve i nteger specify i n g the n u m ber of argu ments t h at m u s t b e supplied to the operator. I f w E n has arity n then w is a fu nction from A n to A . For any n we denote t h e c l ass of a l l n - ary operators in 11 by 11 ( n ) .
An
algebra
is a class
of
=
Examples o f algebra abou n d . You are surely fam i l iar w i t h t he al ge b r a of operators of add i t i on , s u b t r a ct i on , a n d m u l ti p l i ca tion . Boolean al geb r a is t h e a l ge b r a of truth val ues ( ' t rue' and ' fa ls e ' ) and i n teg e r s , w i t h i t s b i nary
the u n ary operator ' n ot . ' O n e nee d n o t l i m i t oneself to t h e realm of m athemat ics t o look fo r exam p l e s o f a l ge b ra ; t hey can be easily fou n d i n o u r d ay- t o- d ay l i ve s . Con s i d e r a c o n s t r u c t i o n kit for bui l d i ng a model of an o c e a n l i ner . T h e kit comes w i t h a sel of con s t r u c t i o n p i eces t hat can be put together o n l y in cert a i n way s . N o w all t hese const ruction pieces , as well as all possible c o n f ig ur a t i o n s l h al c a n has t h e b i n ary operaJ,ors ' an d ' and ' or , ' an d
be assembled by using some or all of
t h e p i eces , can be v i ew.ed a s
objects of
206
Part
II: A
Theory
an algebra. The operators of t h i s algebra are all possible ways i n w h i ch two or more const ruction pieces , or partial assemblies , can be j oi ned together to yield a larger assembly. Not i ce t h at from t h i s viewpoi n t , the final assembled model of the ocean l i ner i s merely an obj ect of the algebra, and the class of obj ect s i n c l udes all possible par t i al assemblies . A t t h i s poi n t , you m ay as wel l fami l i arize yourself w i t h a couple o f example algebras , shown in Figure 6.5 ( a) and ( b ) , t h at are very explicitly and ful l y specified , s i n ce I u s e these exam ples to i l l ustrate m a n y other concepts an d construct ions related to algebras i n the rest of the chapter . F igure 6 . 5 ( a ) shows a n algebra of stri ngs of letters . T h e objects of t h i s algebra are all possi ble non-null stri ngs of letters 'a' . . . 'z' such as : 'a,' ' m m x x n , ' ' zzzzz , ' etc. The algebra h as s i x one- place operators: succ, 7n·ed, copy, 1·e ve1·se, ji1·st, and last; and one two- p l ace operator: cone. The operator succ assigns to every character i t s s u ccessor, w i t h the successor of 'a' being ' b , ' that of ' b ' bei n g ' c , ' . . . , a n d t h at o f ' z ' bei n g ' a ' ; a n d to every string t h e string obtai ned by replacing every character in t he origi nal string by its successor. The other opL rators are s i m i l arly described. The operator p red i s the i n verse of succ and assigns to every stri n g the string obtai ned by replac i ng every character by its p redecessor , where the p redecessor of ' y ' is ' x , ' of 'a' i s ' z , ' e t c . T h e operator copy repl i cates t h e argument t r i n g a n d a n d t hen puts the two in sequence, and re verse reverses the order of characters in a. string. The operators first and last r e t u r n the fi rst an d the l ast character of the argumen t s t r i n g r e s pe c t i ve l y . The two-place operator c o n e accept s two stri ngs as argument , and gene r a t es a s t r i ng t h at i s o b tained by concaten at i n g the two stri ngs. A few i nstances of the stri ngs generated by a l l t hese operators are shown in the fi g u re , and should help one u n derstand t hem bet t e r . I refer to this algebra as S T R I N G . T h e second algebra shown i n Figure 6 . 5 ( b ) , referred to a s INTEG ER, i s al geb r a of signed i n tegers. A s everyone m u s t be fam i l i ar w i t h i t , I t h i n k t h at t h e figure i s sel f- e x p l a.n ator y a n d no fu rther explanation o f its operators is needed here. the
In t hese t wo a lgeb ras you m a.y not i ce t h at some operators are derived from o t h e rs by composition or specializat i on . For instance, in S T R I N G the operator cop y i s the com{t osi t ion of a pair of unary i dentity operators with co n e : that i s , c o p y (11 1), 1) 1 l)o co n e . S i m i larly, t he operator n ext in I N TEGER i s a speciali zation of a dd in which the first a rg u m e n t ( or the second argument ) is fixed to be 1 . The operator sub i s also a composite operator, though i t s expression is so m e w h at co m p l i cat ed . I i n v i t e you to express sub i n terms of other operators of I N T E G E R . A clue i s t h at it uses the operators =
207
Ch ap t er 6: Cogn i t ion : Form al Con cep t s
O bj ec t s : A l l finite strings of letters ' a ' t o ' z ' . Ex: a , aabb, rnrnnnxxppww, etc. (Note: Null string is not included.)
Unary
O perat o r s :
S U C C Replaces every character in the string with its successor.
Ex: SUCC(a)
b; SUCC(z)
=
=
a; SUCC(abz)
=
bca; SUCC(mnxx) = noyy; etc.
PRED Replaces every character in the string with its predecessor.
Ex: PRED(a)
z; PRED(z)
=
=
y; PRED(abz) = zay; PRED(mnxx)
=
lmww; etc.
COPY Appends a copy of the string to itself.
Ex: COPY(a) = aa; COPY(z) = zz; COPY(abz)
=
abzabz; etc.
REVERSE Reverses the order of characters in the string.
Ex: REVERSE(a) = a; REVERSE(abz) FIRST
=
zba; REVERSE(mnxx)
xxnm ; etc .
=
Returns the first character of the string.
Ex: FIRST(q)
=
q; FIRST(zz)
=
z; FIRST(abz) = a; FIRST(mnxx)
=
m ; etc.
LAST Returns the last character of the string. Ex: LAST(b)
b; LAST(kw)
=
=
w;
LAST(abz)
=
z; LAST(mnxx)
=
x; etc.
B i n a ry O p e ra t o rs : CONC Appends the second Ex :
CONC(a,b)
FIGURE 6 . 5
=
s tring a t the back o f the first strin g .
ab; CONC(amn,wxz)
=
(a) : Algebra STRING
amnwxz; CONC(p,p) pp; etc . =
of strings of characters.
Part II: A Th eory
208
O bj ects :
All positive and negative integers including zero.
Ex:
0, 3 1 89, 1 , - 1 , etc .
5, -245 ,
U n a ry O p e rators : NEG Changes the sign of the number.
Ex: NEG(-5) NEXT Adds
=
5; NEG(8)
=
etc.
-8;
1 to the number.
Ex: NEXT(-5)
=
-4 ; NEXT(7)
=
8;
etc.
B i n a ry O perators : ADD Adds the first number to the second number.
Ex: ADD(3 ,5) SUB
=
=
6;
etc.
S ubstracts the second number from the frrst number.
Ex: SUB(-3,-5)
MULT
8; ADD(8.-2)
=
Multiplies
Ex: MULT(5,2)
2; SUB(6,2)
=
4;
etc.
the frrst number with the second number. =
10;
MULT(4.-3) "" - 1 2 ; etc.
FIGURE 6.5 (b): Algebra INTEGER of signed
integers.
Ch ap t er 6: Cogn i tion : Form al Con cep ts
Obj ects Operators arguments a1 a1 al a2 a2 a1 a2 a2
209
{ a 1 , a2 } {!� , h , h }
operators fl h h a 1 a2 a 1 a2 a1 a2 a 1 a 1 a2 a2 a2 a2 Tabl e 6.1: A lgebra A L G l
of a dd, n eg ,
and two b i n ary i dent i ty operators
IJ 1 l a n d JJ2l .
The two other algebras shown i n Tables 6 . 1 and 6 . 2 are somewhat ar t i fi c i al . A L G l has two objects and t h ree binary operators, and A LG 2 h as t h ree objects and two b i n ary operators. The act ion of t hese operators on the objects of t hei r respect i ve algebras i s shown by l i st i n g the res u l t s of apply i n g each operator for all possi ble pairs of i n p u t objects . This can be done because t hey are fi n i te . A n a l ge b r a. ( A , 11 ) i s sai d t o be fi n i t e i f i t s c l a.s s of obj ect s A i s fi n i t e , a n d infinite otherwise. Of t he four algebras we j ust saw , I N T E G E R and S T Rl N G a re
i nfinite, w hereas A LG l
6.5.2
and
A L G 2 are fi n i t e .
D escriptions and St ruct ures
I n t u i t i vely, an algebra i s a class of objects hav i ng struct u re. The operators of al ge b r a e n d ow the c l ass w i t h a s t r u c t u re . An o perator essen t i a l l y s p e c i
t he
fi e s h o w a cer t a i n obj ect c a n b e g e n e ra t ed from o t h e r o b j ec t s . T h e refore, i t
i s poss i b le to associate o n e generat ion h i story-or poss i b l y m ore-w i t h each o t h e r o bj e c t s by ap p l y i n g a sequence of operators . For in stance, i n t he construction k i t algebra, the
o b j e c t s h ow i n g how t h at o b j e c t was ge n e r a te d fr o m
i n s t r u c t i o n s t h at m i g h t acc o m p a n y t h e k i t arc i n fact specify i ng t h e ge n era
t ion history of the object t h at is the final assembled model . Sim i larly, i n the alge b r a S T RI N G , fou r d i ffe r e n t gen era t i o n histories of its o b j ect ' aa b b c c ' are s h o w n i n F i gu re 6 . 6 . Now a generat i o n h i s t o ry of a n obj ect can be v i ewed as s p e c i fy i n g how t h e vari o u s s u b- u n i t s com p r i s i n g t h e object are p u t t oge t h e r to form the obj ect . B u t t h i s i s what i s usually meant by the term 'st ructural descri ption . '
210
Pa.rt II: A Theoq
CONC
CONC
�
Fl� /) CONC
CONC
ab
� � � � � � CONC
sT
s ucc
�
COPY
S UCC SUCC
COPY COPY
a
�
ab
a
(a)
a
CONC
A A
bb
� � � CONC
CONC
cc
aa
S UCC
S UCC
t
aa
S UCC
�
aa
(d)
(c)
FIGURE 6 . 6 :
�
(b)
CONC
aa
S UCC
Four different generation histories of the
string ' aabbcc ' .
Ch ap t er 6: Cogn i tion : Form al Con cep ts
Obj ects Operators arguments bl bl b2 bl bl b3 b2 bl b2 b2 b3 b2 b3 bl b2 b3 b3 h
I
21 1
{ b1 , b2 , b3 } { 9 1 , 92 }
operators 91 92 b, b3 b2 b3 b3 b3 b3 b3 b2 b2 b3 b3 b3 b3 b3 b3 b3 b3 Tabl e 6 . 2 : A lgeb ra A L G 2
I n o w formal i ze t h e notion o f structural descri ption . F i rst I defi n e the c l ass of all possi ble structu ral descri ptions over an algebra, and then asso c i ate structural descri ptions with i n d i v i dual objects of the a l ge b r a . G i ven an algebra ( A , f!) , its class of stntctuml descrip tions, denoted by So ( A ) , i s defined recu r s i v e l y a s follows: 1.
For all
a
E
A,
2 . Whenever w
a
E
E
S0 ( A ) , and
n(n)
and
Sj ,
•
.
.
, sn E So ( A ) , t hen w [s , , . . . , sn]
E
Sn ( A ) . The first part of the defin i t ion essentially says t h at a l l obj ects o f t he alge bra are s t r u c t u ral d es c ri p t i on s , and the second part says that every n-ary operator com b i n e s w i t h n a l r e a d y e x i s t i n g st r u c t ur a l d es c r i p t ion s to gener ate a n e w s t r u c t u r a l desc r i p t i on . ( A reader already fam i l iar w i t h al ge b r as w i l l no d o u b t r e co g n i ze t h at t h e c l ass of s t r u c t u ral
n o t h i n g b u t t h e !1- word i"tlge b r a over A
descri ptions
[ C o h 1 1 1 98 1 , p .
1 1 6] . )
of
( A , !1) is
Notice the
squ are br a c es ' [ ' a n d ']' : t h e y se r ve a d i ffe r e n t p u r pose t h an pa r e n t h ese s ' ( ' a n d ' ) ' . I n fac t , i n s h o w i n g s t r u c t u ra l desc r i p t i o n s g r a p h i c a l l y I oflen d raw t hem as l abeled and ordered d i rected acyc l i c g r a p h s , as i n F i g ure 6 . 6 , and not use the square braces at al l . In that case, a s t r u ct u ral d e s c r i p t i o n s i m p l y becomes a l abeled d i rected acycl i c gr a p h i n w h i c h a l l t h e n odes t h at h ave n o outgoing arcs ( ' leaf' n o de s ) are l n.beled w i t h objects of the algebra a n d e v e r y
2 12
Part
II: A
Theory
i ntermed i ate node h av i n g n outgoi ng arcs ( pointing to the ' c h i l d ren ' nodes ) is labeled w i t h an n- ary operator of the algebra. The graphs are ' ordered ' because t h e order i n w h i ch t h e c h i l d ren of an i ntermed i ate node appear mat ters : d i fferent orders mean d i fferent structural descriptions. Note t h at every structur al descr i p t i on h as one and only one node t h at h as no i ncomi n g arcs . We w i l l call t h i s node the ' root ' node. Next I define an e valuation fu nction, w h i ch I abbreviate as eva!, t h at assigns an object of ( A , f! ) to every struct ural descri ption i n Sn ( A ) as fol lows . For every s E Sn ( A ) , 1.
i f s E A then eval ( s )
=
s , and
2 . i f s i s of t h e form w [s 1 , , sn J , for some w E f! ( n ) , t hen eval ( s ) w ( eval ( s 1 ) , . . . , eval ( sn ) ) . •
.
•
=
A gai n the i n t u i t i ve i dea beh i n d t h i s i s very simple, even t hough the defi n i t ion m ay look somewh at compl i cated . I f we consi der structural descri ptions as labeled ordered d i rected acyclic graph s t hen to eval uate a structural descrip tion we start w i t h its leaf nodes. S i nce leaf nodes are labeled w i t h objects of the algebra, t hey eval uate to t hemselves . Now we move one level u p and consi der all the n odes at level 1 ( t hat is, all t hose i ntermedi ate nodes such t h at all t hei r ch i l d re n a r e leaf n o de s ) . A n y node at this level w i l l be labeled w i t h an n - a r y o p e r a t o r i f, and o n l y i f, i t c on t ai n s n ch i l d ren . Moreover, s i nce it is a l e v e l 1 node, all t h ese c h i l d r en are in t u r n labeled w i t h objects t hat h ave been eval u ated to t hemsel ves in t h e p re v i o u s step . I n ot her words, each level 1 node is l abeled w i t h an n- ary operator and has n ordered objects as ch i l d ren , for s o m e n . E ac h such node eval uates to the object obtai ned by appl y i n g t h e n- ary operator t o t he c h i l dren obj e c t s , in t h at order . T h i s process is repeated u n t i l t he r oot , or t h e top level n o d e , i s evaluated . T h e res u l t i ng object i s p r e ci s e ly the obje c t ass i g ne d to t h e s t r u c t u ral d e s c r i p t i o n by eva!. T h i s p rocess i s shown i n F i g ur e 6 . 7 for t h e struct ural descri ption of Figure 6.6 ( b ) a
N ow
a
(struct11.ml) desc7'iption of an o bject a of an algebra. ( A , !:1 ) i s s i m p l y descr i p t i o n s E So ( A ) such t h at eval ( s ) = a . Note t h at an object
s t r u ct u ral
may h ave more t h an o n e desc r i p t ion . A lso, e v e r y object i s i t s own descri p t i o n . l n fac t , i f an a l ge b r a. h a s no ope r a t o r s ( t h a t i s , !1 = 0) then t h i s i s the only d e s c r i p t i on t h at
an
obj ect h as .
G i ven a desc r i p t i on of a n object , the class o f objects t h at appear a t t h e leaf nodes o f t h e d e s c r i ption are called t h e comp o n e n ts of t he descrip t io n , and t h e descri p t i o n t ree obtai ned by replac i ng e ve r y object at the leaf
213
Ch ap t er 6: Cogn i t ion : Form al Con cep ts
CONC
� � � t � t � � CONC
COPY
CONC
S UCC
SUCC S U CC
C
Y
c py
� � � � � CONC
'------,>
S UCC
aa
S UCC
succ
aa
aa
a
a
il CONC
CONC
�
cc
aabb
� � � CONC
aa
S UCC
bb
bb
il
aabbcc FIGURE 6.7; Evaluation of the description shown in Figure 6.6(b) .
214
Part
A
II:
Theory
node of the descri ption t ree w i t h a variable ( one variable for each obj ect ) i s called the structure of the descri ption . For instance, the descri ption of Figure 6 . 6 ( c ) h as as i t s components the class { aa , bb, cc} , and i t s s t ructure i s con c [ X , con c [ Y , Z] ] , w here X , Y , and Z are variables . 6.5.3
C losures and G e nerat ing C lasses
The notions of closure and generat ing class are very closely related to t h at of descript ion , and s i n ce they are both used later o n , t h i s i s perhaps the best pl ace to i n t rod uce them . Let ( A , D ) be an algebra. Now given any subclass X of A, I define So ( X ) as above. It i ncl udes only those descript ions of So ( A ) that h ave their class of components i n cluded i n the class X . ote, however , that t hese descriptions m ay eval u ate to objects that are not i n X . For ex am ple, consi der the a lgebra S T RI N G , and let X { a } . The descri ption in Figure 6.6 ( b ) is i n c l uded in So ( X ) , s i n ce its class of components is { a } , b u t t h at descri p t ion eval uates to t h e s t r i n g ' aabbcc' w h i ch i s n o t i n X . =
Now i f we take the class o f all objects that can result from evalu at i n g some descript ion i n So ( X ) , i t i s called the closu 1·e of X, a n d i s denoted by Jo ( X ) . In other words, x E Jo ( X ) i f, and only i f, t here is some s E So ( X ) such that eval ( s ) x . S i nce every obj ect i s a descript ion for i t self, we h a v e X � ln ( X ) . A lso, w henever X � Y, we h ave So ( X ) <;: So ( Y ) , a n d consequently lo ( X ) <;: Jn ( Y ) . I n part i c u l a r , s i nce ln ( A ) A , we h a v e =
ln ( X ) <;: A .
=
A l ternately, the not ion of closure can also be defined as fol lows . Start i n g w i t h X <;: A , w e fi rst i n d u c t i vely define a sequence o f i ncreasi ngly larger s u bel asses of A by : X xk u
and
{ x where D(n ) }
For i n stance, i f we carry
algebra
S T RI N G ,
Xo
X1 X2
X =
w ( x l , . . . , xn ) for some
X],
.
.
.
, Xn
E xk
w E
we
o u t t h i s cons t ruct ion for
t he class
X =
get :
{a} { a , b, z , a a } { a b, z , a a , c, bb, y, z z , aaaa, ab, ba , a z , za, aaa, bz , zb, baa , aab, zaa , a a z } ,
{a}
in
the
215
Ch ap t er 6: Cogn i t ion : Formal Con cep ts
etc. I t should be obvious t hat for all k , Xk � Xk+ 1 ; and also that Xk � A . Therefore, i f we take t h e u ni on o f all Xk as k varies from 0 t o i n fi n i ty the res u l t i n g class will be a subclass of A . T h i s i s cal led t h e closu 1·e of X . That
IS:
00
Jn ( X )
=
U Xk
k =O
The concept of closure can be more eas i l y explai ned i n t u i t i vely by using t he construction kit algebra example. G i ven a construction k i t w h i ch has some of the construction p ieces m i ss i ng, one m ay not be able to m a ke t h e complete model of the ocean l i ner, but th ere m ay st i l l be several part i al o r complete models t h at c a n be constructed b y usi ng the avai l able pieces . A l l s u c h m o d e l s form the class generated b y the avai l able con struct ion p i eces . Obviously s i n ce any such model can also be con stru cted w i t h the complete k i t , this generated class i s a s u b class of the algebra. A ny subclass X of A such t hat Jn ( X )
A i s called a g e n e ra t ing class of if it is a generat ing c l ass and no proper subclass of X is a generat i n g class also. A m i n i mal generat i n g class for an algebra, i f i t e x i s t s , need n o t be u n i que. For i n stance, a l l t h e objects o f the algebra I N T E G E R c a n be ge ner at e d b y t he class { 1 } , a n d also
(A, 0) . Further, X is a
=
m i n i m a l g e n e m t ing class
by t he cl ass { - 1 } , bot h of w h i ch are m i n i m a l . be generated by a u y
one
The
of t h e t wenty six classes :
of which are m i n i m al . In fact , i t c a n
be
algebra ST R I N G can
{ a } , { b}
sho w n t h at i f an
,
. . . , and
{ z } , all
al geb ra. contai n s
on e pair of operations t h at are i n verses of e a c h o t h er-m ean i n g t h a t if one of t hem app li es to an object x , w i t h poss i b l y other obj ects, to yield another object y, t he n the other applies to y, w i t h t h e same other objects, to y i e l d x-as addit ion and sub t m ction are i n I N T E G E R , a n d s ucc and p red a r e i n S TRI N G-t hen i t
does not have a u n i que m i n i mal generat i n g c l a s s .
H oweve r ,
t h e con d i t i o n t h at an algebra l acks a n y such pai r o f operat i o n s i s not s u fficient
by i tself to ensure the existence of a. uni que m i n i mal g e n e r it t i ng c l ass . T h i s e as i ly seen b y con s i deri n g the a l ge br a that has t;h ree objects { 0 , 1 , 2 } a n d
is
argument n u m ber and T h u s , adel l (0) I , fl.dd l ( l ) 2 , and m i n i m a l genera, t i ng cl ass e s : { 0 } , { 1 } ,
o n l y o n e one- p l ace operator a d d i w h ich adds l to t h e
t hen converts the resu l t to modulo
add l ( 2 ) an d { 2 } .
0.
=
3.
T h i s algeb ra h as t h ree
=
=
I n fac t t h e m i n i m al generat i n g cl asses of an a l gebra n eed n o t a l l be of t h e same size. For i nstance, two gen e ra t i n g c l asses o f t h e a l ge b r a I N T E G E R a re { 1 } a n d {2, 3}, both of w h i ch are m i n i m al but o n e of them h as o n l y one element and the ot her two. ,
216
Part
II: A
Theory
A l l t h i s i s to poi n t out t h at most ' i nteresting' algebras, at l east from my point of view, do not h ave a unique m i n i mal generat i ng class . T h i s m akes i t s o t h at a concept network , w h i ch i s formalized a s a n algebra, need n o t h ave a u n i que class of pri m i t i ves t hat generates i t ; and , moreover , an object- concept in a concept network may h ave several poss i ble descriptions depend i ng on w h i ch object-concepts are regarded as pri m i t i ve. I beli eve t h at most of our concept networks do, i ndeed , ex h i b i t t hese characteristics. An algebra i s said to be finit ely gen erated i f i t h as a fi n i t e generati ng class. S i n ce its generat i ng class must by defi n i t ion be a subclass of its obj ects, every fi n i t e algebra is fi n i tely generated . An i nfi n i te algebra m ay or m ay not be fi ni tely generated . The algebras S T RI N G and I N T E G E R are both fi n i tely generated . I n contras t , i f we consi der t h e algebra o f al l posi t i ve i ntegers u n der the operat ion of m u l t i p l icat ion, it is not fi n i tely generated as t here does not exist a l argest pri me n u m ber. 6.5.4
C losure Over O p erat ors
J ust as we defi ned c losure over the objects of an algebra, we can also define closure over the operators . The res u l t i s called the class of polyno m ial opera lions. G i ven t h at (A, 0) i s an algebra, t he class of polyn o m ial operations over ( A , 0) , writ ten as P11 ( 0 ) , is t h e s m al l est c l ass t h at sat i sfies all the fol l ow i ng fo u r con d i t i o n s :
1 . n is a
s u b c l ass of
2 . For every n 3. For every n
C�a)
4.
> >
PA ( O ) .
0 , and every
i
:S
n,
the identity operator J�i) i s i n P11 ( 0 ) .
0 , a n d for every object
a
i n A , the constant operator
i s i n P;� ( O ) .
For every n- ary operator (3 i n ?11 ( 0 ) , and al l sequences o f m-ary op erators a , , o o o , an i n PA ( 0 ) , the composition (a, , . . . , a n ) o (3 is also i n P;� ( O ) o
It fol lows from t hese con d i t ions t h at for every of
a·
o:
in PA ( ll ) , a l l B pecial i zatious
are a l so in P;� ( O ) .
6.5.5
Comp utability o f O p erat ors
So far I h a v e n o t d i s c ussed how operat o r s , w h i ch a r e fu n c t i o n s , a r e s p ec i fie d . As w i t h classes [see Sec t i on 1 ] , an operator can be specified i n two poss i b le
Ch ap t er
6:
Cognition : Form al Con cep ts
217
ways: b y enumerat i ng all i t s members , as l d i d w i t h A L G l and A LG 2 ; or by prov i d i ng a r u l e t h at determi nes how , gi ven t h e argument objects to the operators, the res u l t i ng obje ct i s derive d , as 1 did with S T R I ! G and I N T E G ER. Obviously, the former method can o n l y work w i t h fi n i te classes , and for i n fi n i t e classes the operators i n va r i a b l y h ave to be s p e c i fied as rules. However, t here m ay or m ay not e x i s t some k i n d o f p roced u re for carry i n g out the rule. This characteristic is captured p recisely by the notion of computab i l i ty. A computable funct ion or rule i s such t h at an effect i ve procedure exists for i mplemen t i ng i t . ( S ee K fo u ry, M o l l , & A r b i b [ 1 982] or Roger s [ 1 967] for a theory of com p u t able funct ions . ) W e s ay t h at an algebra is co mp u t able if every one of its operators i s com p u tab l e . Notice t h at all fi n i te algebras are com putable by t h i s cri terion .
6.6
Subalgebras and Finite G enerativity
G i ven t h at concept n e t wo r k s are fo rmal i zed as fi n i te l y generated algebras , and t h at a concept network m ay be part ially i nstan t i ated i n a n envi ronment ( as i s typical in metaphorical i nterpretations ) , i t i s i m portant to explore how finite generat i v i ty i s effected when objects and/or o p e rators of an algebra are dropped . This is e x a c t l y what I set out to do in t h i s sec t i o n . T h e c o n c e p t o f s u b c l as s c a n b e e x t e n ded t o a l ge b ras a l s o . H oweve r , care
must be exerci sed to ensure that the algebrai c struct u re-t h at i s , closure under the actions of the ope rators-i s p reserved . T h i s req u i re m e n t m akes i t s o t h at o n l y some subclasses are acceptable a s su balgebras .
A subalgebra of an algebra ( A , !1 ) is a pai r ( B , �) such that B <;;; A , � ( n ) <;;; !l ( n ) for a l l n , a n d whenever b1 , , bn E B a n d (7 E � ( n ) then (7 ( b1 , . . . , bn ) E B . T h u s , we see t h at t here are two ways i n w hich a su balgebra can be obtai ned from an algebra.. The first way is by s h eddi n g i ts operators , t h e reb y m a k i n g i t less s t r u c t ured ( pe r m i t t i n g fe we r s t r u c t u re s ) ; a n d t h e ot her is by d ro p p i n g some o b j e c t s . J loweve r , w he n t h e object s a r e d r o p p ed , one has to m a k e sure that t h e object s t h at arc l eft over arc c l osed u n d e r al l t,hosc •
operators t hat are st i l l t here.
•
•
In other word s , one has to e n s u re t h at rem a i n i ng objects do not generate an object t h at w as dropped out by c o m b i n at i o n of the rem ai n i n g o p e r n.t o r s _
t he
any
A n exam ple wou l d make t h i s c lear. Con s i d e r t h e c l ass or a l l even i n tegers
and zero. T h i s is a s u bclass of the class of obj ects of I N T EG E R. It is also closed u nder all the op erat or s of I N T E G E R . In p a r t i c u la r , t h e n ega t i on of an even n u m ber is another even n u m ber, and ad d i t i on , subt ract ion, and
Part
218
I T: A Theory
mu l t i p l i cat ion of two even numbers also yield an even number. Therefore, the class of al l even i ntegers , together with all the operators of I N T E G E R , form a subalgebra of I N T EG ER. However the class of all odd n u m bers, also a subclass of the c l ass of objects of I N TE G ER, does not for m a subalgebra of I N T E G E R if al l the operators are kep t . T h i s i s because the add i t i o n , subt ract ion , a,M --rm:t+t,ip � of odd n u mbers all result i n even nu mbers , w h i c h have been d ropped out . If t hese t� operators a re dro pped , and o n l y the n eg operatot<; i-s- kept , we then end u p w i t h a subalgebra of I N T E G ER. CA. v L
Though b o t h t h e ch anges-of d ropping operators a n d droppi ng obj ectscan be carried ou t at on ce i n form i n g a subalgebra, i t i s often usefu l to consider changing one at a t i me. VVhen a subalgebra i s formed by sheddi n g some of i t s operators , I refer to i t a s an 5-subalgebra, a n d w h e n a sub-algebra is formed by d rop p i ng some objects , I refer to i t as an 0-subalgebra . Thus, the objects of an algebra are m a i ntai ned i n i t s S-subalgebras ; and al l the operators appear in i t s 0-su balgebras . Notice also t h at i n for m i n g su balgebras of an al gebra-whet her by d rop p i ng objects, or by d ropping operators, or by both-t he structural descrip tions of i t s objects, and consequently its generat i ng classes , are altered . For S-subalgebras , formed by drop p i n g some operators but kee p i n g all the ob jects, their c l ass of structur a l descri ptions becomes smaller, and the size of m i n i mal gene r a t i n g classes can only grow . This i s because if ( A , S1) is an algeb r a and ( A , B) i s i ts S-su balgebra, m e an i ng that B ( n ) <;;; S1 ( n ) for a l l n , t hen every generat ing c l ass of ( A , B) i s also a generat ing class of ( A , s-1) . I n other word s , i f X is a m i n i m al ge n er at i n g c l ass of ( A , B) then the re i s a m i n i mal generat i n g class Y of ( A , n) such that Y <;;; X . However, n o such s i m p l e t rend can b e observed for 0-su balgebras . One m i gh t expect t h e s i ze
of
m i n i m a l generat i n g c l asses t o become s m a l l er as
obj e c t s a r e
d r opp e d o u t , b u t s u c h is not al ways t h e case. For i ns t a n c e con s i der a s i m p l e a l g e b ra formed by the t h ree p o s i t i o n s of a we dg e as shown i n F igu re 6 . 8 . Two p o s i t i on s , rest-left and rest-right are s t able b u t t h e t h i rd one
correspon d i n g t o the wedge balanced on i ts edge, cal led o n - edge, i s u n s t able. The algebra h as t wo u n ary operators: p ush-left and p ush- righ l . A p u s h i s very ge n tle an d t h e weight of t h e wedge i s s u c h t h at i t i s not poss i b l e to move i t from one s tabl e p o s i t i on to t h e other by u s i n g a n y of t h e operators . T h at i s , t hough p ush-left an d p ush- righ t app l i ed to on- edge res u l t i n rest-left and 1·est- right respecti vel y, nei t her operator p rod u ces any ch ange w hen applied to rest-left or rest- righl . N ow this algebra can b e g e n e rated by t h e u n s t able posi t i o n alone, si nce the o t h e r t w o c a n b e obtai ned from t h i s b y app l y i n g t h e
appropri ate operators . However, the 0-subalgebra of t wo stable positions re-
Ch ap t er 6: Cogn i t ion : Form al Con cep t s
push-left
rest-left
219
on-edge
¢::::::1
�l ' I ........ ',
J J
/
push-right
q
t��
/\,"
,•
,/
"\
•,
\\ \
'/ /
rest-right
FIGURE 6.8: A simple algebra of a wedge. The objects of the algebra are three positions of the wedge. The two unary operators correspond to pushing the wedge left or right. The algebra can be generated by the unstable position ' on-edge, ' but its subalgebra containing the two stable positions requires both of them to be in the generating class.
q u i res both of them to be there in the m i n i mal generat ing c l ass , s i n ce neit her of them can be generated from the other. S ince concept networks are defined to be fi n i te l y generated a l ge b r as , i t is worth exploring to see i f subalgebras of a fi n i tely generated algebra are also fi n i tely generated . Let us start w i t h S-su balgebras . We h ave al ready seen t h at the size of a m i n i mal gene r at i n g class of an S - su b alge b ra can only grow . But does i t al ways remai n fi n i te? The algebra I N T E G E R easily provi des a coun t ere x am p le . I N T E G E R is fi n i tely genera t ed , as one of its generating class i s { 1 } . Now let u s consi der an S-su balgebra of INTEGER t h at h as only one operator x . C learly, this subalgebra i s not fi n i tely generated si nce t here does not exist a l a rgest prime number. In fact , many t r i v i al counter examples can be foun d by starti ng w i t h any fini tely generated i nfi n i te algebra, such as I I T E G E R o r S T RI N G , a.n d forming a n S-subalge bra. b y d ro p p i n g a l l i ts operators . How a b o u t O-s u b a l ge br as1 ls it t r u e t h at t h e 0-su b a l gebra
generated algebra
at i v e . A
non - z ero
of a n y Fi n i tely i s also fini tely g enerated ? The answer here i s ag ai n neg
cou nter example i s prov i ded by con s i de r i n g t h e algebra of pos i t i ve
i ntegers under a binary operator addl ad d l ( x , y )
Clearly,
this
a l ge b r a
{
=
i s ge n e r at e d
w h i ch is
(x + 1 )
if y
2
ot h e r w i se
=
defined
1
by t h e c l ass { 1 } , and i s of i t t h at i s formed
ge n e r a t ed . Howeve r , an 0 - s u balgebra
as follows:
t h erefo r e
by
fi n i tely d ro pp i n g J
220
P a r t II: A Theo1y
that i s , w i t h the c l ass of objects being { 2 , 3, . . . } -i s not fi n i tely generated .
6.7
G roupings on A lgebras : A lgebras of C las s e s
Before i nt rod u c i n g the concept of a relation bet ween t w o algebras , i t w i l l be usefu l to extend t h e concept of grou pi ngs to algebras , for a relati o n between two algebras also i n d u ces group i ngs over the algebras . In doi ng so, one must , as w i t h subalgebras, ensure that the algebrai c structure i s preserved . How ever, before t hat , one needs to speci fy how an operator, w h i ch was defined to act only on objects, act s on classes of obj ects; what it means to h ave a group of operators; and how a group of operators act s on groups of obj ects. G i ven a grou p i n g G on A (G i s a class of subclasses of A) and an operator w E !1 ( n ) , we say that G a d m its w if whenever X1 , , Xn E G, t hen t here exists some X E G such t h at the class { x such t h at t here exist x1 E X1 and . . . and X n E Xn and x w( x 1 , , xn ) } i s a subclass of X . I f for every X1 , , Xn , t here is a u n ique such X, t hen we say t hat G adm i t s w u n iqu ely. For i nstance, cons i der the algebra I NTEG ER. A grou p i n g G { A0, A � , Ad on i t s objects i s gi ven below : •
=
•
.
•
•
•
•
•
•
=
Ao At A2
{ . . , -3, 0, 3, 6, 9, 12, . . } { , -2, 1 , 4, 7, 1 0 , 13, . . } { . . . , - 1 , 2, 5, 8, 1 1 , 14, . . . } .
.
.
.
.
.
A l l the n umbers t h at yield the same remai n der when d i v i ded by 3-that i s , the n u mbers t h at are equal modulo 3-are grouped together. H can verified t h at t h i s group i ng ad m i t s-i n fac t , ad m i t s u n i quely-each operator of I N T E G E R ( add, mull, etc . )
O n t he other han d , consider a grouping G
of S T R I N G shown below :
=
{A, B,
A
{ a , aa, aaa, aaaa,
B
{ b, bb, bbb, bbbb, . . . }
Z
{z, zz, zzz, zzzz,
.
.
.
.
.
.
.
.
.
, Z } of t he objects
}
}
There are twenty s i x classes , each corresponding to a character. The class correspon d i ng to a character contains only those stri ngs t h at are formed by
Ch ap t er 6: Cogn i tion : Form al Con cep t s
221
o n e or more occurrences o f that ch aracter on ly. T h i s g rou p i n g adm i t s each of the one-place operators of S T R I N G ( 7'e u e 1·s e , s u cc , etc. )-and ad m i t s i t un i quely-but does not adm i t t h e two- place operator co n e . T h e resu lt of applying co n e to A and B resu Its in the c l ass { ab, a a b, a bbbb, . . . } , wh ich i s n o t i n c luded i n any o f t h e A , . . . , Z . When a. grouping ad m i t s a n operator, what i t means i s t h at i t i s possible to define the action of the operator, which was defi ned to act o n ly on object s , over the grouping. I f G adm i t s w t hen for a n y X1 , . . . , X n E G w e can s i m ply define the operat ion w on the grouping, w ( X 1 , , X, ) , as any X E G such t h at t he class {X such t hat t here exist X ] E xl an d . . . an d x , E Xn and x w ( x 1 , . . . , x n ) } i s a subclass of X . The defi n i t ion of ad m issi b i l ity makes s ur e that at least one such X exists for every X 1 , . . . , Xn E G . H owever, there m ay be more t han one such X for some X 1 , , Xn E G, a n d t h i s a l lows one to define the act ion of w on t he g ro u pi n g in m ore t h a n one way. For i n stance consider the groupi ng { B1 , B2 } over the objects of a l g e b ra A LG 2 , where B1 { b1 , b3 } and B2 { b2 , b3 } . This grou pi n g c learly ad m i ts the operator g1 but does not adm i t it u n i quely, s i n ce the class {x such that x g1 ( y , z ) for any y i n B 1 and z i n B2 } equals { b3 } , w h i ch i s a. subclass o f both B1 and B2 . For this reason, we cou l d set g1 ( B1 , B2 ) to be either B1 or B2 . O f course, i f G ad m i t s w u n i quely, t h e n there i s n o such ambigu i ty. There is one o t h er con d i t ion u n der w h i ch we c a n d e fi n e the act ion of w on G u n i quely, but before cons i deri ng it I would l i ke to extend t h e concept of a d m i s s i bi l i t y to classes ( group s ) of operators . •
•
•
=
•
=
•
•
=
=
C l e ar l y , i n order to meani ngfully consi der the action of a. c l ass of operators on a. group i ng o f o bj e ct s , all operators in the class must h ave t he same a.rity. In o t h e r words, the class of operators can n o t c o n t a i n an m - ary o p e r a t o r an d an n- ary operator, w i t h m =/: n , at the same ti rn e . Now g i ven a.n a l ge b r a ( A , O ) , a g ro up i n g G on A, a n d a c l ass of operators o f t h e same ari ty 6 <;;; O ( n ) , we say that G adm its 6 i f whenever X1 , . . . , Xn E G' , then there is a class X E G s u c h t h at the c l ass { .r s u ch t h at t h ere ex i s t x 1 E X1 , , xn E Xn , fJ E 6 a n d x = fJ ( J: J , . . . , x, ) } is a, subclass of X . If for every X, , . . . , Xn E G there is a unique such X t h e n we s ay t h at G ad m i l s .6 •
uniquely.
Fac t : 6 . 6
lf G a dm its
.6.
th en
G
admits every
fJ E .6. .
.
•
The proof of this fact is very s i m p le an d omi tted here. N o t i ce , however, t h at the c o n v ers e of t h i s fact is not true. The grou p i n g { A 0 , A 1 , A 2 } on I N T E G E R t hat w a s i n t ro d u ced earlier admi t s a d d a n d m ·ult i n d i v i d u a l l y , but d o e s n o t a d mi t the class { add, m ull } . A l s o G m ay ad m i t .6. u n i q u e l y, b u t m ay n o t a d m i t every {; E 6 u n i q uely.
222
Part
II: A
Theory
When a grou ping adm i t s a class of operators , i t means t h at i t is possible to define the act ion of the class of operators , as i f i t were one operator, on the members of the grouping, as if t hey were obj ects. Here agai n , an ambig u i ty would exist u n less the class of operators is adm i t ted u n i quely by t he grou ping. We, of course, have the followin g fact t hat ensures u n i q ueness u nder certai n con d i tions: Fact : 6 . 7 If a grouping is pairwise disjo int-meaning that th e intersection of any t wo m e m bers of il is always th e empty class-th e n all opemlors, and n o n - e mpty classes of opemtors admitted b y it a re admitted u n iquely. The proof i s agai n easy and i s not men t ioned here. S i n ce all parti t i on s are pai rwise disjoint by defi n i t i o n , it fol lows that any part i t ion, if it a dm its an operator (or a class of operators ) , ad m it s it u n i quely. It is i nteresting to see if we can come up w i t h some other way to define the act ion of a class of operators 6 on a grou p i ng G u n i quely even when G does not adm i t 6 u n i quely ( g i ven t h at G adm i t s 6 . ) One poss i b i li ty is to see if t here i s a unique m i n i mal X E G for every X1 , , Xn E G such t h at the cl ass {x such that t here exist x1 E X1 , . . . , Xn E Xn , {j E 6 and x 8 ( x 1 , . . . , x n ) } i s a subclass of X, and moreover, if any other Y E G sat isfies t h i s con d i t i on t hen X <::;; Y . If t h i s i s the case, t hen we can simply set 6 ( X1 , . . . , Xn ) to be t h i s u n i que X for every XJ , . . . , Xn E G . O f course, the e x i s t e n c e of a u n i qu e m i n i m a l such X cannot be gu a r a nteed i n t h e general case . B u t when t h e grou ping G i s closed u n der i n tersection mean i n g t h at if any two c l asses M and N a r e i n G t hen t hei r i n ter s e ct i o n M n N i s also in G-th en we can prove the existence of a u n i qu e m i n i mal such X for every X1 , . . . , Xn E G. .
.
•
=
(A, rl ) is a n algebr·a, G a gro uping on A that is closed u n de r intersection, a n d 6 <::;; rl ( n) for' so m e n such that G adm its 6, then for a n y X1 , , Xn E G, l h e r·e is a unique minimal X E G s u c h that the class { x such thai t h e re exisl X ] E x l ' X n E Xn , {j E 6 a n d X = fi ( x h . . . ' Xn ) } is a s u bclass of X .
Fact : 6 . 8 Given t h a i
•
•
•
I
•
Let
E X,.. , {j E 6
exists
•
us refer to t h e c l ass { x su ch t h at t h ere exist x 1 E X1 , , and x li ( x 1 , . . . , x n ) } as Z . Now s i n ce G a d m i t s 6 t here s ome X E G such t h at Z <::;; X by defi n i tion .
P r o o f: Xn
•
•
•
•
=
Clearly, if X i s t he only c l ass i n G such t hat Z <::;; X t hen t h e re i s no problem . H owever , su p p ose t h at t h e r e are a n u mber of such classes i n G', say { Y; } i > J , s u ch that Z <::;; Y; for all i . We must now show t h at a fami l y Y t h i s fami l y h as a u n i que m i n i mal elemen t . =
F i r s t w e elimi nate a l l non - m i n i mal members from
Y . T h at i s , w h e never
Chapter
223
6: Cogn i t ion : Form al Con cep t s
Yj C h, for any j and k , we eliminate Yk as clearly i t is not m i n i mal . At the end of this process, i f we are left with only one member i n Y , t hen i t i s the u n i qu e m i n i mal elemen t . B u t , what i f w e are left w i t h two o r more classes i n step? We w i l l now show that this cannot be the case.
V
a t the e n d o f last
Let u s assu me the cont rary. Say t h at t here are two m i n imal classes t hat we end up w i t h : Y1 an d Y2 . S i n ce t hey are both m i n i mal ( and disti nct ) neither }} � Y2 nor Y2 � }} . M oreo ve r , because t hey were bot h i n i tially i n c l u ded i n Y , Z � }} an d Z � Y2 . Now G i s c losed u nder i ntersection . So we h ave Y1 n Y2 E G. A l so, s i n ce � Y1 and Z � Y2 , we have Z � Y1 n Y2 . T h i s means }} n Y2 must be in c lu ded i n Y also. A nd since Y1 n Y2 � Y1 and Y1 n Y2 � Y2 , we k now t h at neit her Y; nor Y2 is m i n i m al , contradicting our assumption . Z
Thus, t here cannot exist t wo m i n i mal classes i n Y , proving o u r resu l t .
D
G i ven an algebra ( A , !1 ) , a gmuping on ( A , !1) i s a pai r ( G, 1 ) , such t hat G i s a group i n g on A, 1 is a grouping on !1 t h at respects ari ty of operators mean i n g t h at every member of 1 i s a subclass of !1 ( n. ) for some n-and G adm i t s every member of 1 . If, i n addit io n , G ad m i t s every member of 1 u n i quely we s ay that ( G , 1 ) i s an algebra of classes over ( A , !1) . Agai n , it woul d be i nteres t i ng to ascertain w hether an algebra of classes of any fi n i tely ge n e r a t ed algebra is also fi n i t e l y generated . I do not yet have a p roof, or a counter example, to settle t h i s issue one way or another, but my i n t u i t ion i s t hat i t i s not true; that i s , a fi n i te l y generated algebra might h ave an a l ge b r a of cl asses t h at i s n o t fi n i t ely generated .
6.8
Relations B etween Algebras :
C orresp ondences We are now in a po s i t i on to consider relations between two algebras , w h i c h is how co g n i t i ve relations are formali zed i n t h i s framewor k . l [ o n e d i scounts t h e o p erat i onal s t ru c ture s of algebras , and r e g a rd s t h e m as mere c l asses, the concept of relat i o n s can eas i l y be extended to cover t h e m . However, w hat i s of i nterest is t h e case when t h e re l at i o n s between two a l ge b ras p reser ve t h e i r al ge b rai c s t r u c t u res , for such relat ions correspond t o coherent cogn i t i ve relat ions. I refer t o the relat ions ( bet ween t wo algebras ) w i t h t h i s s t r u c t u re preserving proper t y as C07'respondences. I s t art by i nt rod u c i n g p rod u c t s of al-
224
Part II: A Theory
gebras and correspondences; t hen I consi der groupi ngs i n d u ced over algebras by correspondences; and , fi n ally, I discuss some characteristics of d i fu n c tional correspondences and extend T h eo r em 6 . 1 to correspondences. 6.8.1
Products o f A lgebras and C orresp ondences
G i ven two algebras (A, 0 ) and ( B , I:) t heir p roduct (A, 0 ) X ( B , I:) (C, r) i s such t h at C A x B ; for any n , whenever ( w , a ) E O(n) x I: ( n ) and (a 1 , 6 1 ) , , ( a n , bn ) E C t hen ( w , a ) i s defined to be an n- ary operat ion ove r C w i t h t h e val ue (w( a 1 , . . . , a n ) , a ( b � , . . . , bn ) ) ( t h i s i s w ri t ten as ( w , a ) ( ( a 1 , b 1 ) , . . . , ( a n , bn ) ) ) ; and r ( n ) O ( n ) X L: ( n ) for a l l n . =
=
•
•
.
=
A C0 7Tespo ndence over t wo algebras ( A , D ) and ( B , I: ) is a. rel at ion be t ween t hem that preserves the algebrai c structure. In other words, a pat r ( R, IJi ) i s a corresponden ce between ( A , 0) and ( B , I: ) when : 1.
R
<:;;; A x B ;
2 . IJi ( n ) <:;;; ( O ( n ) x I: ( n ) ) for a l l n ; a n d 3 . w henever (a , , b t ) , . . . , ( a n , bn ) E R and ( w , a ) t h e n (w ( a l . . . a n ) , a ( bJ . . · bn ) ) E R
E
IJi ( n )
A n exam ple of a corres pondence from A L G I to A LG2 i s shown i n Fig u re 6 . 9 ( a ) . I n 6 . 9 ( b ) I also s h o w a relat ion from A L G l to A L G 2 that i s not a correspondence because (a 1 , b 1 ) and ( h , g 2 ) are both i n the r e lat i o n but ( h ( a J , a 1 ) , g 2 ( b1 , b, ) ) i s not i n i t .
There a r e t w o c o r r es p o nd en c es bet ween I N T E G E R a n d S T R I N G t hat a r e i nteresting and I ment ion them here. T h e first one, w h ich I call M O D U L O , i s from S T R I N G to I N T E G E R a n d relates al l t hose stri ngs t h at contai n o n e or more occu rrences of c h a r ac t e r ' a ' on l y, w i t h all the numbers t h at a.re 0 modulo 2 6 ; all t hose st r i n g s t hat cont ain one or more occu rrences of character ' b ' on l y, w i t h all the n umbers t h at are 1 mod ulo 2 6 ; et c . ; and operator s u cc w i t h n exl. T h i s relat i o n s h i p i s graph ically shown below :
{ a , aa, aaa, . . .} { b, bb, bbb, . . . } { z 1 zz, zzz, . . } .
succ
+------> +------>
+--> +-->
{ . . . 26 0 26 52 . . . } { . . . , -25, l , 27, 53, . . . } ,
-
,
,
,
,
{ . . . , -1, 25, 5 1 , 77, . next
. .
}
Ch ap t er 6: Cogn i t ion : Form al Con cep t s
a!
OBJECTS
a2
A L
G 1
fl f2
OPERATORS
f3 (a)
225 bl b2
OBJECTS
b3
A
gl g2
L G
2
OPERATORS
A correspondence from ALG 1 to ALG2.
OBJECTS
OBJECTS
A L
A L
G
G
2
1
OPERATORS
(b)
A
OPERATORS
relation from A LG1 to A LG2 that i s not a correspondence.
FIGURE 6.9: Examples of a correspondence and a non-correspondence.
Part II:
226
A
Th eory
\"'here every member of the class at one end of the arrow i s related to every member of the class at the other end of t he arrow . It is simple to ver i fy t h at t h i s relation i s , i n deed , a correspondence. The second correspondence, called L E N G T H , i s from I N T E G E R to S T R relates every pos i t i ve non-zero i nteger w i t h a s t r i ng contai n i ng t h at m any characters ; and operator add w i t h co ne. Us i ng the same notat ion a.s above , t h i s relations hi p is depi cted below : I N G . It
{1} {2} add
� �
{ a , b, . . . , z } { a a , a b, . . . , zz }
�
cone
Here, agai n , it i s easy to veri fy that t h i s relationship preserves the algebrai c st ructure and is , therefore, a correspondence. By con d i tion ( 3 ) in the defi n i t ion of a correspondence, we k now t h at a correspondence i s closed u n der pai rwise operat ions ( as defi ned for products of algebras ) . This d i rect ly leads to the fol lowing fac t :
co 1Tespondence ( R , lli ) o v e r ( A , !1) and ( B , �� i s a n algebra un pairwise opemtions. fn ]Ja 1'i icu lm·, it is a subalg ebra of ( A , !1) x (B, �) .
Fac t : 6 . 9 A d e ·r
O ften, I wou l d l i ke to assert that some x is an element of an algebra ( A , D ) wit hout spec i fying whether x i s a n object ( x E A ) o r a n operator ( x E !1 ) . I n t hose s i t uations I write x E ( A , !1 ) t o mean x E A o r x E !1 . Thus, i f ( R , lli ) i s a. correspon dence then ( x , y ) E ( R , lli ) means t h at ( x , y ) E R o r ( :c , y ) E iii . S i n ce the class of objects of any algebra. i s d isj oint from i t s class of operators, t here i s no ambigu i ty i n this notat i o n .
The inverse of a corres ponden ce a n d the c o m pos i t ion of two correspon dences are defined i n a way s i m i l ar to relat i o n s . G i ven a. co r re s p o n d en c e ( R , iii ) over ( A , !1 ) and ( B , � � i t s inverse ( R, iii ) - 1 i s defincd to be (R - 1 , l]i - 1 ) ; 1 or i n other words for a l l T E ( A , D) and for all y E (B, � ) , (y, x) E ( R, iii ) i f a n d o n l y if (x, y ) E ( R, 'I' ) . S i m i larly, given anot her correspondence (5,
) over ( B , �) and ( C , f ) , t h e co mposition o f ( R, \1! ) w i t h (5, ) , w r i t ten as (R, iii ) o ( 5, ) , is defi ned as (R o 5, l]i o ) ; or in other words for all x E ( A , !1) a n d all y E (C, r ) , ( x , y ) E ( R , iii ) o ( 5, <1> ) if a n d only if t here is some z E ( B , � � such t h at ( x , z ) E ( R , iii ) and ( z , y) E ( 5 , ) . It is easy to see t h at the i nverse of a correspondence an d the compos i t ion of two correspondences are themsel ves correspondences . In part i c u lar, (R, lli ) - 1 is a correspondence over ( B , �) an d ( A , !1) and ( R, 'I' ) o (5, ) i s a correspondence over ( A , !1) an d (C, f) .
Ch ap t er 6: Cogn i t ion : Form al Con cep t s
6.8.2
227
G roupings Induced by C orresp ondences
L i ke relations, correspondences also i n d uce gro up i ngs on the objects and operators of t hei r domai n and codomai n algebras . We have al ready seen the groupi ngs i n duced by M O D U L O and L EN G T H . In Figure 6. 1 0, I show the group ings i n d u ced on A L G l and A L G 2 by the correspon dence of Fig ure 6.9 ( a) . Not i ce t h at t hese groupi ngs are algebraic i n t h at groupi ngs on the objects admit the groupi ngs on the operators of their respecti ve alge bras . T h is raises the i nterest in g quest ion whether t h i s is always the case. The fol lowing theorem provi des the answer: Theore m : 6.2 Let (A, !1) a n d (B, E) be algeb ras, and let ( R, \li ) be a co n·e spondence over th em . Let C be the gmup ing induced by R over B , a n d f be the gmuping induced b y \li over E . Th e n C adm its e ve 1·y m e m be1· of f. In other wo 1·ds, (C, f) fo rms a gmuping over ( B , E) . P ro of: Let 6. E r . Then by defi n i tion of correspondence, 6. i s a class of n ar y operators of E, for some n . Moreover, by defi n i tion of i n d u ced grou pings, 6. i s t he i m age of some a E !'l ( n ) under \li . That i s , \li ( O' ) 6. . =
Now t ake any Y1 , , Yn E C . By defi n i t i o n of i n d u ced grou pin g agai n , each o f Y1 , . . . , Yn i s t h e i m age o f some object i n A u n de r R. Let these obj ects be a 1 , . . . , a n respect i vely. Thus, R( a 1 ) = YI J . . . , an d R( a n ) Yn · •
•
•
=
I must now s h o w t hat the class { y such t h at y = 8 ( y 1 , . . . , Yn ) for s o m e 5 E 6. , Yl E Yi , . . . , Yn E Yn } , which we w i l l refer to as Y , is a s u b cl as s of some
member of
C.
Consider a n y b E Y . Now b {3 ( b 1 , . . . , bn ) , for some {3 E 6. , b1 E Yi , . . . ,and bn E Yn . B u t s i n ce \li ( O' ) 6. , R ( a J ) Y, , . . . , and R( a n ) Yn , w e get ( 0' , {3) E \li , (a 1 , b1 ) E R, . . . , an d (an , bn ) E R . From the defi n i tion o f correspondence, we con c l u de t h at (a(ah . . . , an ) , {3 ( b1 , . . . , bn ) ) E R ; or ( a , b) E R where a = a ( a 1 , . . . , a n ) · Now s i n ce for every b E Y it is the case t h at (a, b) E R, we get Y � R( a ) . =
=
=
=
G i ven t h a.t C i s a. grouping on B induced by R, we k now that R( a ) m u st be i n C . Thus we have proved the t h eor e m . D Noti ce however , t h at (C, r) m ay not necessar i l y form an al g ebra of classes over ( B , E ) ; t he reason bein g that t hough C ad m i t s e very m e m be r of f , i t m ay n o t adm i t i t u n i q u e l y . For instance, t h e grou p i ng i n d u ced b y the correspondence of 6.9 (a) on i t s codom ai n a l geb r a ( A LG 2 ) is not an algebra of classes . I n particular, the grou p i n g on the objects of A L G 2 do e s not admit the group of operators { g2 } u n i quely, a s r pointed out earl ier.
Part II:
228
A
Theo1y
(a )
.... � --...'.._
I !
b2 \
\
b3
(
\,
,
I
I ,/
}
_ _
.... ... . ....,'
I
/ gl \
/'·-...... I
\
!\ g 2
!\ g 2 I) ...... __ ./
!
i
I
\
.-' .... .
:\ g l Il •
'
.......
/
''- �--·/
(b) FIGURE 6.10: Groupings induced by the correspondence of 6.9(a) on (a) its
domain ALG l , and
(b)
its codomain ALG2.
Cha.p t er 6: Cogn i t i on : Formal Con cep t s
229
S in ce the i n verse of a correspondence i s also a co r respondence , this the orem also shows that the group i ng i n d u ced by ( R, \ll ) on ( A , D) is also alge brai c . 6.8.3
D ifunct ional C orrespondences
A correspondence i s sai d to be fu nctional if the grou p i n g i n duced by i t on its domain algebra i s a part i t i on ; cofunctional if the grou p i ng i n d u ced by it on its codomai n algebra i s a part i t ion ; a n d difunctional if i t i s fu nctional as wel l as cofunctional .
S i m i lar to relation s , correspondences also give rise to ch a i n s of su balgebras i n their domai n and codomai n . A l l the results th at were deri ved for relations woul d extend to correspondences provi ded one can show that correspon dences p reserve algebraic closure-mean i n g t h at the i m age of a su balgebra i s another subalgebra. This i s easily proved in the fol l ow i n g t heore m :
Theore m : 6 . 3 Given t h a t ( R , iii ) i s a correspondence o v e r algebms ( A , D ) a n d ( B , L. ) , a n d (X, 6. ) i s a subalgebra of ( A , O) , then ( R, iii ) ( (X, 6. ) ) i s a subalgebra of ( B , L. ) .
P r o of: Let us denote ( R , iii ) ( ( X , 6. ) ) by ( Y, A) . C learly, Y <:;; B and A <:;; 2: . S o w e only n eed t o show t h at Y i s closed under i\ . I n other words, g i ven any A E A ( n ) , a n d Y I , . . . , Yn E Y we must show t h a t .A ( y 1 , . . . , Yn ) i s also in Y .
S i nce Y
R( X ) w e know t h at t here are
x1,
.?: n
E
X
s u c h that
( x i , Yl ) , . . . , ( x n , Yn ) E R. S i m i l arly, we k now t hat t here exists 6 E 6- ( n ) such t h at (6, .\) E \ll . From the defi n i t ion of correspondence, we i n fer t h at ( 6 ( .7: 1 , , x n ) , .\ ( y 1 , . . . , Y n ) ) i s also i n R. B u t si n ce (X, 6.) i s a su balgebra, 6 ( x 1 , . . . , x n ) i s i n X . T herefore, i t fol l ows that .\ ( y 1 , . . . , yn ) must b e i n Y . 0 We can now general i ze Theorem 6 . 1 to a lge b r as . However, before doi ng =
•
•
• ,
•
•
•
t h at I woul d l i ke to i n t roduce t he concepts of homomorphism and i somor phism. A n A s i d e : H o m o m o r p h i s m s a n d Iso m o r p h i s m s
G i ven a correspondence (!, o ) over ( A , 0 ) a nd ( B , L. ) we say t hat it is a homomorphism from ( A , 0 ) to ( B , L.) i f and on l y i f for every x i n ( A , 0) there is exactly one y i n (B, L.) s u c h that ( x , y ) i s i n ( !, o ) . T h u s, homomorp h i sm s are fun ctions that p reserve algebrai c struc t ure. The pai r ( B1 , L- 1 ) s u c h t h at y E ( B1 , L- 1 ) if and only if t here i s s o m e x E ( A , 0) such t h at ( x , y ) E (!, o)
Pa. r t II :
230
A Theory
is sai d to be the image of (!, a) . From Theorem 6 . 3 we i n fer that the i m age of any homomor p h i s m is a subalgebra of i t s codomai n algebra. C learly, it fol lows from the defini tion that every homomorphism is func t ional . I n particular, t he grouping i n d u ced by a homomorphism on its domai n algebra i s a part ition. Using Theorem 6 . 2 and Fact 6 . 7 we can i n fer t hat t h i s grouping i s a n algebra of classes. It i s called the kernel of the homomorp h i s m . I denote t he kernel of a homomorph i s m (!, a) b y ka( ( f, a ) ) . When a homomorphism i s cofunctional also ( mean i n g that i t i s d i func t ional ) we say t hat i t i s an ep imo1·phism. Com pos i t ion and i n verse of homomorphisms are defined s i m i l arly. I t is easily shown t h at the composit ion of t wo homomorph ism i s another homo morphi sm . The i n verse of a homomorph is m, t hough u ndoubtably a cor respondence, m ay not be a homomorph i s m . Whenever (!, a) is a homo morphism such t hat (f, a ) - 1 i s also a homomorphis m , we say t hat it is an iso m o 1·ph ism . Resumption : D i functional Corresp ondences We
can now t ransport Theorem 6. 1 to algebras .
Theore m : 6 . 4 Let ( R , Ill ) be a difunclional con·espondence fro m ( A , n ) to ( B , L: ) , and ( F, 6) a n d (G, A) be gro up ings in duced b y (R, Ill ) on ( A , n ) and (B, E) respect ively. Th e n : 1.
( F, 6) a n d ( G , A ) are algebras of classes, a n d
2.
there exists a u n ique iso morphism, s a y ( R , 111 ) * , fro m ( F, 6 ) to ( G , A ) s u c h that th e pai1· (X, Y ) i s in ( R , Ill ) * if, and only if, ( R , III ) ( X ) = Y a n d ( R , 111 ) - 1 ( Y ) = X .
P ro of: The first part follows
d i re c t l y from T h eorem
6.2
a n d Fac t
6 . 7. For
the second par t , we i n fer from T h eorem 6 . 1 t h a t there is a bij ection from ( F, 6) to (G, A ) that assigns to every X in (F, 6) the u n i que non-empty Y
i n ( G , A ) such t h at ( R , III ) ( X ) Y and ( R , w ) - 1 ( Y ) = X . We only need to show that this bijection preserves the algebraic structure-or, what is the same, is a.n i somorph i s m . =
Let X1 , , Xn be i n F a n d 11 be i n 6 ( n ) . A l so, l et t h e c l ass { x s u c h t hat rr ( x 1 , . . . , X n ) for some x1 E X 1 , . . . , X n E Xn and 1r E 11} be denoted by U. S i n ce (F, 6) is an a l ge b r a of c l asses, t here m u s t be a u n i qu e c l ass in F , say M , su c h t hat U i s a subclass of M . •
x
=
•
•
23 1
Ch ap t er 6: Cogn i tion : Formal Con cep t s
S i m i l arly, let Y1 R(X 1 ) , , Yn R ( Xn ) be i n G r IJ! ( TI ) be i n A ( n ) . Note t h at Theorem 6 . 1 guarantees the existence o f u n i q u e such }) , . . . , Yn and f . A l so let us denote the class { y such that y 1 ( y 1 , . . . , Yn ) for some y 1 E }) , . . . , Yn E Yn and 1 E f} by V . S i n ce (G, A) is an algebra of classes , t here i s a u n i que N i n G such that V i s a subclass of N . =
•
•
•
=
=
=
We m ust now show that R( M )
=
N
and R- 1 ( N )
=
M.
To show R ( M ) N , si nce N is t h e u n i que member o f V , it is sufficient to show t hat V is a subclass of R ( M ) . =
G
that i n c l udes
S i n ce R i s a d i functional relation from A to B and M is in the grouping i n duced by R on A , we k now that M i s not empty and for any m in M , R ( m ) R( M ) ( see the p roof of Theorem 6 . 1 ) . From t h i s , and k now ing that U i s a subclass of M , we concl ude that R ( U ) R ( J\11 ) . Thus, we must now show t hat V i s a subclass of R( U ) . , Vn E Take any v i n V . By t h e defi n i t ion o f V , t here m u s t be v 1 E Y1 , Yn and I E r such that I ( V] , . . . , Vn ) v . B u t s i n ce yl R( XJ ) , etc . , we must h ave u 1 E XJ , . . . , un E Xn and 7r E TI such that ( u l , v l ) , . . . , (un , vn ) are all i n R an d ( 1r , 1 ) i s i n IJ! . By the defi n i t ion of correspondence t h i s i n t u r n i m p l ies th at (1r ( u � , . . . , un ) , 1 ( v� , . . . , vn ) ) i s i n R also. In other words, i f we write 1r ( u 1 , . . . , un ) as u , then ( u , v ) i s in R. But by defi n i tion of U , u i s U also. So we h ave proved t hat v is i n R( U ) , or that V i s a. su bcla.ss of R( U ) . The other half of t h e pr o of , t hat R- 1 ( N ) M , i s s i m i l ar . o =
=
•
=
•
•
=
=
There are two special cases of this t heorem that are more fam i l i ar. The fi rst of t hem concerns homomorphisms. Not i ce first that epimorphisms are eli functional by defi n i t ion and so the theorem d i rectly appl ies to them . But t hen any homomorphism can be m ade an epi morph ism by repl aci ng t he codomai n w i t h i t s subalgebra that i s the i m age of the dom a i n u n der the homomor p h i s m . Thus, every homomorphism generates a un ique i somorphism between the grou p i ngs on i t s domai n and codomai n . T h i s res u l t i s co m m o n l y k n o w n as the first iso m o rphism theore m . ( See M al ' cev [ 1 973] , p p . 4 7-48; and Co h n [1981] , p . 60 . ) The second case concerns t hose correspondences over an algebra and itself that are also equivalence relat ions. S uch correspondences are called congru ences. T h u s , a congru ence is a correspondence ( R, IJ!) of an algebra ( A , 0 ) over itself such that for a l l x , y , z E ( A , O) :
1 . (x , x)
E
( R , IJ! ) ,
(y , x)
E
( R , w ) w h e ne ve r ( x , y)
2.
E
( R, w ) , and
Part II: A
232
The01y
3 . ( x , z ) E ( R , lli ) whenever (x, y ) E ( R , lli ) and ( y , z ) E ( R , lli ) . S i nce Fact 6 . 1 applies t o al l equ i valence relat ion s , we k now t h at every congru ence i s d i func t iona l , though the converse i s not the case. Fro m Theorem 6 . 4 we can then i n fer t hat the grouping i n d u ced by a congruence i s an algebra of classes.
6.9
Cognitive Models
A cogn i t i ve model , as you may rec a l l from the l ast chapter , has t h ree compo nents: a concept network, an environment , and a cogni t i ve relation between the two. I had also i n d i cated that the concept network and the environment are formalized as algebras , an d the cogni t i ve relation as a correspondence be tween the two algebras . Now t h at I have i nt roduced algebras , I can p resent the t h ree components of a cogni t i ve model more formally. I start out t h i s section b y g i v i n g a formal defi n i t ion o f cog n i t i ve models. T h e n I i nt roduce t he concepts of local coherency and coheren cy. F i n al ly, I define some of the terms l i ke ' complete' and ' fu l l ' t h at can be applied to cogni t i ve models and t h at were i n form a l l y i n t roduced i n the last chapter [Section 5.7.4] , and relate t hem to the characteri stics of cogni t i ve rel ations.
6.9.1
B asic D efinition
A co n cept netw07'k i s an algebra. ( A , 11) w i t h t he following characteristics: 1.
The class of operators 11 i s either fi n i te, or i s i n c l u ded in the class of polynomial operat ions generated by a fi n i te subclass of 11 . I n other words, t here i s a finite s u b c l ass n l � n such t hat n � PA ( \1 1 ) .
2 . E ve r y
operator i n
n
is
a.
com p utable fu nction.
3 . The algebra is fi n i tely generated . That i s , t here i s s o me fi n ite such t hat J0 ( X ) A .
X
� A
=
A l l t he se requirements o n co n c e pt networks h ave t o d o w i t h finite represent a b i l i ty. That i s , assuming that our m i n ds are fini te, and concept networks are mental structures that we can access and manipulate, it should be possible to represent concept networks w i th finite means . A concept network i s said to b e fi n i te i f the class of objects A i s fi n i te, and i n fi n i te otherwise.
Ch ap t er 6: Cogn i t ion : Formal Con cep ts
233
I should note here that the con d it ions of com putabi l i ty an d fi n i te gener ati v i ty are rather weak . Consequent l y, the above characterization of concept network i s quite broad . Depen d i n g on what t h i s framework i s bei n g used for , one mi ght wish to i mpose st ronger const rai nts on concept networks. For i n stance, an u pper bound on the com plex i ty of the operators i n !1 can be specified, t hough this woul d exclude certain scientific theories from bei n g re garded as concept network s . Or, one might put an upper bound on the ari ty of operators. This l atter condi t ion seems quite appeal i ng for two reasons. One i s t hat any algebra having operators of arity greater than 3 can be em bedded i n an algebra w i t h at most b i n ary operators. [Coh n 1 98 1 , Chap. I I I , Theorem 7. 1 ( p . 1 47)] . Second ly, Halford and W i l son [ 1 980] have demon strated t hat a chi l d ' s abil i ty to use u n ary operators , b i n ary operators, and the compos i tion of operators-whi ch i s needed to get the effect of ternary an d quaternary operators-can be l i n ked to t he stages of the chi l d 's cog n i t i v e development . A cognitive m odel i s a tri ple ( ( A , !1 ) , ( R , w ) , ( B , L; ) ) such t h at all of the fol low i n g con d i t ions are sat i s fied : •
( A , !1) i s a co ncept n e t work as defi ned above.
•
( B , L;) i s any algebra,
re p rese n t i n g
what I h a v e been
re fe r r i n g
to as the
e n viro n m e n t . •
(R, lli ) i s a rel at ion ( represen t i ng a cogn itive 1·ela t i o n ) from ( A , !1) t o ( B , B ) -that i s , R <::;; A x B and ili ( n ) <::;; !1 ( n ) x B ( n ) for a ll n-with the fol lowing characteristics:
1 . Every operator i n B i s related to some operator in !1 . l n other words, for al l a in B, w - 1 ( a ) =J 0 . 2.
T h e su balgebra o f ( A , !1 ) t h at i s related t o t h e environment algebra ( B , L;) by ( R , Ili ) - t h at i s , ( R , Ili ) - 1 ( ( B , L; ) ) <::;; ( A , n ) - is a l so a c once p t n etwork as de fi n e d above . I n pa.r l i c u l ar , ( R , iii ) - I ( ( B , L;) ) i s a fi n i t e l y ge n e rated alge b r a .
These con d i tions c a.l l for a. fe w words of e x p l a n at i on . comes from one of the u n der l y i n g ass u m p t i o n s o f m y t h at
the o bjects in the e n viro n m e n t" acqui1·e
a
T h e fi rst con d i t i o n framewor k , n am e l y
sb·u c t u re only via
/h e
opera
tional stru c ture of the con cept n e t work. I n other words , t he operators i n the environment , or transformations a. s I called t h e m i n t h e l as t c h a p t e r , can n ot e x i s t without being related to some o p e rator i n t h e co n c e p t n e t w o r k .
234
II: A
Part
Theory
The second con d i t ion is merely to make sure that t hough I allow for a concept network to be part ially i n terpreted-meani n g that only a part of the network has been i nstant i ated in the envi ronment-the part that i s related must be a proper concept network , s i n ce otherwise, finite representab i l i ty of t he cogn i t i ve model can no longer be assured . Note that of all the re q u i rements on a concept network , the only ones that m i ght not be met i n (R, w ) - t ( ( B , I:) ) are t hose of being an algebra and being fi n i tely generated . A cogn i t i ve model i s fi n i t e i f i t s concept network i s fi n i te-mean i ng that the c l ass A i s fi n i te-and i s infin ite otherwise.
6.9.2
Lo cal C o herency and C o herency
Notice t h at I defined a cog n i t i ve rel at ion to be a relation and not a corre s po n d e n ce It is t h e coherency con d i t ion that t u rns a cogn i t i ve relation i nto a correspondence. However, fi rs t I would l i ke to i n t roduce the notion of local coherency, and t hen use i t to define coherency. .
G i ven a cogn i t i ve model C = ( ( A , fl) , ( R , w ) , ( B , I: ) ) , and a class X s;;; A , w e say that C ( o r ( R , W ) ) i s locally coh e ren t i n X i f an d only i f whenever :t' 1 , , xn are all in X, w i s in fl ( n ) , and w ( .T 1 , , xn ) is i n X t h e n for any y � , . . . , Yn in B a n d u in I:( n) such t h a t ( x 1 , Y t ) , . . . , ( x n , Y n ) E R and ( w , a ) E W ( n ) it i s the case that (w( x 1 , . . . , xn ) , u ( yh · · · , Yn ) ) i s also i n R. S i m i l arly, gi ven a class Y s;;; B, w e say t h at C ( or ( R, 11i ) ) i s lo ca l ly coh e 7'e n t i n Y i f and only i f whenever y t , · . . , yn are all in Y, u i s in L: ( n ) , and a ( y 1 , , yn ) is in Y t hen for any X t , . . . , Xn i n A and w i n fl ( n ) such that ( x t , Yt ) , . . . , ( x n , Y n ) E R a n d ( w , a ) E W ( n ) i t i s the case t h at (w ( x t , . . . , xn ) , u ( y1 , , yn ) ) i s also i n R. The fol lowi ng fact can now b e easily deri ved f rom t hese defi n i t ions: Fact : 6 . 1 0 A cog n it i v e model C = ( ( A , fl) , ( R , w ) , (B, E)) is locally coh ere n t in A if, and only if, it i s locally coh e n� n t in B . W h e n C ( or ( R , w ) ) i s locally coherent i n A (or B ) w e say t hat i t i s fully c o h e re n t or s i m p l y coh e re n t . T h u s , the cogni t i ve relat ion of a. fu lly coherent cogni t i ve model i s a correspondence between t he algeb ras of the concept network and the environ ment . •
•
•
•
•
•
•
.
The c ohere n c y
con d i t i on
•
•
•
•
ensures that i n a c og n i t i v e model .the concept
network a n d t h e e n v i ronment preserve the
structures of each other via the
I e m p h as i zed i n t h e l as t c h a p t er, this is necessary i f t h e cogni t i ve model is to provide a reasonable basis fo r p re d i c t i ng changes in the env i ronment , an d for plan n i n g one's actions. O b v i o u s l y, si nce we i nteract w i t h a small c h u n k of our envi ron ment at any gi ven t i m e , and s i nce, w i t h our m i n d s bei ng fi n i te, w e can access only a. fi n i te portion of a concept network at cogn i t i ve relat i on .
As
Ch ap t er
6:
Cognition : Forma./ Con cep ts
235
any t i me, the concept of l ocal coherency i s much m ore i m portant and usefu l t h an ful l coherency. However, for mathemat i cal s i m p l i c i ty I l i m i t myself to ful l y coherent cogni t i ve models from here to the end of Sect ion 1 1 . The question of how the coherency of i n fi n i te models m ay be establi shed by fi n i te m inds is addressed i n Sect ion 1 2 . 6.9.3
S ome C haracteristics o f C ognit ive M o dels
Let C ( ( A , D ) , (R, \li ) , ( B , � ) ) be a cogn i t i ve model . A n y element x of i t s cogni t i ve model ( A , D) is said to be releva n t if (R, \li ) ( x ) =f. 0 , a n d irrele va nt otherwise. If every x i n ( A , D ) i s relevan t t hen the cog n i t i v e m odel C i s sai d to be full. A nother way of defi n i n g fu l l ness of a c o gn i t i ve m o d e l i s to say t h at the group i n g i n d u ced by i t on the env i ronment does n o t contai n the empty class. For any pai r of elements of the cogn i t i ve model ( A , D) , say x and y , we say t h at x i s syn onymous w i t h y i f ( R, \li ) ( x ) ( R, \li ) ( y ) . If there are no synonymous pairs of distinct x and y i n the cogn i t i ve model ( A , D ) , t hen we say t h at t he cogn i t i ve model C is optimal. =
=
A ny element y =f. 0 and in visible
of
the en v i ro n m e nt
o t h e rw i se .
( B , �) i s sai d to be
visible i f
( R, IJ.!) - I ( y ) ( B , E) i s
I f every e l e m e n t o f t h e e n v i ro n m e n t
v i s i b l e , we say t h at t h e cogn i t i ve model C i s
co mplete.
A n o t h e r way t o spec i fy
comp leteness of a cogn i t i ve m o del i s to say t h at t h e grou p i n g i n d u ced by i t
on t h e environment i s fu l l . I f t h e group i n g i n d u ced by t h e cogn i t i ve relation ( R, ll! ) o n t h e envi ronment ( B , �) i s pairwise d i sj oi n t , we say t h at t he cogn i t i ve model C is u n a m b iguous. Two elements x and y i n the en v i r o n m e n t ( B , E) a re indis tinguishable if ( R, \li ) - 1 ( x ) = ( R , \li ) - 1 ( y ) . If t he envi ron ment ( B , � ) h as no pair of i n d i s t i n gu i shab le elemen ts, the cogn i t i ve model C i s fully resolved. No t i ce t h at t hese two ch aracteri s t i c s are i n depen den t : t h at i s , a fu l l y resol ved
model need not be unambiguous, and an un a m b i guous model need not be ful l y resol ved . The fol l ow i n g fact s c a n n ow be deri ved t h at of cogn i t i ve models depend on their cogn i t i ve Fact : 6 . 1 1
s h ow how t h ese characteri s t i c s re l a.t i o n s :
1. A
cognitive model is fu ll , complete, a n d u n a m b iguous if, a n d o n l y if, it s cognitive relation is difu n ctional.
2. A
cognitive m odel is full, comple t e , u n a m biguous, a n d fully resolved if,
Part II: A
236
The01y
a n d o nly if, its cognitive relation is an epimorphism fmm th e cognitive model to the envim n m e n t . 3. A
cogn itive m odel i s full, complete, optimal, a n d u n a m b iguous ij, a n d o nly if, its cognitive relation i s a n ep imorphism fro m the envim n m e n t to the cognitive m odel.
4-
A
cognitive m odel is full, complet e, optim al, u n a mbiguous, and fully 1·esolved if, a nd o nly if, its cognitive rela tion is an iso m o rphis m .
T h e proofs of al l t hese facts are s i m ple, a n d I leave t h e m for you to work t hem out . They are merely an exercise in recal l i ng the defi n i tions and using the facts t h at were deri ved earlier i n t h i s chapter. For any element y in the env i ronment of a cogni t i ve model , whenever t here is some element of its concept betwork x such that (x, y) is in the cogn i t i ve rel at i o n , we say that x i s a rep1·esentation of y . Moreover , any struct u ral descri ption of x is t hen said to be a description of y . A cogni t i ve model can induce operators i n i t s envi ronment . Here i s a n ex ample. Consider the correspondence L E N G T H from T ! TEGER to S T RI G , which was i ntrod u ced earlier i n t h i s c h apt er [§6 .8.2], to be a cogn i t i ve rela tion. Techn i cal l y, t here i s a slight problem h e r e si nce not every operator of STRING is related to s om e t h i n g i n I N T E G E R . B u t we can remedy i t by tak ing an S-subalgebra of STRING contain i ng only t h e operator co ne t o be the codomai n of L E N G T H . The algebra I N T E G E R i s then the concept networ k . 1 ow not i ce t h at the operator n ext i n I N T E G E R i s a speciali zat ion of add. S i n ce add i s related to co ne, i t s uggests t hat we can i n d uce operators l i ke n ext i n S T R I N G t h at are speci a l i zations of co ne, as shown i n Figure 6 . 1 1 . S i m i larly, the correspondence M O D U L O [§6 . 8 . 2] can i nd uce an operator l i ke p red i n I N T E G E R t h at is the i n verse of n ext. (This process of i nducing operators i s s i m i lar to the a ugm entation of I n d u r k h y a. [ 1 986] . ) ,
6.10
Cognitive Models O ver an Environment
O ften one wou l d l i ke to com p are cogni t i ve models t hat s hare t he same en v i ron ment . Are they equivalent? Does one of t hem prov i de more detai l ed i nform ation about the e n v i r o n m e n t ? Does one of t hem give more complete i nformat ion about t he environment? And so on. I n t h i s se c t i on I charac terize t hese n ot ions formal ly, and t hen der i ve a fact t h at is used in the next ,
Chap t er 6: Cogn i t ion : Formal Con cep ts
INTEGER as a concept network
237
A n S-subalgebra of S TRING as an environment
a
z
LENGTH as a cognitive relation
aa
zz
etc.
ADD
------
CONC
df NEXT (X) = ADD ( l ,X) CONC-a C ONC -b
NEXT
induced
operators
CONC-z [CONC-z (ab)
=
zab; etc.]
FIGURE 6. 1 1 : An example to show how a c ognitiv e relation can induce operators in the environment.
Pa. r t II: A Theory
238
chapter to show w hy certain kinds of metaphors are i ncapable of generat i n g any n e w i n formation about t he envi ron ment . F i rst consi der the notion of equi valence. We wou l d l i ke to say t h at two cogn i t i ve models over the same environment are equivalent w hen they both i n d u ce t he same grou ping on the envi ron ment . If, in add i t ion , their concept networks are also i somorp h i c , then t hey are said to be str·o ngly equivale nt. N ow consi der the rel ations of extension and restri ction , which are the i n verse of each oth er. I n t u i t i vely, a restrict ion of a cogn i t i ve model m akes the environment less visible while keepi n g the structure of the envi ronment t h at i s s t i l l visi ble the same as before. To define it formally, let C = ( ( A 1 , fh ) , ( R , 'l! ) , ( B , E ) ) and D = ( ( A2 , !12 ) , ( S, ill ) , ( B , E ) ) be two cogni t i ve models over the environment ( B , E ) . Now we wou l d l i ke to form ally state t he con d i t ions u nder w h i ch D is a restriction of C . C learly, t he first cond ition is t h at l e s s of the env i ronment ( B , E) shoul d be visi ble u n der D t h an u n der C . T h i s i s eas i ly formalized by saying t hat ( S, ill ) ( ( A 2 , !12 ) ) C ( R , 'l! ) ( ( A � , !1 1 ) ) . For the n 1 her con d i t i o n , w h i ch says t h at the environment that i s visi ble un de r D sh oul d be structured the s a m e way as u n der C , w e c an use the notion of equ i valence. Let us use the notation ( R , w) I (B, , E, ) ' where ( B, , E , ) i s a s ubalgebra of ( B , E ) , to mean ( R , w ) restricted to ( B 1 , E 1 ) , where ( x , y ) i s i n (R, 'i! ) I ( B1 , E 1 ) i f. and o n l y i f, ( x , y ) i s i n (R, w ) and y i s i n ( B1 , E 1 ) . Now we can defi ne the relation of restrict ion between two cogn i t i ve models over the same environment as fol lows. D is a 1·estriction of C provided: l . ( S, ill ) ( ( A 2 , !1 2 ) )
c
( R , w ) ( ( A 1 , !1 1 ) ) ; and
2 . the cogni t i ve models ( ( A2 , !12 ) , ( S, ill ) , ( S, ill ) ( ( A 2 , !12) ) ) and ( ( A , , !1 , ) ' ( R, w ) I ( S, ill ) ( ( A 2 , !12 ) ) , ( S , ill ) ( ( A 2 , !12) ) ) are equi valent . The relat ion of extension is the reci p rocal of rest riction . That i s , C i s an ext ension o f D if D is a rest riction of C . F i n ally, I introduce the concept o f refinemen t . I n t u i t i vely a refinement o f a cogni t i ve model m akes the env i ronment more resolved without restructuring i t otherwise. To defi ne i t formally, we first define a relation of indislinguish a b ility over the env i ronment of a cogni t i ve mode l . G i ven a cogni t i ve model C ( ( A , !1 ) , ( R, 'l! ) , ( B , E) ) , t he indistinguishab ility relation i nduced by C over the environment ( B , E ) , wri tten as tc , i s a relat ion such that for any x and y i n ( B , E ) , the pai r ( x , y ) i s i n tc i f, and only i f, .r and y are i ndist i n guishable i n C ; or i n other words , i f, a n d only i f, ( R, w ) - 1 ( x ) ( R, w ) - ' ( y ) . I l i s easy t o see that tc i s a n equ i valence rel ation , though i t i s not necessari l y a congruence. =
=
Chapt er
6:
Cogn i tion :
Form al Con cep ts
239
( ( A 1 , D 1 ) , ( R, Ill ) , ( B , E ) ) a n d V = ( ( A 2 , D z ) , (5, <1> ) , (B, E) ) N � w let C be two cogni t i ve models over the same envi ron ment ( B , E) . T he n we say t h at C i s a refinement of V provided : =
1 . T hey both m ak e ex a c t l y the same parts of the en v i ro n m en t visible: t h at 2. C
is,
( R, W ) ( ( A 1 , 0 1 ) )
s t ru c t ur e s
=
( 5, ) ( ( A2 , D z ) ) ; a n d
the envi ronment i n the same way
i t more resol ved : i n other wo r d s ,
tc
C
tv.
as
V
e
x c e pt for m a k i n g
We can now p rove t h e fo l low i n g fact t h at i s u sed i n t h e n e x t chapter: Fact : 6 . 1 2 Lei. C ( ( A , D) , ( R, Ill ) , (B, E)) be a cognit ive m odel, and let ( A 1 , 0 1 ) be some concept n e t work. Given a co n·espo ndence, say ( 5, ) , fro m ( A 1 , D 1 ) to ( A , D ) we ca n fo rm a n o th e 1· cognitive model, say V, ove1· ( B , E) as V = ( ( A 1 , D 1 ) , (5, ) o ( R, W ) , ( B , E) ) . Th e n V can n e ith er· be an ext e nsion of C nor a refinement of C . P r o of: To show th at V ca n no t b e an extension o f C we merely note t hat ( 5, <1> ) o ( R , lli ) ( ( A 1 , 0 1 ) ) is t h e sa me as ( R, W ) ( ( 5, ) ( (A � , 0 1 ) ) ) ; an d si n ce ( 5, ) ( ( A 1 , 0 1 ) ) i s a s u b c l as s of ( or i s e q u a l to ) � ( A , O ) , i t fol lows t h at ( 5, ) o (R, W ) ( ( A " 0 1 ) ) i s a. s u b c l ass of ( or i s equal to ) ( R, Ill ) ( ( A , 0) ) . T h u s , i t cannot be t h e case t hat ( R, W ) ( ( A , 0 ) ) i s a. proper s u b c l ass of (5, ) o (R, lli ) ( ( A 1 , D 1 ) ) =
To show that V c a n n o t be a. refinement of C , we w i l l a ss u m e t h e con trary and derive a . c ont rad i ct i on . So assume that V i s a r e fi neme n t of C . I t means t h at t here are a t l e as t two d i s t i n ct eleme n ts i n t h e en v i r o n m e nt ( B , E ) , s ay y1 and y 2 , t h a t a r e d i s t i n gu i s h a b l e u n d e r V b u t not u n d er C . 1 I n ot h er words , ( R, W ) - 1 ( y! ) = ( R, Ill ) - 1 (y2 ) ; b u t ( (5', <1> ) o ( R, W ) ) - ( y 1 ) of. ( (S', ) o ( R , W ) t ' ( y z ) . ( 5, <1>) - t ( ( R, \li ) - 1 ( y t ) ) , a. n d t he s am e for y2 . Bu t ( (5 , ) o ( R , W ) ) - 1 ( y t ) Thus, we have (5, <1>) - \ (R, \I! ) -1 (y 1 ) ) is no t eq u al t o (5, ) - 1 ( ( R, \li ) - 1 ( y2 ) ) ; 1 an d from (R, l.li ) - 1 (;r;t ) eq u a.l s ( R, W ) - (;r;2 ) w e get (5, ) - t ( ( R, \I! ) - I ( Y t ) ) i s 1 n o t equal to (5, ) - ( ( R, W ) - 1 ( y 1 ) ) w h i ch i s clearly a contrad ic t ion . D =
6.11
P roj ective and A ccommodatin g Models
In the previous chapter we saw that t he c oh e r en c y of cog n i t i ve m o d e l s i s m ai n t ained essent i ally from a n i nterplay of two d i ffe r e n t mechan i s m s : projec tion and accom modation . I n proj ect i o n the s t r u ct u re of the c o n c e p t n e t wor k
240
Part II: A Theory
is kept i nvari ant, an d the cogn i t i ve rel ation of the model i s altered to m ai n tai n coherency. I n accommodat i o n , t h e cog n i t i ve rela t ion i s kept fixed , and it is the struct u re of the concept network that is altered . We also saw that t hough i n most cases proj ection and accommodation act i n consort , t here are sit uations in w h i ch one or the other plays a domi n at i ng role, giving rise to proj ecti ve or accommodat i n g models . The question I would l i ke to address in t h i s section i s whet her t here are any d i s t i n c t i ve formal characteristics of proj ecti ve and accom m o d at i ng models . Let u s beg i n b y considering project i ve or concept d r i ven models. A s mentioned above, i n projection , the cogn i t i ve agent starts out w i t h a concept network , and then varies t he correspondence between t he concepts and parts of the envi ron ment to find a coherent fi t . ( See Figure 5 . 1 5 . ) The result is t hat t he grouped envi ronment appears as an i somorph i c copy of the concept network to the cogn i t i ve agent . This suggests that a proj ect i ve model may be characterized by the fact t h at t he grou p i n g i n d uced by it on t he environment is an algebra of classes that is i somorph i c to the concept networ k . H owever, t hat wou l d preclude the possi b i li ty that the concept network may contai n synonyms. B u t t h i s i s easi l y remed ied b y requ i r i n g that t h e correspondence from the concept network t o t h e a l g e bra of classes ( t hat i s i nd uced by t he cogn i t i ve relation of the cogn i t i ve model ) on the envi ron ment be a homomorph i s m . Now when a cogn i t i ve agent views t h e envi ronment t h rough t h e concept network , what i t sees i s the algebra of classes i n the envi ronment that i s i n du ced b y the concept networ k . So w e m i ght a s well take t h i s algebra of classes to be the envi ronment of the cogni t i ve model . In that case, the cogni t i ve relation i tself becomes a homomorphism from the concept network to the envi ronmen t . Thus, a cogn itive m odel is p mjective wh e n its cog n itive ?'ela tion is a homomorphism fro m the concept netwo1·k t o the environmen t.
1ow consider accom modat i o n . I t works b y keep i n g t h e corres p o nden ce between the concepts and parts of the envi ronment fi xed , and then adap t i n g the structure o f the concept network to reflect the structure o f the envi ron ment ( See Figure 5 . 1 4 ) . In other words , we start w i t h a fixed grouping on the envi ron ment . This grou ping then reveals a structure consis t i n g of t hose operators, and classes of operators, of the envi ronment t h at are admi t ted by the grouping. The struct u re of the concept network is adapted t i l l it becomes an i somorph i c copy of the visible structure of the envi ron ment . In order for a cogn i t i ve agent to adapt i t s concept network to the structure of the envi ronment , t he group i ng on the envi ro n m en t must be u n am b i g u o u s ; or, what i s the same, pai rwise disj oi n t . O t herwise, if there i s some ambiguous
Ch ap t er 6: Cogn i tion : Form al Con cep ts
24 1
obj ect i n the environment that belongs to two d i fferent grou ps, the cogni t i ve agent4li,vould not know w h i ch group i s present w henever i t sees the ambiguous obj ect . Moreover, since the grouping on the envi ron ment i s determi ned by the bias of t he cogni t i ve and perceptual apparatus of the cogn i t i ve agent , which i s kept fixed i n accommodat ing models, we m ay assume that the grou ping extends to cover all t he envi ronmen t . In other words, accommodating models are also complete. Both t hese observations are i ncorporated by say i n g t h at a cognitive model i s accommodat ing i f its cognitive rela t ion i s a homomo1·ph ism from t h e en
vironment to th e concept network. ( It is i nteresting to note here that Q morphisms of Holland et al. [ 1 986] become, i n my fram ework, accommodat i ng cogni t i ve models over the same environmen t , with successi ve layers b e i ng refinements of p revious l ayers . )
6.1 2
Finite Representability and Cohere ncy
Earlier, I emphasized that coherency i s an i m portant con d i tion on cog n i t i ve model s . It i s coherency th at ensu res that the result of a long sequence of reason i n g or con s t r u c t i on carried out i n t h e concept network w i l l also hold
in the environment . However , with my emphasis on fi n i te r e p resen t a bi l i ty , this i mmediately raises a major question: How can we estab l i s h coherency w i t h our fin ite minds? Not i ce t h at the problem exists not only for i n fi n i te models but also for fi n i te ones, since even t hough the con cept network of a cogni t i ve model m ay be finite the env i ron ment i s st i l l poten t i ally infinite and coherency i nvolves both the concept network and the environmen t . Of course, i t i s precisely to address t h i s p roblem t h at I i n t roduced the concept of local coh e re n c y , w h i c h i s coherency l i m i ted to a part of the c on ce pt network or the envi ronment . Local coherency i s fin i tely representable and , consequently, a more u seful concept t h an ful l coherency. However, for cer t ai n cogn i t i ve act i v i ties-and science comes i m m e d i a t e l y to m i n d as a prime exa, m p le- l oca, l coherency i B not enough . A B c i e n t i B t i B u 5 u a, l l y not i n ter ested in t heories that are locally t rue, but seeks u n i versal t heories t hat are ful l y coherent . At least that remai ns an i deal to which the scient ific commu n i t y as p i re s . And t herefore, the problem of the fi n i t e rep re s e n t abi l i t y of ful l coherency is an i m p ortant one, and must be add ressed i n t h i s fr am ewo rk . I t turns out t hat by using algebras , w i t h fi n itary operators, to formalize c on ce pt networks and env i ronments , and by requiring the c o n ce p t network to h ave computable operators and to be fi n i tely gene rat ed , we h ave m ade ful l
Pa.rt
242
II: A
Theory
coherency-of even i nfin i t e cog n i t i ve models-fi n i tely representable i n some cases . For i n stance, i n coheren cy of any cogni t i ve model , whether fi n i te or i n fi n i te, i s al ways detectable by fi n i te means. Recal l t h at a cogn i t i ve model C ( ( A , D ) , ( R, 1Ji ) , ( B , I; ) ) is said to be ful l y coherent i f, and only i f, i t s cogn i t i ve relation ( R, 1Ji ) i s s u ch t hat whenever (x1 , y1 ) , . . . , (xn , Yn ) are all i n R ( x h · · · , Xn are i n A and Yl , · · · , Yn are in B), and ( w , a ) i s i n 1Ji ( n ) ( w E D ( n ) and a E B ( n ) ) , then the pai r (w ( x 1 , . . . , xn ) , a ( y l , . . . , Yn ) ) i s also in R. It means t h at i f C i s i ncoheren t , then t here exi s t , for some fi n i te n, n objects i n A , say a 1 , , a n , an n- ary operator i n D , say a , n objects i n B , say b1 , . . . , bn , and an n- ary operator i n I; , say (3 , such t hat ( a � , b1 ) , . . . , (a n , bn ) are al l i n R, ( a , (3 ) i s i n 1Ji , but ( a ( a 1 , , an ) , (3 ( b1 , , bn ) ) i s not i n R. S i n ce a i s a com p u table fu nction, b y the defi n i tion o f concept networks, and n i s fi n i te, t h i s shows t hat the i n coherency of any cogn i t i ve model i s always fi n itely representable. =
•
•
•
•
•
•
•
•
•
This characteri s tic of cogn i t i ve models i s well known in the phi losophy of science: a scientific t heory i s req u i red to be refu t able by some k i n d of experimentati on an d /or empiri cal observations. ( See Popper [ 1 959; 1 962] . ) There i s one other way i n w h i ch ful l coherency i s fi n i tely representable t h i s time for project i ve model s . I show how any concept network ( wh i ch i s req u i red to be fi n i tely generated ) can be projected coherently onto an envi ronment by finite mean s . This res u l t i s deri ved from a slight adaptation of a well-known t heorem i n algebra t h at says t h at given an algebra ( A , D ) , a s u bclass X of A , and any other algebra ( B , D ) ; any fun c t i on from X i nto B extends to a u n i que homomorphism from the algebra ( Sn (X ) , D ) to ( B , D ) . [Cohn 1 98 1 , Chap. I I I , Theorem 2 . 6 ( p . 1 20 ) ] . The adapted version o f t h i s t heorem t h at i s u sefu l for m y p u r pose here i s p resented below :
Theore m : 6 . 5 Given a co n cep t n e twork ( A , D) ; a finite generating class X of ( A , D ) (X � A ) , a n en viro n m e n t ( B , I; ) ; a n d a 7'elation (R, 1Ji ) between (A, D ) and th e en vi7'0 n m e n t such that R � X X B, R is full in X (m ean ing that every x in X is rela t ed to at least one y in B by R), 1Ji ( n ) <:;:; D ( n ) x L:; ( n ) fo 7' all n , I}! is full i n both D a n d L:; , a n d ( R , w ) is locally coh e re n t i n X ; th e n there is a cognitive relation ( R' , 1Ji ) between ( A , D ) a n d ( B , I;) such that R <:;:; R' <:;:; A x B and ( R' , 1Ji ) is fully coh e 7'e n t . Pro of: To prove th at ( R' , 1Ji ) exists w i t h the s a i d properties , I show here how to construct i t .
Consi der t h e class o f all struct u ral descri ptions i n ( A , D ) t hat are rooted in X: in other words, the class of all those structural descriptions over ( A , D ) that h ave all t hei r leaf nodes i n X . T h i s class i s denoted b y Sn ( X ) .
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N �w for m a relation , say , from Sn ( X ) to SE ( B ) as fol lows . For every in Sn ( X ) , relate it to all t hose structures in SE ( B ) t h at can be obtai ned from s by rep lacing every leaf node x in s by some e l em e nt of R( x ) , and every i ntermedi ate node w i n s by some element of W ( w ) . The ful l n ess of R and W i n X and n , respecti vely, guarantees that every s i n S11 ( X ) w i l l be related to at least one structure in SE ( B ) . s
N ow define R' as fol lows . For any x i n A an d y i n B , ( x , y ) i s i n R' if, and only if, t here e x i s t some s i n Sn ( X ) a n d t i n SE ( B ) w i t h ( s , t ) i n
From t h e construct ion , i t should b e clear that ( R' , W ) i s , indeed , a corre spondence from ( A , !! ) to ( B , 2:: ) . M oreover, s i n ce X is a ge n e r a t i ng c l ass of ( A , f! ) . G i ven ( A , f! ) , ( R' , W ) is fu l l i n ( A , f! ) : t h at i s , ( R' , W f 1 ( ( B , I: ) ) th at ( A , f!) i s a concept networ k , we have p roved t h at ( R' , iii ) i s a fu l l y c o herent cogni t i ve relat ion . D I shou l d note a few t h i ngs regarding t h i s t heorem . F i rst of al l , t h oug h the construction of ( R' , w ) i n the p roof of the theorem is determ i n i stic, and t herefore yields a u n i que cogni t i ve relation , there m ay well be other cog n i t i ve relations from ( A , f! ) to ( B , 2:: ) that are an exten sion of ( R , iii ) . Secondly, t h i s construction does not preserve fun c tional i t y : t h at i s , i f ( R, w ) is taken to be a function from (X, f! ) to ( B , 2:: ) , then ( R' , iii ) need not come out as a homomorphi s m . In fac t , in cer t ai n cases it m ay be i m p o s s i b l e to extend a locally coherent function, from ( X , f!) to ( B , L:) , to a homomorph ism from ( A , f! ) to ( B , E ) . =
T heorem 6 . 5 makes coherency of p roj ect i ve models fi n i tely rep resentable as fol lows . S ince every concept network h as a fi n i te generat i n g class, we can start out by forming a r e l at i o n b e t w ee n a fi n i te generat i n g class of the concept network and the environ ment , and over the class of operators .
We then ensure
t he local coherency of this fi n i te rel at ion over the generat i ng class. Now we can extend t h i s relation, by the proced u re e x pl ai n e d in t he p r o o f of the t heorem , to cover the whole concept network. O f course, i t is not necessary to carry out the fu l l ex t e n sio n at any one t i rn e-i f t he concept n et work i s i n fi n i t e i t s i m p l y cannot be done-b u t as long as the p roper p roced u re i s fol l owed in extend i ng the relat ion to the relevant part of the concept n etwor k , the coherency will be guaranteed . T h i s mech an i s m i s often u sed i n proj ec t i n g mathemati cal concept networks to the real-world s i t uat ions.
C hapter 7 An Interaction Theory of Metaphor
7.1
Introduction
In my framework of cognition, the paradox of i nteract ionism is resol ved by pointing out that while i t is the c og n i t i ve agent who gi ves an o ntol ogy t o the external worl d b y i n s t an tia t i ng concept networks, the s t r u c t ure of the world, as seen from this ontology, i s determi ned by reali ty. Thus, i t is only by i nstan t i at i ng different concept networks that the cogn i t i ve agent can ' see' different structu res i n reali ty. In other words , any reorganization and re structu r i ng of the worl d view is essentially the process of rei n stantiati n g the concept networks-a p rocess I have been cal l i ng pmjeclion .
M y main o b j ect i ve i s to extend t h i s approach t o give a n account of s i m i l arity-creat i ng metaphors and resol ve the paradox of creat ion of simi l arity . However, I would l i ke to do so by developin g a gen era l t heo r y of metaphor which addresses s i m i l a ri t y- bas e d metaphors and c e r t a i n other is s ues related to metaphor such as the thesis " A l l k nowledge is metaphorical ," and the apt ness and cor r ect n ess of metaphors . I n this chapter I am concerned with laying out my accou n t of metaphor. T h e met a p h o r - re l a te d iss u e s are d i scus sed in t h e n e x t cha p te r . chap ter
i s organi zed as fol lows. I n Section 2, I present argu ments proj ective c o g n i t i ve relatio n . As t h i s conclusion m i ght not be obvious , ( what is the ' e n viro n me n t ' of a met ap h o r ? ) , and give n t h at i t is t h e keystone of my account of metaphor , I take special care i n l ay i n g down my arguments, using the exam p l es i n t roThis
l e ad ing t o t h e conclusion t h at a met aphor i s essent i a l l y a
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246 d u ced i n Chapters
1
and 2 .
Then , i n Section 3 , I i ntroduce nomenclature associ ated w i t h metaphor t hat i s used in art i cu lat i n g my theory. The i mportant t h i n g t here is to i n corporate the d i s t i n ct ion between the concept network and the environment orthogonally to the di chotomy between the source and the target that is used in the trad i t ional characterization of metaphor . Most exist i n g t heories of metaphor do not make any disti nct ion analogous to concept network environmen t , but i t i s crucial to the abi l i ty of my framework to explain simi larity- creat i ng metaphors . I n Section 4 , l analyze s i m i l ari ty- based and s i m i lari ty-creat i n g metaphors , comparing and contras t ing the two w i t h respect to t he role each k i n d plays in cogn i t i o n . I class i fy s i m i l arity- based metaphors further i nto syntactic and suggestive metaphors depen d i n g on whether or not they are open-ended , s i n ce t hese two kinds of metaphor aid cogn i t ion i n d ifferent ways. I also resolve t he paradox of creat ion of s i m i l arity here by d iscussing, w i t h some exam p les, how a metaphor can create s i m i lari ties, w i t hout the creat ion bei n g arbi trary. F i n a l ly, Section 5 s u mm arizes the mai n t heses of t h i s chapter .
7.2
Metap hor as P roj ec t ion
Earlier in Chapter 1 , you m ay recall , I characterized metaphor as an u n con vent ional way of descri b in g (or representi ng ) some obj ect , event or situation ( real or i m agi ned ) . The object of descri ption i s t he target , and the object t h at i s being used to u n convent ionally describe the t arget i s the source. We al so saw that the source part ici pates i n the process as a structured set of symbols that have to be appl ied to the t arget in u n conven t i on al ways i n order t o render the descri ption mean i ngfu l . I n t h e i nt eract ionist approach to cognit ion I have outli ned i n t h e l ast two chapters , a stru c t u red set of symbols i s referred to as a concept network , a n object of descri ption is referred to as an environmen t , and an i nterpre tation is referred to as a cogn i t i ve relat ion. While regarding the source of a metaphor as a concept network seems q u i te reasonable, some of you m i ght fi n d i t quite odd to think of the t arget as an environmen t . Consi der i n g some examples m ight make it seem even more strange. What is the envi ronment in Boland ' s ' w i l d flowers as water' metaphor? O r in Spender's 'ocean as a h arp ' metaphor? O r i n Mondrian 's Composition with Blu e and Yello w ? O r i n A ntonion i 's ' G i u l i ana's emot ional state a s blotches o f pai n t ' metaphor? ( The first th ree of these fou r examples are presented in Chapter 2 [§2.2] ,
Ch ap t er 7: Met aph or
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and the fourth one i s presented i n Chapter 1 [§ 1 . 5] . ) T h e problem i s t h at an environmen t , i n my framework of cogn i t ion , i s the external worl d that h as be� given an ontology by i nstant iating a concept network i n i t . But in u nderstan d i n g each of t hese metaphors , the external world does not seem to be d i rectly i nvol ved . ( You can u nderstand each of these metap hors even t hough you are not experiencing the correspon d i n g sen sory s t i m u l i at that t i me-the s u n l i ght p l aying on t he waves, i n the case of Spender's metaphor. ) The key to harmoni z i n g t h i s apparently d i scordant note i s to use the notion of multi-layered cogni t i ve systems [§5.8] , w h i ch are a more realistic way of describing human cognition . I n a l ayered cog n i t i ve system , you may recall , a cogni t i ve relation m ay be formed between any two adj acent l ayers. Thus, the t arget becomes an autonomous structure in the layer below the concept network layer. Even this conclusion m i ght seem baffi i ng . What i s the autonomous struc ture in the l ayer below the con cept network l ayer for Bol an d 's ' w i l d flowers as water' metaphor? In fac t , it m i ght not even be clear what the concept network l ayer is for t h i s metaphor. The other t h ree metaphors ment ioned above face a s i m i lar problem . To clarify these issues, let us back track a l i ttle and recon sider some of the i denti fy i n g character i s t i cs of metaphor that were art i c u l ated i n Chapter 1 [§ 1 . 2 , § 1 . 3 and § 1 . 5] . We observed t here that every metap hor ( an d non metap hor) i n volves a. description and an object or s i t u at i on to w h i ch the description i s i ntended to apply. In applying the desc r ip tion to the obj ect , t he t arget , parts of the desc r i ption m ight not apply to t he target usi ng the conventional i nterpretat ions. I t i s the concepts occur r i n g in these part of t he description ( an d related concepts ) that forms the sou rce of the metaphor. Consider Bolan d ' s poem now . It i s a description of w i l d fl owers grow i ng on a h i l l i n the Irish countr y side, w h i ch become t h e t arget. T h e te x t of the poem , the description , becomes the potential source. There shou l d be no problem in regarding the text of the poem as a . concept network . The words are e s s e n t i a l l y c o n c e p t s t h at are s t r u c t u ral l y i n terre l a t e d i n a certai n way i n the poem . Moreover, words, by v i r t u e of t hei r 'mean i n g' ( as i n ' d i ctionary mean i ng ' ) , are related to each other i n certain ways . Both t hese i nterrelations give the text of the poem an autonomous structur e . T h e situation i s not s o s i m p le wit h regard to the target, b e c a u se i t cou l d be a. real or i m aginary obj ect . L e t us focus on the easier case fi rst , when the t arget is a real obj ect . Consider the scenario w here the poem was con cei ved w h i l e observing w i l d flowers in the I ris h count ryside. Or, con sidering Spender's Seascape, suppose t h at you are read i n g i t while s i t t i ng on a beach
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and observi n g the s u nl ight play in g on the waves . I n such situations, t he exter nal worl d i s prov i d i n g a set of stimuli ( sen sori motor data set ) to the cogni t i ve agent, of which t he poem is a descri ption. Moreover, t h i s set of s t i m u l i i s struct ured i n dependently o f any descri ptions that m ight be attached to i t . ( You might recall here m y earlier d i scussions i n Chapter 2 [§2.4.2] about cre at ion of s i m i l arity i n the context of percept ual proportional analogies , and i n Chapter 3 [§3.2] about the S t ar of Dav i d example of B lack . ) The process o f giving descri ptions ( i n terms o f concept networks ) i s essen t i al l y what I h ave referred to as conceptualizat ion (or i nstanti at i n g a cogni t i ve relat ion ) i n my framework of cogn i tion . The p rocess i n volves i nteraction be tween two structured level s-the level of concept networks and the level of t he sensori motor data set . A s t he words in any language are related to each other in cert ai n ways and the set of stimuli h as its own i ndependent char acteristics, not j ust any arbitrary descri ption w i l l qual i fy as a description of t h e stimu l i . Now whether w e focus on t h e process o f comi ng u p w i t h a description ( as i n concei ving the poem ) or i nterpreti n g a gi ven description ( as i n trying to u nderstand the poem while experiencing more or less the same set of stimuli as the poet ) , the i m portant t h i n g i s that a cogn i t i ve relation between the concepts of the concept network and pieces of the sensori motor data set needs to be estab l i shed . Part of t h is cogn i t i ve relation might be conventional in the sense that the cog n i t i ve agent habi tually i nterprets the concept in that way. For i nstance, the concepts 'from a d istance , ' 'sharp flowers , ' and 'stirring on t hose h i l l s ' in Bolan d ' s poem wou l d all have to be i nterpreted convent i on al ly. However, there are other concepts, such as 'splashes , ' 'shyness , ' ' su persti tious aura, ' ' i vory, dow n h i l l rush , ' and ' fl uency only water h as , ' that cannot be con nected to parts of the s t i mu l i i n a conventional way. I t i s t hese concepts, and other related concepts, t h at form the source of the metaphor. At this point the person rea din g the poem h as t hree options. She can d i scard t he descript ion as anomalou s , si nce i t cannot be made to fi t the struc tured set of stimu l i . This is someth i n g an u n i mag i n at i ve person might do. O r she can ch ange the descri pt ion to fit the st i mu l i , w h i ch woul d correspond to accom modat ion . This change can be affected in two ways, as t here are two structural components to the source concept networ k . One is to change the text of the poem , so t hat it becomes a conventional description of the stimul i . The other i s to redefi ne the words 'splashes , ' ' su persti tious , ' etc. so t h at their d i ctionary mean i ngs are changed in a way t h at m akes them cor respond to parts of the stimuli in a conventional way. Though the second of t hese two ways of accommodation m ay seem somewhat drasti c , it can , nev-
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ertheless, be evi denced , albeit in a smal l way, in the p henomenon by w h i ch a novel metaphor , t h rough repeated use, becomes a conven t ional metaphor , and eve�tually fades i nto polysemy. The t h i rd opti on is to i nstant i ate the t ro u blesome concepts ( words and p hrases) in an u n conventional way. Though the person ( cogn i t i ve agent ) is constrained by the autonomous structure of the concepts ( i n how t hey are related to other concepts i n the text of the poem an d t h rough t he d i ctio n ary ' mean ings ' ) and the i ndependent struct u re of t h e set of stimul i , she h as freedom in i nstanti at i n g t he concepts. lt i s t h i s option t h at leads to a metaphori cal i nterpretat i on . However, t h i s i s precisely what I have referred to as ' p rojection' in my framework of cogni t i o n . Thus, a metaphor becomes an i nstance of projection . Now cons ider the case when t here i s no s t i m u l u s present. Obviously, one can read and u n derstand Bolan d ' s and Spender's poems w i t hout being i n t he envi ronments descri bed i n t h e poems. In fac t , m o s t poems, an d other metaphors of language, are u nderstood in t h i s way. How i s a metaphor an i nstan ce of projection in t hese situations? The key to answeri n g this question l ies i n an alyzi ng w hat exactly goes i nto ' understanding' a metaphor. We can start by con s i deri ng w hat goes on i n ' u n derstanding' a. non-met aphorical descri ption ( p iece of tex t ) . Supp os e someone tells you "It i s snowing outside." You ' u n derst and ' t he ut terance. But what exactly does t hat mean? There exist two schools of thoughts here . A ccording to one schoo l , w h i ch i s dom i n ant i n much of t he cogn i t i ve scien ce and arti fi cial i ntelligence research , to ' u nderstand ' i s to represent i n ternally, i n t he for m of an appropr i ate network of concepts, the i n format ion contai ned i n the u tterance. A s concepts are related to each other in certai n ways ( i n the sense of ency clop e d i c and d i c t i onary meani ngs ) , t h i s i n ternal representation can be used to i n fer a. number of other t h i ngs that are not ex p l i c i t ly mentioned i n t h e ut terance , such as i t i s cold outside, and it i s not s u n ny outside. A ccordi n g to the other s c h o o l of t ho u g h t suc h as t he one proposed in Neisser [ 1 976, C h ap 8] a n d i ncorporate d i n a few accounts of metaphor (Johnson & Malgady [1 980] , and Verbrugge [ 1 980] )-' u nderstand i ng' means i m ag i n i n g a perceptual experience t hat coul d have been descri bed by the u t terance. Of course, in t h i s i m agi nation some subject ivity is b o u n d to o ccur You m i ght im agine big snow fl akes fal l i ng ge n t l y or a b l izzard w i t h gusty wi nds, depen d i n g on what e l se you kn o w about the weat her outsi de ( o r if the sentence occurs i n a n ov e l what else h as been descr i bed about the weather ) . B u t the i mportant t h i ng i s t h at certai n characteri s t i cs remai n i nvar iant across t he d i fferent ways i n w h i ch one can i m agine that i t i s snow i ng -
.
.
,
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outside. Moreover, t hese i nvari ant characteristics reflect the person 's past percept u al experiences that were descri bed as ' snowi ng. ' ( Th i s process of i m agi nation is the i n verse of what Dretske [ 1 98 1 , Chap . 7] h as referred to as ' digi tali zation . ' ) It i s t h i s second approach t o ' unders t a n d i ng' that I adopt here. To fully j us t i fy t h i s choice would be a distraction from the mai n l i ne of argumen t . Suf fice i t to say that in the i nternal representation approach, ' u n derstan d i n g ' ca n o c c u r w i t hout experience, which , to me a t least , i s quite an unacceptable consequence. This is not to say that in order to ' understand ' anyth i ng we must have experienced it at some t i me or anot her. We u nderstand many fict i t i ous words and descri ptions such as ' u n i corn , ' 'a mou ntai n of gol d , ' and ' i t was rai n i ng m i l k and honey from the sky. ' But in any such si tuati o n, the words and ph rases are necessarily descri pt i ve, and we have perceptual acquai ntance with the i n d i v i d u al terms mak i ng up t he descri ption . Fur t her evi den ce of the l i m i t ation of the i nternal representation approach to u n derstanding is provi ded by the fail u re of the the computat ional models of metaphor based on this approach to address s i m i l ar ity-creat i ng metaphors. This issue i s d i scussed at lengt h in Chapter 1 0 . To i n corporate t he i magi nation approach t o ' understan d i n g ' i n m y frame work of cogni t i o n , I need to bring in t he notion of the l ayered cogn i t i ve system that was i n t roduced in Chapter 5 [§ 5 . 8] . In a. l ayered cog n i t i ve system , the i ntermedi ate l ayers contai n struct ures that are less abstract than the con cepts, an d yet t hey derive their struct u re ( i n part ) from the autonomous structure of the sensori motor data sets encountered in the pas t . Moreover, t hese struct ures can be comb i ned to prod u ce 'derived ' structures in the i n termedi ate l ayers. G i ven a l l t h i s , t he ' i magi ned ' percept ual experience that r efl e ct s the u n d er s t a n d i n g of t h e u t terance (a. concept network) can be placed in t he i ntermed i ate l ayers.
I n ' u n derstan d i ng' the utterance "It i s snow i n g outside" the cogni t i ve agent produces a deri ved structure i n one of t h e i nt e r m e d i at e l ay e rs This structure woul d be an i nstant iation ( conven t i onal i n t h i s case) of t h e con cepts l i ke ' snow i ng' and 'outside . ' However, this i nstant i at ion i s const rained by the already exi s t i n g structure of the i ntermedi ate l ayer, w h i ch reflects the cogni t i ve agent s past experiences w i t h fall i ng snow , being outside, etc . Moreover, t h e i nstan t i ated structure of t h e i ntermedi ate l ayer i s 'derived ' i n t h e sense that i t i s n o t rooted i n t h e sensorimotor data set , but i s m ade up by combi n i n g previously exist i n g e xperi en t i a l structures i n the l ay e r In other words , the cogn i t i ve rel at ion term i n ates at the i ntermedi ate l ayer , an d does not go al l the way to the sensori motor data set l ayer. .
'
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Ch apt er
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25 1
W i t h t h i s notion of ' u n derstanding' i n the backgrou n d , i t is easy to see how a metaphor can be seen as an instance of proj ect ion in the absence of sensoty stimuli . When read ing Bolan d 's poem , one i m agi nes the expe rience being described i n the poem , and the descript ion of the poem ( t he concept networ k ) forms a cogn i t i ve relat ion w i t h t h i s i m agi ned experience. W h i le some of the concepts are interpreted convent ional ly i n the context of the i m agi ned experience; other concepts cannot be so i nterpreted . This is because one's previous experiences w i t h watch i ng w i l d fl owers growing on a h i l l gi ves the i m agi ned experience an autonomous struct u re t h at cannot be viol ated in the descript ion . For instance, w i l d flowers are not ' fl u i d ' and do not ' flow ' l i ke water . Faced w i t h the gi ven description and the autonomous structu re of t he i m agined experience, the cogn i t i ve agent agai n has three choices : ( 1 ) consi der the description anom alous, ( 2 ) use accommodation to change t he description , or ( 3 ) instantiate t he t roublesome concepts in a non conventional way. Exerci sing the t h i rd of t hese options leads to metaphor. And s i n ce the structure of the concept network is not alte red i n the process, i t amounts to project ion. To t ake another example, consi der Spender's poem . That the poem i s about t he ocean is signaled exp l i ci t ly b y t h e relevant concepts i n t h e tex t . To u n derstand t h e poem , one needs to i m agine t h e ocean vivid l y, a n d i t i s t h i s v i v i d i m agination t h at becomes t h e domai n i n w h i c h t h e text o f t he poem i s interpreted . The i m agined scene of ocean must i nc lude the waves i n the ocean , t he w i n d m ak in g patterns on the waves, t he s u n l ight reflect ing on the waves in a certai n way, and so on . A l l t h i s i n formation, which i n corporates one's prior perceptual experiences w i t h watchi ng the ocean and the waves, gi ves the domai n of ocean an autonomous struct ure that resists bei ng described arbi t rari l y. Moreover, i t i s less abstract and more detailed t h an the textu al descri ptions. Otherwise, i f one lets t he concept networks of ' ocean ' and ' harp ' ( as reflected in their d i ctionary mean i ngs ) i n terac t , t hen t he poem wou l d h ave to be deemed anomalou s , as there is no way to recon cile the two disparate concept networks . The poem i s rendered meani ngful by i nterpreting, through projection , so m e of t h e concepts i n t h e text i n a non-convent i onal wa.y i n the i m agined domai n of ocean . ( This account of metaphor i ncorporates the observations of Ri coeur [ 1 9 78] , the 'vividness t he sis' of Ortony [ 1 980, p. 78) , and the observat ions of Joh nson [ 1 987, Chap. 6] on the nature of i m agi n ation . ) A consequence of t his accou nt of metaphor i s that a. perceptual acquain t ance with t he domain of i nterpretat ion i s necessary for u n derstanding a metaphor, for i t i s t h i s perceptual acquaintance t h at makes i t possi ble to i m agine the domain v i v i dly. Of course, i t i s not necessary to actually ha.ve
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seen t he ocean in order to be percep tually acquainted w i t h i t . It i s sufficient to h ave seen i t in a movie or on television . I t i s even sufficient to have read descriptions of t he ocean . B u t at some level , the terms of t hese descrip tions ( i ncluding t he i m ages being seen on the movie or the television scree n ) must be groun ded perceptual ly, t hereby m ak i ng i t possi ble for the cogni t i ve agent to i m agine what the ocean might look l i ke. I am sure that if someone has never seen the s u n light playing on the waves and being reflected i n the water ( or watched it on t he television , or seen photographs of i t , etc . ) , then she wou l d not be able to understand or appreciate Spender's poem at all . I n the examples di scussed so far, the domai n of i nterpretation was ex p l i c i t l y signaled by the concept networks. This, however, i s not always the case. I n A nton ion i ' s 'emotional st ate as blot ches of paint ' met aphor [§ 1 . 5] , the domai n of i nterpretat ion i s only hi nted at i n a subtle way. I n the case of Mondrian 's Co mposition with Blu e a n d Yellow [§2 . 2] , the domai n of i nterpre tation is not even h i nted at . One is left to one's own devices to find a suitable domai n , and carry out an i n terpretat i on . C learly, whether the metaphor is comprehended or not crucial ly depends on being able to find an appropriate domain of i nterpretation . A s qui pped by Johnson and M algady : " [ l ] t m ay be that Metaphor com prehension is the i n vention of a context or circumstances in w h i ch the metaphor might h ave been conceivably produced . " ( Johnson & M algady [ 1 980] , p . 266. Emphasis Johnson & M algady 's. ) Not surpris i ngly, such metaphors are somet i m es lost on the audience, j ust as the 'glass telephone booth as t he cage of m isery ' metaphor from H i t chcock 's Th e Bi7'ds [§ 1 . 5] was lost on Truffaut [Truffaut 1 984, p . 288] . B u t once a domai n of i nterpret ation i s selected , say t he moral opposi tion of good and evil for i nterpreti n g the Mondrian , as i n the quote from Mondrian i n C h apter 2 [§2.2] , t he autonomous structure of the domai n resists being de scri bed arbitrarily. And s i n ce the pai n t i ng (t h e concept network ) h a.s i t s own i ndependent st ruct ure ( t he squares and the li nes in the Mondrian are related to each other in a certai n way ) , the process of i nterpretation must respect both t hese structures . A s neit her structure i s altered , the only recourse is to a lte r the cogn i t i ve relat ion by gi ving a new ontology to ( new way of looking at ) the domai n of interpretation so that i t s structure w i t h respect to the new ontology reflects the structure of the concept network . B ut t h i s i s not h i ng . but p roj ection .
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7.3
Nomenc lature A s sociated with
Meta. p hor
253
Metap hor I now i n t rodtfte some nomenc l ature to allow me to refer to the di fferent com ponents parti c ipat i n g in a metaphorical proj ection . There is the domain of i nterpretat ion ( t he real or i m agined experience of the s u n l i gh t playing on the waves of t he ocean for Spender's metaphor ) , w h i ch i s ' an autonomous struc t u re i n the layer below ( less abst ract than ) the concept n etwork l ayer . ' To avoid using t h i s awkward phrase every t i me, I borrow Good man's term 1·ealm ( G oodman [ 1 976] , I I , 6, p. 72 ) to refer to the less abst ract , but autonomous structure of the ' domai n ' layer, of w h ich the env i ronment is a special case . I n fac t , i n doi ng so, I am not changi ng the sense of Good man 's ' real m ' al l t h at much . I n keepi n g w i t h the sou rce- target di chotomy l have been using t h roughout this book , I refer to t h i s realm as the ta1'!)el realm . I n order to ident i fy t he source, w e m u s t disti nguish between t w o concepts networks in the gi ven descri ption. One concept network i n c l udes t hose con cepts t h at h ave a conventional i nterpretation in the target realm ( and related concep ts ) . In Boland's poem , concept s such as ' from a d i s tance' and ' s t i r ring on t hose h i l ls ' belong to t h i s first concept network. The other concept network i nc ludes those concepts t hat ca n n o t be conve n t i o n a l l y i nte r p r e t e d in t h e t arget realm ( an d related concepts ) . The water-rel ated concepts i n Bolan d ' s poem and h arp- related concepts i n Spender's poem constitute the second concept networks for their respecti ve target real m s . This second con cept network t h at must be given a metaphori cal i nterpretation , I refer to as the source con cept n etwork. Often , t here might exist a concept network t hat has a c o n ve n t iona l in t arget real m . I n Bol an d ' s and S pender's poem s, there exist conventional descriptions of the real m being described . ( I n fac t , some of t h e conventional description i s ac t u al l y u sed in each poem . ) I n the exam ples of A n t on i on i 's and Mondrian 's meta.phors, it is possi ble to descr i b e t h e t arget realms ( t he emoti onal stale of G i u l i ana, a.nd the moral o p p o s i t i o n of go o d and e v i l ) using conventional terms. Of cou rse, t h i s might not a l w ay s be possible, s i n ce c e rt a i n real m s cannot be adequately d e s c r i b e d u s i n g only conventional words and p hrases . ( In fact, as 1 argue i n the n e x l section, even i n t he metaphors of Bolan d , S p e n de r , and Mon d r i an , w here t h e t arget real m can be described convent ional ly, t h e conven t i on a l description is not equ i va lent to the metaphorical descript ion , for each of these metaphors works by giving a new ontology to the target realm , and reveal i ng a new structure t here. ) B u t whenever a convent ional descri ption of the t arget real m exists, t erpret ation i n t he
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whether it be equ i valent to the metaphorical description or not , a s t he t a 1'g e t concept n e twork.
J
refer to i t
J ust as the target concept network , when it is exp l i c i t l y mentioned , evokes the i m age of t arget realm , the source concept network m ight also some t i mes evoke the i m age of a real m . For i nstance, i n readi n g Bolan d ' s poem , you might i m agine water flow in g , rushing down t he h i l l . O r i n read i n g the Spender, you might i m agine someone gently stru m m i n g a harp . ( Agai n , t h i s m i ght n o t always be possi ble. I n seeing t h e Mondrian , for example, t here i s no realm i n which t h e concept network o f t h e pai nt i ng has a conventional i nterpretat i on . ) Whenever such a realm exists, I refer to i t as the sou7'Ce 7'ealm. It fol lows then t h at the source concept network h as a conventional i nterpretat ion in the source real m . A cogn i t i ve relation i nstan t i ated between t he source concept network and the t arget real m as a res u l t of the proj ection process is called a m e t aphorical rela tion, or sim ply a metaphor. F i gure 7 . 1 shows all t hese terms grap h ically. Thus, the ' i nteraction , ' i n my account of met aphor, i s an i nteraction between the source concept network and the target realm . Besides t he fact t h at each of them h as an autonomous struct ure, t here is also a d i fference i n their degree of abst ract ion . Concept networks are more abstract , and realm s are less abst ract and more detai led . I n i n stan t i at i ng the source concept network in the target real m , parts of the real m are 'grouped ' together and made to correspond to the concepts of t he concept network . In this process, the t arget realm i s g i ven a new ontology, and i t s structure, as seen from t he more abst ract concept network layer, is changed ( wi t h the new stru c t u re depen d i ng on the autonomous structure of the realm and how the groupi ng was carried out ) . Most theor i es o f metaphor d o not m ake a disti nction between w h at I have been cal l i ng the ' concept networks' and the ' real m s . ' In l i terat u re, when the terms ' source domai n ' and ' t arget domai n ' are used to refer to the two i n teracti ng com ponents of a metaphor, each of them refers to the cogn i t i ve age n t ' s conceptualizat ion of the source an d the target respect i vel y. The same i s t rue when other terms, such as ' vehicle' and ' tenor , ' or ' secondary system ' an d ' pri mary system , ' are used . This, i n my opinion , has been the m ajor hurdle for such theories of metaphor to sat i s factoril y explai n the phenomenon of creat ion of s i m i l ari ty. A s long as the i nteraction i s l i m i ted to the source and the target concept networks, only s i m i l arity- based metaphors can be accounted for , as I show in the next section . One shoul d note here that t he asym met ry of metaphor i s rather obvious
Ch ap t er 7:
255
Metaphor
,,,,,,,,,,,,,,.,,,..,.,,u .-.,,,,,,,,,,, u..... , ,,,,,,,,,,,,,,,,,,,,,u�-.
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,...,.,•,·,·.•,•,·,·,·.·· .......-.. ..
conventional cognitive relation
�
FIGURE 7 . 1 : Nomenclature associated
w
i th Metaphor.
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256
i n my accou n t . The source concept network an d the source realm are two d i fferent structures ; and so are the target concept network and the t arget realm . So, in reversing a metaphor, when the target concept network i s used to describe the source real m , the i nteraction i s between t w o d i fferent structures, and it should not be surprising at all if t he result is d i fferen t . l should also m ake i t explic it here that a metaphorical relat ion c a n b e part i al . I n other words, i t i s n o t necessary t h at a l l o f t h e source concept net work be i nterpreted i n the target realm in order to i nstantiate a metaphorical relation .
7.4
Modes of Metap hor
In C h apters 1 an d 2, I i dent i fied two d i fferent modes of metaphor depend ing on w hether there were s i m i larit ies between t he source and the t arget befo re the metaphor or not . Using the nomenclature i n t roduced i n the previous sec t ion, the s i m i l ar i t ies in question are s i m i lari ties between t he source concept network and the target concept network, si nce s i m i lari ties are properties of concept ualizations. Thus, s i m i l arity- based metaphors become t hose meta phors i n w h i ch there are s i m i larit ies between the source and target concept networks, before the m e taphor i cal rel ation i s formed . In s i m i l ari ty- creati ng metaphor , on t he other han d , t here are no such s i m i larit ies , and only after the metaphorical relation i s formed are t here s i m i l arit ies between the two concept networks. In t h i s section I present an account of t hese two modes of metaphor, and dis ti nguish between them on the basis of the role played by the target concept network in forming the metaphorical relation from t he source con cept network to the target realm . ( See also l n d u rk hya [ 1 99 l b] . ) 7.4 . 1
Similarity-Based ( Comparative) Metaphors
In a s i m i l arity-based metap h o r , t he conventional desc r i p t ion of t h e t arget real m ( t he target concept ne twor k ) is used to mediate the process of proj ect i ng the source concept network onto the t arget real m . For example, consider A ntonioni 's m e t a p ho r of 'emot ional state of G i u liana as blotches of pai n t ' O n ce t h e target re a l m i s i d e n t i fi e d , the possible emot ional states can all be conventionally descri bed . ( A n d , to emphas ize the point once agai n , t he metaphor can be completely m issed if the t arget realm i s not i dentified . ) The source concept network i s made meani n gfu l in this real m by connecting the structural relationships between the blotches of pai n t , described as ' l acking
Chapter
7:
Metaphor
2.57
any regular pattern' or ' h aphazard , ' wit h the convent ional descri ption of a possible emot ional state, descri bed as ' d i st u rbed ' or ' i rrational . ' O r consider a. more mundane exam ple, "The sky i s cry i n g . " H ere, the target realm of possi ble weat her con d i t ions h as convention al descri ptions for each con d i t ion . I n i n stantiat in g the source concept network in t h i s real m , one looks for some con d i t ion that h as a descri ption s i m i l ar t o t h e descri ption of ' crying. ' ' Rai n i ng ' becomes the obvious choice, and so the sou rce concept network i s i nstan t i ated accordi ngly. Of course, once a set of con cepts from the source con cept network h as been i n st an t i ated , add i tional con cepts can b e i n stant i ated in a way th at does not correspond to any t h i ng in the t arget concept network ( w h i ch does not h ave a conventional descri ption ) . l n t h i s example, o n e c a n ' see' the sky i n a s a d moo d , perhaps overwhel med b y some tragedy. T his is certai n l y not a part of any convention al descript ion of some weather con d i tion . I n thi s way, a s i m i l arity-based metaphor can be open ended . The open-endedness of s i m i l arity-based metaphors i s often l i n ked w i t h the mode of analogy I have referred to as ' pred i c t i ve' analogy ( i n ferr i ng further s i m i l arities based on exi sting si m i l arities ) i n Ch apter 1 , a mode t h at is quite troublesome as I show i n Chapter 9 . In order to isolate this open-endedness , I break u p simi lari ty- based metaphors i nto two c l ass e s : syntactic m e taphors and su gg estive m etaph o rs. Syntact ic metaphors are not open-en ded , b u t s ugges t i ve metaphors a re. @f course, t h i s di vision i s som ewhat arti ficial , and very m u ch depends on how much of the source concept network one decides to i n stanti ate in the t arget realm . The same metaphor c an be a syntacti c metaphor for one person and a suggestive metaphor for anot her. Or, a single metaphor coul d be a syntact i c one to the same person at one time and suggest i ve one at another t i me. Nevert heless , it will be useful to m ake t h i s d i s t i n c t i o n for my pu rpose here, so t h at T can re fe r to open-ended metaphors e x p l i c i l l y and no t e thei r ch a. r l\c teristics, before contras t i n g them w i t h p redictive analogy i n Chapter 9 . I now discuss each of t h ese cl asses of s i m i larity- based meta.phors i n d i vi d u a l l y . Syntactic Metaphors
A syntactic metaphor i s characterized by the fact t h at the cog n i t i ve relation from the source concept network to the t arget realm i s com pletely mediated by the t arget concept networ k . Here, the cogn i t i ve agent is usually quite fam i l i ar with the t arget realm . I n terms of its conceptualizat i o n , we m i ght say t h at i t h as a sufficiently rich ( st ructurally speak i n g ) t arget concept network.
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Syntac t i c metaphor works by first creat i n g a correspondence from the source concept network to t he target concept network, and t hen extend i n g t h i s correspondence to the t arget real m via the conventional i n terpretation of t h e target concept network . This p rocess is grap h i cally shown i n Figure 7 . 2 . The nodes of the concept networks represen t the symbol s , and arcs represent the struct ure. Each arc can be t hought of as a one-place operator such t hat , when applied to the symbol at one en d , i t generates t he symbol at i t s other end, and remain s a n identity operator w h e n applied to any other symbol . S i nce a cogni t i ve relation can be m any-to- many, i f one considers all t he objects in t he realm t h a t a symbol of t he concept network i s connected to, we w i l l , i n general , get a. set of objects, w h i ch i s t h e ' group ' of t he real m correspon d i n g to t h e sym bol . I n Figure 7 . 2 , the shaded areas represent s u c h groups i n the t arget real m , and the arcs between t hem represent the autonomous structure of the real m ( as seen by the cogn i t i ve agent ) w i t h respect to the group i ngs.
I n t h e figure, Cr is the convention al i nterpretat ion from the target concept network to the target realm , and the correspondence between the source and the target concept networks i s Csr - The cogni t i ve relation i nstan t i ated by the synt act i c metaphor is Csr o Cr . Using the formal i zation of the previous chapter, i t is easy to see that the cogn i t i ve relation Csr o Cr w i l l be coherent p r o v i ded t h at t he cor res p o n d e n ce Csr pre s e rv e s the stru c t ures of the source and t he target con cept networks. ( Th i s is ass u m i ng , of course, t h at the i nter pretat i on Cr i s coherent . But si nce Cr i s a conventional cogni t i ve relation, i t seems reasonable to assume that i t i s coherent as far as t he cogn i t i ve agent i s aware. To avoid h avin g to state this exp l i c i t ly every t i me, I assume, for t he rest of t h i s chapter, t h at al l convention al i nterpretations are coherent . ) ( Syntact i c metaphors correspond to the strongly coherent T - M A P s i n t he form a l i zation of l n d u r k hya [ 1 986] . )
A n example t a k e n from Gentner & Gentner [ 1 983] i s hel pfu l here i n i l lustrat i ng h o w syn t ac t i c met a phors work . Consider the t heory o f hydrau l i c sys t e m s a s t h e source concept network, a n d the domai n o f electri cal c i r c u i t s as t he t a rget rea l m . The sou rce concept net work contai ns various concepts such as ' p i p e , ' ' p ressure , ' ' narrowness , ' ' viscosity' and ' flow- rate , ' as wel l a s a n operational structur e i n t he form o f laws t h at relate t hese concepts by making it possi ble to derive some concepts from other concepts. For i nstance, a. n operator ' J 0 I N ' generates a ' s i m p le-hydrau lic-system' from a ' pu m p ' and t h ree ' p i pes . ' S i m i larly another operator F l deri ves t he value of the con cept ' flow- rate, ' gi ven the val ue of ' p ressure, ' by multi plying pressure w i t h a constant . A portion of the source concept network is shown i n Figure 7 . 3 .
2.59
Ch ap t er 7: Met aph or
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Part
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Theory
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The target realm consists o f electri c networks of resi stors, wi res an d bat teries , w i t h currents flowing t h rough them . Here, we also h ave a target con cept networ k , which reflects the cogni t i ve agent's k n owledge of elect ricity. It contain s various electrical concepts, such as ' c urrent , ' ' voltage ' and ' battery ' ; a n d t h e l aws , s u ch a s ' O h m 's law ' a n d ' K i rchhoff's l aws . ' A small part o f t h e t arget concept network i s also shown i n Fi gure 7 . 3 . T h e conventional i nterpretat ion between the target concept network and the target realm con nects concepts of the concept network with the approp riate physical objects. C learly the cogni t i ve relation i s coherent, as far as we know, si nce the real m respects the ' laws ' of t he concept network . Now one coul d construct a corresponden ce between the con cepts of the source and the t arget concept network, as shown i n Figure 7 . 3 . T h u s ' p res sure' is assoc i ated w i t h ' voltage , ' 'flow- rate ' is associated w i t h 'curr en t , ' etc . Coherence o f t h i s correspondence can be estab l i shed w i t h ease s i n ce both concept networks are accessible to the cogni t i ve age n t . O nce t h i s correspon dence is i nstant i ated, the hydraulic concept network can be applied to elec trical networks of batteries, w ires, and resi stors coheren t ly-mean i ng in such a way t h at it makes correct pred i ct ions about the beh avior of the electrical networ k. ,
t h i s point i t i s natural to a s k a n i mportant quest ion : W hat possible a . syn t ac t i c met a p h o r h ave , s i n ee o b v i o u l y a. n y p red iction about the target realm that one might derive by usi n g the sou rce con cept network can as well be deri ved by using the target concept network w i t hout doing the extra work of h avin g to construct the coherent correspon dence between the two concept networks? It turns out that t h ere are four d i fferen t ways i n w h i ch a syntact i c met aphor can lend i tself to cog n i tion . At
advantage might
•
Easier C o g n i t i ve Access
to the Target Real m : One use of a
synt a ct i c metaphor i s t h at i f the cog n i t i ve age n t i s m o re fam i l i ar a n d consequent ly more at ease with accessi ng and manipu l at i ng the so ur ce concept network, t hen it wou l d prefer i n t e r a ct i n g w i t h the target real m by u s i n g t h e source concept ne t work as much as possi ble. T h e coher ent correspondence between t he source and target concept networks needs to be constructed only once, and after that the sou rce concept network-or at least a part of i t-becomes useful in i nterac t i n g w i t h the t arget real m .
I must emphasize here that t h i s role o f syntac t i c metaphors does not i nclude p rovi d i n g an increased u n derstan d i ng o f some u n fam i l i a r and poorly u nderstood realm and creat i ve problem solving. These roles of metaphors are explai ned later. I n a . syntac t i c metaphor, the cogn i t i ve
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agent has an adequate u n derstanding of the t arget realm via the t arget concept network ; or, in other words, the metaphor adds not h i ng new , at least as far as understan d i ng about t h e target realm i s concerned. It does , however, bring i n new i n formation , s i nce not i ci n g t h at two concept networks are s i m i lar has cogni t i ve value.
A n example m ight perhaps illustrate t h i s point better. I recall that when I was an u ndergrad uate st udent i n electri cal engi neering, we wou ld often analyze mechan i cal systems by converti n g t hem to t heir electri cal an alogs , solving the equat ions of the resulting circu i t s , and then convert ing the results back to the mechan i cal systems . Now i n doing t h at , we ful ly knew the propert ies o f the mechani cal systems, how to wri te thei r equat ions, how to solve them , etc. I n fac t , i t is t h i s know ledge t h at made us confident t h at we coul d analyze t hem as electri cal systems, and the results wou l d s t i l l be correct . However, we preferred using the electri cal analogs because we were much more used to deal i n g with electri cal quant i t ies than mechani cal quanti t ies. •
Highlight i n g and Downplaying: A syntact i c metaphor ca.n make a part of the t arget real m i nvisi ble. For i nstance, to take an example from B lack [ 1 979] , the metaphor " N i xon is a. halo surroun d i ng a. va.ccum" h ides the si g n i fi cance of wh atever for m e r U . S . pres ident N i xon might h ave ach ieved i n hi s pol i t i cal career. ( See also B lack [ 1 962] , p . 4 1 ; and Lakoff & Johnson ( 1 980] . )
T h i s p henomenon i s explained i n my account as follows. I n formi ng the correspondence between the source and t he t arget concept networks, it i s poss i b le t h at some parts of the t arget concept network are not related to anyt h i n g in the sou rce concept networ k . Consequently, any part of the t a rget real m t h at was related-by t he convent ional i nterpretation Cr-only to those parts of the t a rg e t concept network t h at are not i n c l uded in Csr , w i l l not be v i si ble under the m et aphor i c a l relation Csr o Cr . Thus, the highlighted parts of the target realm are t hose parts of it that are s t i l l visi ble u nder the sou r c e concept network via the metaphorical relation. The downplayed parts are t hose that were v i sible u n der the target concept network but are no longer v i s i ble under the source concept network . I n Figure 7.2, the highlighted portion of the t arget real m is shown with darker l i nes. The example of the hydrau l i c model of elect ricity is again helpful i n elaborat i n g t h i s explanat i o n . N o t e t h at the electrical concept network contai ns the concept-networks corresponding to m agneti c , heati ng, and l i ghting effects of elect ricity w h i ch are not related to anyth i ng in the
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hydrau l i c concept network. ( The part i al depiction of the eleciri cal con cept network shown in Figure 7 . 3 does not contai n all the i n formation pertai n i ng to these effects . ) Therefore, these effects become invisible when the hydrau l ic concept network i s app l i ed metaphorically to the electri cal real m . For example, t h e hydrau l i c concept network can not be used to predict the current t h rough a solenoi d when an alternati n g volt age i s app l ied across i t . Thus, a syntact i c metaphor p rovides a mechan i s m b y which attention can be focussed on a part of the t arget realm . Th is , obviously, m akes i t a double-edged sword t h at can be used to advantage as well a s abused . For i nstance, M i l ler [ 1 9 76] observed: " . . . [ I ] n educat i onal writing meta phors are typically used to gloss ove1· matters w hich cannot be wel l explai ned or clearly speci fied . . . [and] metaphors are often used i n a m i s leadi n g way to play upon the emot ions or carry an argu ment by means of d i stortions and over e m p h as i s . " [ p . l 74 ] . N u m e r o u s m i suses of metaphor can often be foun d in pol i t i cal rhetoric and propaganda. ( See, for instance, Lakoff [ 1 99 1 ] . ) •
A bstract ion : The t h i r d way i n which a syntactic metaphor makes i tself useful is by mak i ng it possible for the cogn i t i ve agent to construct n e w c o n cep t networks t h at a r e abstracted from the source an d target concept networks based on the similar it ies b e t ween t h e m as rep r e s e n te d i n the correspondence Csr - After the correspondence Csr i s formed , the struct u re carried by i t-that i s t he struct u re t h at the source and the t arget concept networks h ave in common and t h at i s the bas i s for Csr can be broken free from both concept networks and gi ven the status of a concept network i t self. I n the example of Figure 7 . 3 t h i s process can be c ar r i e d out by s tar t i n g out w i t h e i t her the sou rce c o n c e p t n e t w o rk or the t arget c once p t networ k , d iscardi n g all t hose concepts of the network t hat are not i ncluded in the corre s p o n d e n ce Csr , and re p l ac i n g e very c o n c e p t t h at is left , with an appropriate abst ract. concep t . The r<'sulting concept network, i n t h i s example, will be a graph theoretic 'network flow ' concept network .
The process of abstracti on i s illustrated graphically i n Figure 7 . 4 . ( lt shoul d b e noted t hat my abstraction corresponds to sch e m a - induction of G i ck & Holyoak [ 1 98 3 ] ) One of the ways i n which abst raci ion plays an i m p or t a n t r o l e in cogni t i on i s by al l ow i n g us to c r e a t e hierarchies of concept networks . It i s t h e process of ab s t r ac t i o n t h at m a ke s mat he matics possi ble. The abst racted concept network might have no con ven t ional interpretation in any realm , and its structure can be studied .
Part II: A
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Ch ap t er 7: Metaphor
265
non- referent i ally. A ny i nsights i n to its struct u re can then be used ref erenti al l y, by proj ecti ng the concept network to any real m i nto which i t seems to fi t ( as i n applying the method of t riangulation to mark a certain locat ion; see also M ac Lane [ 1 986] . ) Thus we see t h at syntact i c metaphors are quite a val u able asset to cogn i t ion . Let us now exami ne thei r l i m i t s . Obviously, s i n ce the metaphorical rel at ion is formed by composing the correspondence CsT between the source and the t arget concept networks with the conventional i n terpretat ion C r between the t arget concept network and the target real m , the m et aphorical rel at ion i s always a r·esl1'iclion [§6. 1 0] of CT . T h i s con d i t i on can be better stated i n terms of the fol lowi n g two ch aracteristics of syn t ac t i c metaphors, w h i ch reveal thei r l i m it ations. 1. A syntacti c metaphor can never i n crease the visi b i l i ty of t h e target realm . To do t h i s woul d require that parts of t h e target realm not represented i n the t arget concept network be related to some concepts of t he source concept network . This wou l d be i m possible to ach ieve w i t h a syntacti c metaphor. Thus, if the cogn i t i ve agent was not aware of the m ag n e t i c an d h e at i n g affect s of c u rr en t s , t h e sy n t ac t i c metaphor of F i g u re 7.3 wo u l d not reve a l t h e m .
2 . A syntactic metaphor can never i n c rease the resol u t i on of t he tar get realm . That i s , if a part of the target real m was gro u ped u nder one concept by t h e con v e n t i o n al i nterpret at i o n from the t a r get concept networ k , then it cannot be broken into two or more con cepts by the metaphorical relation . For instance, t he sy n t act i c m e t a p h o r of Fig u re 7.3 c a n n e ve r i n t ro d u c e a d i s t i n c t i o n bet ween t h e sol ar b at t eri e s and alkal i n e bat t e r i es , or between carbon res i s t ors a n d metal resistors . A for m al
in
proof
of t h i s was p r e s e n ted i n
the prev ious c h a p ter [ Fact
6.12
§6. 10] and here I make an i n t u i t i ve a.r gumenl. S u p pose t h at a syn
tac t i c metaphor does i n c rease the rsol ution of t h e target real m . This woul d mean that t here are at least two objects (o r transformations ) i n the target realm that are related to non - i denti cal sets of symbols ( o r operators ) i n the source concept network b u t to a single s e t of symbols (or operators ) in the t a rget concept network . W i t h o u t any l o ss of ge n erali ty, let us t a k e them to be objects . A s these obj ects a r e r e l ated t o t wo non-i denti cal sets of symbols in the sou rce con cept n e t wo r k , i t i m p l i es t h at t here i s a.t least one symbol t here t h at i s related to one object and not the other. However, s i n ce the metaphori cal relation i s formed
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by composing the correspondence between t he two concept networks w i t h t he conventional i nterpretation of t he t arget system, the symbol in the source concept network must be related to at least one symbol in the target concept network t h at i s related to one object but not the other. S uch a symbol cannot exist in the target concept network because, as the two objects are i nd i s t i nguishable in the target concept networ k , every symbol in t he t arget concept network is either related to both the objects or to neither of t hem . Therefore, our premi se must be false. A syntact i c metaphor results essentially from an i nteraction between the source and the target concept networks. The t arget realm plays a com p letely passi ve role in recei ving t he source concept network. The coherency of metaphorical relation i s guaranteed if the correspondence between the two concept networks is coherent . In other words, a metaphori cal relation i s established between t he source concept network and t h e t arget realm b y ex ami n i n g the structures of the source and the t arget concept networks alone. Because t hese structures are syntac t i c objects from the point of view of the cogn i t i ve agent , I h ave chosen to call such metaphors syntac t i c metaphors . ( Note t hat syntact i c metaphors correspond to s i m ple analogies [§ 1 . 6 . 2] . ) S u ggestive ( O p en-Ended) Metaphors
O nce a metaphorical relation is formed by a syntacti c metaphor, it can be ex tended by i nstan t i ating other related concepts of the source concept network that are i nstant i ated in the target realm . The extension , however, can be car ried out w i t hout the aid of the t arget concept network . When this happens, the syntac ti c m e t ap h o r t u r n s into a s ugges t i ve m et ap ho r The metaphor "The sky is crying" d iscussed above , which heightens the i nte rpre t at i o n of the metaphor to i nclude an aura of t r agedy and sadness attributed t o t he s ky provides a s i m p le example of how a syntactic metap hor can turn i nto a sugges t i ve metaphor. .
,
Thus, t he target concept network plays a parti al role in forming the metaphorical relation ; it provi des an i n i t i al footi n g for the sourct: concept network , based on which further i nteraction between t he source concept net work and the target realm can t ake place. Many suggestive metaphors are also characterized by the fact t h at the cogni t i ve agent i s not very fami l i a r w i t h t he t arget realm . That i s , t h e t arget concept network ( w h i ch i s a convent ional description of the t arget real m ) h as very l i t t le struct u re to i t . ( I n t u i t i vely, ' l ittle structure' means t h at t here are very few l aws relat i ng con-
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cepts to one another: so that i t h as lit t le potent ial to provide predi ctab i l i ty with respect to the target real m . ) A nother typi cal ch aracteristic of many suggest ive metaphors is t h at the target realm is really the 'envi ron ment . ' In other words , t h e cogni t i ve agent , i n i nstant iating new concepts from the source concept network, i nteracts with the external world by carrying out experiments, si n ce the questions about what i s ' possible' i n the target real m cannot always be answered by consult in g the structure of the i ntermediate cogni t i ve l ayers . T h i s process i s graphi cally demonstrated i n Figure 7 . 5 , t hough a n ex ample I d i scuss at length l ater m ay help to u n derstand it better. The cog n i t i ve agent first creates an i n i t i al correspondence between the sou rce and the t arget concept network s , resu lting i n a syntact i c metaphor. Obviously, this correspondence w i l l be sparse si nce the target concept network has l i t t le structure. The correspondence CST i n the figure gi ves rise to the metaphor i cal relation CM Csr o CT from the source concept network to the target real m . T h i s metaphorical relat ion eM w i l l always be a restrict ion of the re lation CT between the target concept network and the t arget real m , as we h ave seen before . However, si nce the source concept network is structurally richer, t here i s a poten t i al for i nducing more struct u re i n t h e target real m based on the i n i t i al relation e M a n d subj ect to mai ntai n i ng coherency. T h u s beg i n s the process of exten d i n g the rel at ion CM . =
I i l l ust rate t h i s p rocess w i t h an example d i scussed i n G i ck and Holyoak [ 1 980] . ( See also Holland et al. [ 1 986] , Sect ion 1 0 . 1 . 1 . ) G i ck and Holyoak studied how an analogy from army maneu vers helped m any subjects (cog n i t i ve agents ) solve the problem of how to use electromagnet i c radiation to destroy a t u mor w i t hout destroying the s urrou nding heal thy t i ssue. The t arge t real m of electromagne t i c rays and t h e i r effect s on t i ss u e was conven tionally u n derstood to some extent . The target concept network gave it a. clearly defined ontology ( terms l i ke 'ray s , ' ' t umor , ' ' heal t hy t i ssue,' etc . ) but i t had very l i t t le structure. I n their experiment t h ey presented t h e subjects w i t h a source concept network of army m a n e u vers t h at can be used to cap t ure a.n enemy fort ress . T h i s source concept network was ri cher-com pared to the t arget concept network-i n t h at i t had several operators, l i ke divide the army into several smaller u n i t s , look for an unguarded approach to the fort ress , etc. ( Actually G ick and Holyoak div ided the subj ects into groups and each group was presented with a story highl ighti n g one of the operators of the source concept network . On be i n g presented w i t h the target real m , the subj ects, as woul d be expected , tried to apply the operator from the source concept network to the t arget real m . ) On encounter i n g the problem, the subjects had little t rouble i n making an i n i t i al correspondence between the
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source and the target concept networks. The fort ress was iden t i fied w i t h the tumor, electromagnet i c rays were identi fied w i t h the army, heal thy tissues were i dentified w i t h the m i nes lying aro u n d the fortress , and so on . oti ce that there i s some stru c t u re i n the t arget concept network that i s preserved by thi s i n i t i al correspondence. I n iden t i fying heal thy t i ssues w i t h m i nes , one i s preservi ng the fact that a contact between heal thy t i ssues and radiation is d isastrous , and to be avoided . The fact that the m i nes are a nuisance, and t h at their eli m i n ation m akes the goal of occupying the fortress i s easier to achieve, i s i n coherent w i t h the structu re of the target concept network , w h i ch requi res that the heal t hy t i ssue be preserved . It is for t h i s reason t h at an operator i n the source concept network th at works by exploding all the m i nes , and then sen d i n g the army, is not even con si dered for testi n g operat ionally in the t arget real m . H owever, t h e other operators t h at are not i n coherent w i t h t h e i n i t i al m apping form a r i ch source of heuri s t i cs i n suggest i n g new operators i n the target real m . These operators, of course, must be operat ionally tested to determine their coherency. The fact t h at a part of t h e source concept network i s analogous to t he target concept network , and thereby appl icable to the target realm , does not i mply that the rest of the source concept network can also be app li ed to the t arget realm w i t hout further i n vestigation . M uch of t h e a b u s e of metap hors and analogies origi nates from peo p l e e x p l o i t i n g t h e i l l u so r y plaus i b i l i t y of this fa.u l ty reaso n i ng-pol i t i cal rheto r i c bei n g a r i ch sou rce of exam p les . ( See Chapter 9 . ) Often , some fine tuning i s n ecessary to make the operator workable i n t h e target real m . For example, i n G i c k and H o l yoak ' s e x p e r i m e n t s , some subjects t ried to apply the operator i l l u m i n ated by a scenario in w h i c h the general discovers an u n g u ar d ed and u n m i ned road to the fort ress a n d d e c i des to sen d the entire army along i t . Because t h e r e was not h i ng correspon d i n g to ' an unguarded and un m ined road to t h e for t ress ' i n the target concept network t hey had to m ake up somet h i ng for i t before the operator can be appl i e d . This was
not merely a m atter of com i ng
up
with
a
concept in t h e
ta rge t concept networ k ; the concept had to correspond t o s o m et h i n g in t h e target realm . Moreover, because ' m i nes' and ' fortress ' were al ready made to correspond to ' healt hy tissues ' and ' t u mo r , ' respecti vely, of the target concept network , and to the chunks of ta rge t real m via the conventional i nterpretation , any part of the target real m t h at was made to correspond to ' an u ngu arded an d u n m i ned road to t h e fort res s ' ( vi a some concept i n the t arget concept network ) had to be ' a path to the t u mor, free from i n te rven i n g healthy t issues and along w h i ch electromagnet i c rays can t ravel . ' Some of
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the subj ects, i n fac t, came u p w i t h the i dea of a ray-proof flex i ble tube that coul d be i n serted i n the body of the i l l pat ient u n t i l making contact w i t h the t u mor. Elect romagnetic rays cou l d then be sent along it. This process of fine t u n i ng obviously req u i res i ngenuity and origi nali ty. Several researchers have noted the characteristics of suggestive metaphors and the i m portant role p layed by t hem in cogni t ion . For i nstance, in Gordon 's em p i r ical research on creati ve problem sol v i ng, some of the examples of what he characterized as m aking the strange fam ilia r [Gordon , 1 96 1 , p . 35] are i nstan ces of s ugges t i ve metaphor. ( The use of the horse's anal sphi ncter analogy i n solvi ng the d i s penser problem mentioned in Chapter 2 [§2. 5 . 1 ] i s a case i n point . ) As the name suggest s , i n ' maki n g thel fami l i ar stran e' one tries to u n derstand an u n fam i l i ar problem or sit uation by apply i n g some fam i l i a r conceptu al system . T h i s conceptual system gi ves an ontology to the u n fam i l i ar s i t u at ion that al lows the structure of the system to be t ransported to the p roblem by suggesting possible solutions. These suggestions must , of course, bP operat ionally tested to see if t hey really wor k . Sugges t i ve metaphors are also evi denced i n H esse's account of m aterial ' models as an i ndi s pensable aid i n the growt h of science. [Hesse 1 966, 1 974, 1 980.] M aterial models can often be seen at work beh i n d scientific t heories when they are at an exploratory stage . O ften the subj ect of the scientific t heory, the target real m , i s not well u n derstood, and scanty knowledge of i t m i ght suggest an i ni t i al correspondence with some other theory or well u n derstood phenomenon . Based on this correspondence, further hypotheses can be m ade abou t the target real m . Attemp t i n g to operationally verify these hypotheses resu lts in an i n creased k nowledge of the t arget realm , w h i ch i s reflected i n a larger and more comprehensive t arget concept network . I t i s i n t h i s sense that material models can be said to determine t h e direction of growth of our knowledge by affect i n g the questions t h at are posed about the target real m . F i n al ly, I shou l d emphasize once again that the mechani s m u n derlyi ng sugges t i ve metaphors should not be confused w i t h predi c t i ve analogy. I n pred i c t i ve analogy, t h e exi st i ng s i m i lar i t ies between the source a n d the tar get concept networks are seen as somehow justifying t h at t here m ight be other s i m i lar i ties as well . Th i s , in t u rn , suggests that in trying to solve some problem about a real m , one's best bet m ay be to fi n d a concept network t hat i s most s i m i lar to whatever i s known about the t arget realm , and use t h at concept network to form hypot heses about how the problem m i ght be addressed . S uggestive metaphors , on t he other hand , carry no such j ustifi cation . The fact t h at certai n parts of the source concept network h ave been
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successfu l l y i nterpreted i n t he target realm , says nothing what soever about w hether other parts of the concept network m ight also be so i n terpreted . I n part i cu l ar, i t does not carry even a h i nt o f t h e suggestion that a concept network that is very s i m i l ar to the target concept network is l i kely to lead to the solution of whatever problem one might be facing w i t h the target realm .
7.4.2
S imilarity- C reat ing ( P roj ect ive ) Metap hors
I presented several examples of s i m i lari ty-creat in g metaphors in Chapter 2. T hey all had the characteristic of having no s i m i l arit ies between the source and the t arget concept networks prior to the metaphor. O n ly after the metaphor was u nderstoo d , if it was understood at al l , were there s i m i lar i ties between the two concept networks . I refer to such metaphor , wh ich are k nown to be the hal l m ark of a truly creat i ve gen i u s , as p mjective m e tapho1·s. ( The term ' proj ect i ve' i s act ually borrowed from S chon [ 1 963] , but also fits naturally w i t h the sense in which l have been using the term 'projection ' i n m y framework of cogn i t i on . ) P rojective metaphors work by completely d is regard i n g the structuri ng of the target realm u nder the target concept networ k , an d project ing the source concept network on it anew , as i f t h e target real m w e r e bei ng encou ntered for t h e first t i m e . In t h e proces s , the s t ru c t u re of the s o m c e concept net work is kept more or less i n var i ant , but the ontology of the t arget realm is varied so that i t s structure , as seen from the concept network l ayer , is i so morphi c ( as far it can be) to the structure of the source concept networ k . Whatever part of the source concept network h as been i n stant i ated i n t h i s fashion i s n o w consi dered the n e w description o f t he target real m . There fore, it foll ows nat ural ly t h at the new descr i p tion of t h e target real m w i l l be s i m i lar to t h e source concep t net work . T h u s , though there m i g h t be n o similar i t i es between the old target concept network and t h e s ou r c e network, t here will always be similarities between the source concept network and the new description of the target real m ( which w i l l be a s u bnetwork of the source concept network ) . The only t i me this cannot happen i s when the proj ection attempt fai l s , causing the metaphor to be d u bbed mean ingless or anomalou s . Creation of s i m i lari ties by a proj e c t i ve m e t a p h or i n this fashion i s shown grap h i cally i n Figures 7.6(a) and 7 . 6 ( b ) . Let u s now consi der a few exam ples an d an alyze how t h e si m i l arit ies are created in t h e m . First let us focus on those proj ect i ve metaphors t h a t req u i re an i n teraction w i t h the envi ronment-that i s , t he t a r ge t real m i s actually t he t arget environment . S u ch metaphors can be fou n d i n the h istory o f science
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SOURCE REALM
CONCEPT NETWORK
conventional cognitive relations
TARGET CONCEPT NETWORK
TARGET REALM
FIGURE 7 . 6 (a) : Projective (similarity-creating) metaphor: Before. The source and the target concept networks group their respective realms quite differently. There are no existing similarities between the two concept networks
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conventional cognitive relation
SOURCE REALM
TARGET REALM REGROUPED BY THE SOURCE CONCEPT NE1WORK
FIGURE 7 . 6 (b): Projective (similarity-creating) metaphor: After. The stucture of the target realm is regrouped so as to reflect the structure of the source concept network. Now there are similarities between the source and the target (as seen through the new groupings . )
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and creat i ve problem sol ving. ( They can also be foun d i n perceptual domai n s , s u c h a s the domai n of geometric figures discussed i n Chapter 2 [§2 . 4 . 2] . See l n d u rkhya [ 1 99 1 a] for an explanat ion of the creation of s i m ilarity using t he example of t h e figure of the S t ar of David i n t h i s domai n . ) To start w i t h , cons ider S chon 's example o f ' pai ntbrush a s a pump' metaphor t hat was i n troduced i n Chapter 2 [§2.5 .2] . You m i g h t recall that a product-development team came u p w i t h t h i s metaphor in trying to develop an i m p roved syntheti c fi ber pai n t brush . It was already emphasi zed i n C h apter 2 t h at the metaphor did not result from not i ci ng some existing s i m i l ari t ies between pai n t i n g and pumping. Moreover, t he metaphor gave a totally d i fferent ontology to the process of pai n t i n g , and the role of a paintbrush in the p rocess was rad ical l y t ransformed. I t i s n o t that the source concept network of ' p u m p ' a n d ' pump i n g ' was m apped onto the i n i t i al target concept network of 'pai ntbru s h ' and ' pai nting,' but rather the chunks of the t arget environment were regrouped and renamed , thereby acquiring a new ontology in t he process of projectio n. T h i s p oi nt w a s very aptly em p h asized b y S chon [ 1 979, p p . 259-60] . This new ontology of t he target envi ronment was by no means a mere extension of the i n i t i al target concept network , as was the case w i t h Holyoak and G i ck 's rad i ation problem . Let me eluci date how projection might h ave worked i n t h i s example by consi dering the h u man vi s u al system as a l ayered cogn i ti ve system . Let us say t h at a cogni t i ve agent views some sit uation and a corresponding i m age is formed on its ret i na. The research on the human v isual system i n t h i s cen t u ry h as conclusively demonstrated t h at the situation as ' seen ' by the cogni t i ve agent at a h igher percept ual level i s not s i m p ly deri ved from the ret i n al i m age by p rogressive refinemen t , but rather that the reti n al i m age i s i ntegrated i nto some concept at a h igher level . I n other words, the operati o n of lower- level perceptual apparatus is not epistemi cally neutral , but is heav i ly b i ased by t he organ i zation of the higher l ayers. Of course, some of t h i s organization is hard- w i red . I n the visual system , for instance, the reti nal cells are so connected w i t h the next perceptual l ayer that the eye i s actually looki ng for contrast , straight edges, corners , l i nes w i t h fixed orientation , and so o n . The hard- w i red n at u re of t h i s organi zation is revealed in n umerous paradoxes of v ision . ( See Th e Min d 's Eye, readings from Scientific A m e rica n , W . I-I . Freeman & C o . ( 1 986 ) , New York, N Y , for a very read able collection of art i cles on the human visual system . ) However, not all the organization i s hard-w i red-at least not i n humans and this fact i s the key to metaphor. This makes proj ect i ve metaphor possib le and also accounts for i t s usefu l ness i n cogni tion , especially in creati n g new perspective. To see t h i s le t us el aborate o u r example a l i ttle more. S ay
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t h at a cog n i t i ve agent i s pai n t i ng a wall by us i n g a pai n t brush , or w at c h i n g someone else do i t . A pattern of im ages i s formed i n the cogn i t i ve agent 's eye as t he paintbrush i s d i pped i nto pai n t , gi ven a few shakes to shed the excess pai nt off, and then moved i n u n i form , broad st rokes across the wal l . If the cogni t i ve agent believes t h at the paintbrush work s by smeari ng pai nt on the wal l , then this pattern of i m ages i s d i v i ded into groups accord i ngly and a causal structure i mposed upon it (or ' seen ' in i t ) . O n being presented the ' paintbrush as a pump' metaphor, the cogni t i ve agent regroups the pattern of i m ages-w h i ch i t h as to, in order to m ake sense of the metaphor. The mai n t h i n g to note here i s that the pattern of i m ages on the cogn i t i ve agent ' s eye h as not changed. The process of pai nting has not changed . I t is the cogn i t i ve agent 's perception of i t t h at h as ch anged , and changed consi derably. I f we keep i n m i n d t h at percept ion is not epi stemi cal ly neutral then we can say t h at t he p rocess of pai nting, as seen by the cogn i t i ve agen t , bas ch anged as a result of the metaphor. It is in t h i s sense t h at it can be sai d that the metaphor c1·eated a new perspect i ve. Several other instances of proj ect i ve metaphor are noted by K u h n in the h istory of science. Though most of the time science proceeds in a . widen i n g s p i ral , w i t h n e w hypotheses consistent with the cu rrent theory con stantly bei ng expl ored-a process in w h i ch s ugge sti ve metaphor p l ays a. crucial role. However, t here are occasions when a totall y new t heo r y , w i t h a r a d i c a l l y d i fferent ontology, i s called for; an extension of the e x i s t i n g t h eo ry j ust w i l l n o t do. K u h n mentioned a t least t hree s u c h occasion s : ( 1 ) the r e p l ace m e n t o f Ptolemaic astronomy w i t h Coperni cus ' ast ronomy, ( 2 ) t h e replacement of t h e p hlo gi s t o n t h eo ry o f che m i s t ry w i t h Lavoisier's oxygen theory o f combust i on , and (3) t h e replacement o f Newton i an mechan ics w i t h E i n stei n 's t h eory of re l a t i v i t y. ( S ee Kuhn [1 962] , C h . V I I ; an d also I\ u b n [ 1 9 5 7] . ) On al l t hese o c c asio n s , a scientific revol u t i on took p l ace; the scien t i fi c com m u n i ty t h rew away the existing parad igm in favor of a new and rad i cally d i fferen t one. ( O f course, t h i s p rocess is not as abru pt and sudden as this statement i m plies. There i s i n var i a b l y a period o f adj u s t m e n t when var i o u s a t t e m p t s a r e made to stretch the existing paradi gm to ass i m i l ate the anomalous d ata, and t h e new p aradigm i s subjected to a harsh criticism and stringent tests. See K u h n [ 1 962] for a d et ail e d d i scussion of the process of adj u s t m e n t to t h e new paradigm . ) I n fac t , a truly creati ve o r revolutionary m e t a ph o r almost i n variably works by d isregarding t he e xi s t i n g ontology of the target en v i ro n m e n t as s ee n from t he target concept network. Projecti ve metaphors are often necessar y be cause t he structure o f the t arget e n v i ronme n t , as seen t h rough t h e target concept networ k , reflect s the earlier goal s and p r efe r e n c e s of t he c o gn i t i v e
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agent , and i t m ight not be possible to extend i t i n any way to explai n some unusual phenomenon or to solve a d i fferent type of probl em . Kuhn's scien tific revolut ions, Schon's ( 1 963] generati ve metaphors , and Gordon 's ( 1 96 1 ] ' m aking the fam i l i ar strange' are prime examples. H ow does a proj ecti ve metaphor create a new perspecti ve? Obviously, proj ecting d ifferent source concept networks leads to different organizations of the target env i ron ment , w h i ch might or m ight not be useful for sol v i n g a cert ain problem . For exam ple, i n the pai ntbru s h example discussed above, S chon rem arked t h at the researchers also cons i dered the ' pai n t i ng as masking a su rface' metaphor but i t d i d not res u l t in any usefu l i n sight . What then makes a. source concept network more successfu l than others? For an answer, we must look at the envi ronment in whi ch the source concept network has a conventional i nterpretation; t hat i s , the source envi ronment . I t i s the only thing that can provi de a l i n k between the source concept network and the target environment (given that we do not wish to use the target concept network as a. possi ble l i nk ) . R eali ty, the I<: ant i an t h i ngs- i n - t hemselves , i s richly connected . We m ight even say that i t i s totally connected : gi ven any two objects, one can always find some way of relat i n g them to each ot her , and find somet hi ng t h at they have i n c om m o n I t is only o u r percep t u al and cogni t i ve apparatus t h at groups the ' real- worl d ' into chunks and i mposes the struct ure of our cogn i t i ve concept networks on t hem . However , i n carving up t wo env i ronments i n t h i s fashion-t hat i s , i n i mposi ng a concept ual struct ure o n each o f t hem t h i s connec t i v i ty is lost . The envi ron ments , viewed t h rough t hei r respec t i ve concept networks, are no longer seen as s i m i lar. However, i n projec t i n g the source concept network , which mi ght h ave origi n ated t h rough an i nteraction w i t h t h e sou rce en v i ronment , onto the target envi ronment , t h i s connec ti vity i s parti al ly recovered , as the cogn i t i ve agent i s forced to regroup the ontology of the target envi ron ment to create one that is i somorph i c to the source concept networ k . T h i s is what Schon may have had in m i n d when he wrote in con nection w i t h t he ' pai ntbrush a.s a . p um p metaphor: .
'
" It i s i m portant to note t h at the researchers were able to see pai nting as s i m i l ar to pumping before they were able to s ay 'sim i l ar w i t h respect to what . ' At first , t hey had only an unarticu l ated percept ion of s i m i l ar i ty which t hey coul d express by doing the painting and inviting ot hers to see i t as t hey did, or by u s i ng the terms l i ke 'squeezing' or ' forcing' to convey t he p u mpl i ke quality of t he action . O n ly later, and i n an effort to account for their earlier percept ion of s i m i l ari ty, d i d t hey develop a.n exp licit
Ch ap t er 7: Metaphor
277
account of s i m i l ar i ty, an account w h i ch l ater s t i l l became part of a general t heory of ' pumpoi d s , ' accord i ng to w h i ch t hey cou l d re gard paint brushes and pumps, along w i t h wash-cloths and mops, as ins tan ces of a. s i ngle technologi cal category. " [ 1 979, p. 260] I n other words, t here are potent ial s i m i lar i t i es between the process of pai n t i ng and the action of a pum p-potential s i m i l ar i t i es t h at are d iscarded i n group ing the process of pai n t i n g as a smear i n g p ro cess . And i t i s t hese potent i al s i m i l ar i t i es t h at are made real by the metaphor ' pai ntbrush as a p u m p . ' T h i s account of proj ecti ve metaphor also explai n s why i t i s such an i n valuable asset to cogni t i o n . Cogn i t ion typically i n vol ves grou ping. Various objects and transformat ions, i n t h e worl d t hat i s m ad e avai lable to us by our percept ual and motor apparat u s , a re further grouped i nto categories and operations. Thus, t he world as seen from the cogn i t i ve l ayers i s con si derably more s i m p lified and struct u red than the one seen from the lower perceptual l ayers. T h i s s i m p l i fi cat ion i s necessary to make us s urvive i n an i n fi n i tely complex worl d of t h i ngs- i n - t hemsel ves with our fin i te and l i m i ted m i n d s . However, an a c t of grouping i nvar i ably i nvol ves loss of i n formation . ( See also Hesse [ 1 9 74 ] , p. 48-5 1 , for argu men ts lead i ng to the con cl usion t h at any clas sification necessar il y results in a. loss of verba.l i zable e m p i ri cal i n formation . ) When a b u n c h of o b j e c t s are p l aced i n a. category, t h ei r pot e n t i al d i fferences are o ve r l o o k ed ; one m i gh t say t h a t t h ey are d i scarded by the p rocess of cog n i tion . S i m i l arly, i n pu t t i ng two o b j ects in d i fferent categories t h e i r potential common grou n d s are di scarded as wel l . I n grou p i ng t h e worl d i n one way t h o u g h the res u l t i n g s i m p l i fied wor l d v i e w m a k es i t easier for the cogn i t i ve agent to interact w i t h t h e w orld - t he c ogn i t i ve agent i s d e p ri ved of a horde of alternate world v i e w s . I f t he cogni t i ve relations between al l layers were predetermi ned for each c o gn i t i v e agent-whether b i o l ogically or c u l t u ra l ly - t h e n the lost worlds wou l d b e lost foreve r . The parts of the world t h at are i n d i s t i nguisha b l e i n the co g n i t i ve model woul d rem ai n i n d i s t i n g u i s h ab l e permanen tly. T h e co g n i t i ve age n t coul d n ever recover t h e i n for ma t io n lost i n cog n i t ion and reorgan i ze i t s worl d views.
However, i f t h e c o g n i t i ve age n t can p r o j e ct d i ffe r e n t c o n c e p t n e t wo r k s s am e en v i ro n me n t , it can partially recover t hese lost worl d s . S o me of the poten t i al d i s t i n c t i o n s between d i ffe r e n t part s of the e n v i ro n m e n t t h a t are d i s carded in g ro u p i n g it c o n ve n t i o n a l l y can be m ade v i s i b le u n der t h e u n c o n ventional grouping i n d u ced by anot her c o n c e pt n e t wor k . T h u s , a . p ro j ec t i ve metaphor allows t h e cogn i t i ve age n t to p a r t i a l l y rec l a i m t h e lost i n fo r m a t i o n that i nevitably res u l t s from cogn i t ion .
on to t he
278
Pa.r i
II: A
Theory
A s i mi l ar explanat ion can be given to t hose s i m i l ari ty- creati ng metaphors that do not requ i re a di rect i nteraction w i t h t he environ ment-as in Bolan d ' s ' w i l d flowers a s water' a n d Spender's 'ocean a s a harp' metaphors. T h e t arget is reall y a target realm here, which is an i m agined t arget environment in the i ntermedi ate cogn i t i ve l ayers. ( That i s , i f the cogni t i ve agent were experienc ing the stimuli th at are being described in the poem , t hen i t m i ght result i n the i m agi ned structure i n the i n termediate cogni t i ve l ayers . ) Moreover, this i m agi ned scenario i s based on the cogni t i ve agent ' s past experiences, w h i ch endow i t w i t h a struct ure t h at i s i ndependent of how i t might be described . I t i s t h i s autonomous structure that constrai n s w h i ch source concept networks can be i nstant i ated in t he t arget realm , and how t hey can be be i nstan t i ated , t hereby ruling out arbit rary metaphors . I h ave already emphasized all t hese poi nts in Section 2 . In understan d i n g Boland's poem , the target realm of ' w i l d flowers grow ing in a h i l ly countryside' i s gi ven a new ontology by i nstantiating the source concept network of ' bodies of water ( lakes , waterfalls , etc . ) and related con cept s . ' Notice t hat while the t arget realm has a conventional description , the conventional descript ion is not equ i valent to the metaphorical descrip tion. I n i nstant i at i n g concept s l i ke ' water rushing dow n hi l l ' and ' fl u idity, ' t he i m agined target real m becomes ali ve i n a way that it cannot under any convent ional description. As hawthorns start bloom i ng, one can i m agine the effect as that of flowi ng water. It i s as if one took a fi l m of the h i l l y coun tryside over a period of several days (or even weeks ) , and were now viewing the film very fas t . Of course, the detai l s of i m agery are quite subjecti ve, and d i fferent people m ay experience t he metaphor i n different ways. But my point i s t h at t he ontology of the i m agi ned experience i s quite different from wha.t it woul d be i n a . conventional descri ption . ( Ot herwise, one should be able to see simi l arit ies between w i ld flowers and water before hav i ng read t he poem . ) A fter t he poem i s understoo d , the structure of the target realm w i t h to t h i s n e w ontology i s b o u n d t o be si m i lar t o the source concept networ k , as t he ontology is created by i nstant i at i ng t he source concept net wor k . This is exactly how the similarit ies are created between wild flowers and water i n the cogni t i ve agent 's m i n d . res p ect
T h e same explanation c a n be put forward for Mondrian 's i nterpretation of his pai n t i ngs as the dynam i c oppos i t ion between good and evil . Mon d r i an 's i nterpretation , for i nstance, gives a completely new ontology to t he moral opposit ion of good and evi l . Evil is no longer something that must be destroyed . R ather, it becomes an essential i ngredient of life and order
Cl1apter
7:
279
Metaphor
in t he wor l d. Un less the d y namic op p osition of good and evil is seen from t h i s new o n t ology, Mondrian's i n terpretation would not be meaningful, even after the target rea l m i s expl icit l y pointed out. And it is creat i n g t h i s new ontology that t he met aphor c reates t h e similarities between t he pai n ting and t he m oral opposi tion of good and ev i l. Where do the c reated s i m ilarities come from? As wit h t h e ' p aintbrush as a p u m p' met aphor, we again look at the source real m. In reading Bol a n d ' s p oem, t h e metap hor evokes t he im age of water rushing downhill , s pl ashin g , creati n g p u d d les, and so on. realm.
( In
This i m age i s seen as similar to the t arget
fact, t h i s is why t h e source concept can be instantiated as it is.)
However, t hese s i m i l arities are not present in the convention a l descriptions of ' water r u s h i n g dow n h ill' and 'wi ld flowers growing on a hill.' If one tried to u nders t a n d the met aphor by p rocessing the con cept networks al one, the metap h o r would be c o n s i dered anomalous. But once the realms are evoked, the p oten t i al simi lari ties are partial l y recovered. Moreover, these simil arities can now (after t h e met aphor is unders tood) be seen from the concept n et work l ayer, s i nce the t arget rea l m h as been gi ven a new onto l ogy and a new s t r u c t u re by the met aphor. Of cour se, one can counter here by say i ng that it all depends on what one takes t o be the conventional descript i o n of 'w i l d flowers grow i n g o n
a
hill' (the t arget rea l m ). It is certai n ly p ossi b l e to include the relevant i nfor mat i o n so that the met aphor can be u n derstood fro m
a.
c o mpari s on of t he
s o ur ce and the t arget concept networ k s , t hereby t u rning it into a similarity based metaphor. l do not deny t his at all. In f a c t , every similarity-c reating
metaphor, afler it is understood and the new ontology for the t arget rea l m h a s been seen, can b e p resented a s a similarity-based met aphor. But then, for any giv en conventional description of the target rt>a.Jm, no matter how det ai led, t here are a l w ay s ot her metaphors that cannot be analyzed on the basis of that description. I h ave already
em p h asized
this point in connection
with proportionaJ analogies i nvo l v ing geo m etric figures will alw ays be similarity-creating metaphors as long as
[§2.4.2]. some
Thus, there
i n for m ation 1s
lost in concep t u alization .
7.5
Summary
In this c h apt e r , I b egan by argu i ng t h at the process underlying metaphors is essentially t h a t of projection. This argument res t s on t h ree separate points. T he first is t h at t h e 'source' of a metaphor i s a syste m of symbols (for ex ample, the text) t h at has its autonomous struct ure (the words i n the text
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a re arranged i n a certain order , and the words are related to other words in certai n ways, as i n d i c t ionary mean i n gs . ) Using the ter m i nology of my framework of cogn i t ion, t h i s is referred to as the ' source concept network ' The second poi nt i s t hat the domai n of i nterpretat ion ( t he ' t arget ' ) ei t her is some object in the external worl d t h at has been converted i nto an autonomously st ructured sensori motor data set by our sensory apparatu s , or i s an i m agi ned experience of the object that is more detai led than a concept network , and has an autonomous structure that reflects the cogn i t i ve agent 's prior percept ual experien ces w i t h the object . Thi s i s referred to as the ' t arget realm . ' T h e t h i rd poi nt i s that the structure of the source concept network i s not altered in i nterpret i n g a metaphor, but the concept s are given a new i nterpre tat i on , t hereby giving a new ontology to the target realm . The autonomous structure of the target real m endows t h i s new ontology w i t h a new struc t u re. Thus, a metaphor becomes an i nstance of an u nconventional cog n i t i ve relation formed by proj ect i on . A m ai n novelty o f t h i s account i s the i n t roduction o f a d i s t i n ction between an object or an experience ( whether act ual or i magi ned ) and i t s represen tat ion. Mak i n g t h i s d i st i n ction has been crucial to the accoun t ' s abi l i ty to resol ve the paradox of creation of s i m i l ar i t y . I t hen argued that there are t h ree d ifferent modes of metap hor, each w i t h its own set of ch aracteristics that make it useful to cogni t ion in certai n ways but not i n others. These modes must be d i s t i nguished to make sense of the d i fferent characteri s t i cs of met aphor, and t he many d iverse roles i t plays i n cogn i t ion . The modes are d i s t i nguished o n t h e basis of t h e degree of part i c i pation of the t arget concept network ( a convent ional representat ion of the t arget real m ) and the sou rce realm ( t he object or experience, real or i magi ned, that i s conventionally represented in the source concept networ k ) i n the process of i n stant i at i ng t h e metap h o r i c a l relation.
Syntact i c and sugges t i ve metaphors fal l u n d e r what I h ave been call i n g s i m i lari ty- based metaphors. I n syntac t i c metaphors , the process of i n terpre tat ion i s completely medi ated by the target concept networ k . Even t hough syntac t i c metaphors do not provide any new i n formation about t he target realm ( i n formation t hat is not al ready present in t he target concept network ) , t hey are, nonetheless, useful to cogn i tion i s several ways. For i nstance, t hey can prov i de an easier access to the t arget realm , if t he cognit i ve agent finds i t easier to manipulate the source concept network. Or, t hey can be used to d raw attention to cert ai n parts of t he t arget realm by highlighting t hem. In sugges t i ve ( open-ended ) metaphors
the
tar get concept network is used
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281
only to provide an i n i ti al ontology for the target real m , on w h i ch t h e i n i tial i nterpret at ion of t he source concept network i s anchored . A fter the i n i t ial i nterpretat i o n , however , add i t i onal st ruct ure can be i m ported from the source concept network to enhance the structure of the target realm ( e nhan ced from what is already there i n the target concept network), as long as the i mported structure is coherent w i t h the autonomous stru c t u re of the t arget real m . A s sugges t i ve metaphors come close t o what I have termed as ' pred i c t i ve analogy ' ( t he process of i nferri ng further s i m i lari t i es between two objects or s i t uations given some exist i n g s i m i l ari t ies ) i n C h apter 1, great care must be taken to d i s t i nguish the two. I n sugges t i ve metaphor, t here i s no 'j usti ficat ion' at tached , so t h at the fact t h at certai n parts of the sou rce concept network h ave been successfu l l y i n terpreted in the target real m does not in any way j ust ify t hat other parts can be i nterpreted as wel l . Pred i c t i ve a nalogy, on the other hand, carries preci sely s u ch a. j us t i fication . (I d i scuss pred i c t i ve analogy i n Chapter 9 . ) I n projecti ve ( s i m i l ari ty-creat i ng) metaphors, t h e target concept network is competely d iscarded , and the source concept network i s i nterp reted i n t h e t arget realm, a.s i f t h e target realm i s bei n g encoun tered for the first t i me . Here, it is the source real m that ends u p playi n g a. role by deter mining (indirectly) the result of projecting the source concept network onto the t ar get realm. It is the potential similarities between the source and the target realms-poten t i al s i m i l ari t i es that were d i scarded i n the convent i onal conceptual ization-t hat are d i scovered in t he process of p roject ion . O f these t h ree modes, project i ve metaphors might wel l be con si dered the of metaphors . W h i le syntac t i c metap hors and suggest i ve metaphors also i n volve some original i ty in mak i ng corresponden ces between the source and the target concept networks, an d in i mport i n g structure from the source concept networks; i t is p r oj e ct i v e metaphors that require the ability to break ' the shackles of one s l anguage and c u l t ur e , and to be able to u n group and regroup the sensorimotor data set int o different meaningful patterns. If the primary role of cognition i s to braid the k a l e i d o s c op i c Aux of impressions we get from our senses i nto a mean i ngfu l pattern , i t i s project i ve metaphors that make it possible for different patterns to be woven i nto the braid, thereby c reat i n g d i fferent modes of reali ty. pneuma
Part III
The Implications
Chapter 8 Some Metaphor-Related Issues
8 .1
Int roduct ion
Now t h at I have art iculated my account of metaphor, and have ad d ressed the phenomenon of creation of s i m i l arity w it h in it, it woul d be useful to exam i ne what consequences it has for some ot her issues rela. t ed to metap hor. For instance , t here is the thesis "All knowledge is metaphorical," which is as vehemently supported by some scholars as it is opposed by others. Since I have characterized the metaphorical in co n t r ast wi t h the conventional, i t m i g h t seem that my account o f metaphor i m p l i citly rej ects t h i s thes i s . On the contrary, I show in Section 2 that proponents of t h i s thesis do not use the term ' metaphor' in the same sense as I have been using it; an d with their sense of me taph or my account comes ou t strongly favoring t h e thesis. I also show i n t h i s section how usi n g the term metap h o r i n d i fferent senses h as created a needless debate over l i teral- metaphori cal d ichotomy. ,
So f ar I have characteri zed met ap h or as a. meaningful i n terpretat ion How ever, this is a rather broad characterization, Often, one w i s h es to apply the strict e r criteria of C01'1'ectness (or truth) and 11ptness. For instance, consider the met ap h or "Nixon is a halo surrounding the vacuum'' An admirer of t h e former Uni ted St ate s p re si dent Richard Nixon might consider this statement quite incorrect (or false) even though she clearly understands the metaphor (since otherwise, she woul d not be able to declare it incorrect). How is t h e understanding (meaningfulness) to be d i s t i ngu ish e d from correctness? Then there is also the problem of distinguishing between literal and m e t a ph o ri c a l correctness, for a very literal-minded c ritic of Nixon might also declare the above statement false, but obviously for a d iffe r e nt reason. These i ss u es are discussed i n Section 3. .
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Part III: The Implications
F i nally, there is the quality of met ap hor . Some met aphors seem more com pell i n g t h an others. For i nstance, Q u i n n [ 1 986, Chap . 3] recounts how d isgruntled the attendants at a wed d i ng were , when t he sermon compared marriage to an i ce cream cone: you can eat it up all at once, or make i t l ast a long t i me. One can certai nly make some sort of coherent interpretation of m arriage as an i ce cream cone (you can eat i t u p all at once, or make it last a long t i me), so the metaphor can be dubbed meani ngfu l , and even correct. Yet i t wou l d be consi dered not very compel l i ng and of poor quality by most people. What m akes a metaphor better than another? I d iscuss t h i s i ssue i n Section 4. .
8.2
The Thesis 'All Knowledge Is Metaphorical'
A certai n thesis, w h i ch I refer to as t he stmng th esis of m e tapho r, i s often ad vanced , accordi ng to w h i ch the process of metaphor is not only an i n d ispens able tool to cogn i t ion , but i s the very basis of cogni t ion . Then all k nowledge essentially a product of cogni t ion-i s metaphorical too. P roponen t s of the st rong thesis i n c l ude Arbib & Hesse [1986], Berggren [1962-63], Black [1962, 1 979] , Cassirer [1955] , Emmett [ 1 945], Hesse [1974], Richards [19 3 6 ] , Ricoeur [ 1 976, 1 977, 1 978] , Sewell [ 1 964], Turbayne [ 1 962] and W heeler [1987]. At least t wo schools of t hought , led by M ac Cormac [ 1 985, Chap . 3] a n d Lakoff and h i s col leagues [ L akoff & Turner 1 989, Chap. 2] respectively, h ave ar ticulated detai led arguments, c it in g empirical evidence, to rej ect the strong thes i s . G i ven t h i s state of affairs , i t is i mportant to clar i fy where my account of met ap hor stands w i t h respect to the strong t hes i s . It m i g h t seem a t first t hat my account o f m e t a phor a u tom a t i c a l l y re jects t he strong thes i s , for I have characterized the metaphorical in contrast with the convention al, the re by i n corpor a t i n g a conventional-metaphorical di chotomy right from the start. However, it turns out that the proponents of the strong thesis do not use the term ' metaphor' in the same sense as I have been using i t . Actual ly, there are significant variati ons, in how the term ' met aphor' is used , even amongst the proponents of the str on g thes i s . To a d d to the con fusion , the opponents of the strong t h e s i s h ave articu l ated their arguments b ased on th eir defi n i t ions of ' metaphor . ' For i nstance, t hough Mac Corm ac and Lakoff h ave b o t h reject ed the strong thesis, they have harshly cri ticized each ot her for u s i ng the term 'metaphor ' i n a con fused manner, to say the leas t . In fac t the debate over the strong thesis of ,
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metaphor provides an excellent exam ple of the u n necessary confusion and the needless controversy t h at i s created when d i fferen t people use a term with different, b ut related mean ings. For metaphors , t h i s con fusion bas served only to draw the researchers ' attention away from some of the key i ssues. I t is my obj ecti ve in this section to l i ft this fog by i dentify i n g the different senses of the strong t hesis, and exposing the unnecessary controversy over t he strong thesis created by the Lakoff- M ac Cormac debate. I start by di scerning t h ree versions of the st rong thesis t h at I consider to be prom i nent. One versi on maintains t h at all k now ledge i s metaphorical in the sense t hat it involves an element of proj ection. The second version holds that al l thought is metaphoric and proceeds by comparison . The t h ird version argues t hat all l anguage i s , or once was, metaphorical . I analyze each of these versions in t u rn, and t h en go on to d i scuss t he Lakoff-Mac Corm ac debate on l i teral metaphorical di chotomy. 8.2.1
Version 1: All Knowledge is P roject ive
The first version of the strong t hesis , embraced by Cassirer, Emmet t , Tur B erggren , and Sewell, starts out by emphas i z i n g t h e creati ve role played by th e human mind in a n y conceptu alization-or, w h ich is the same, in for ming systems of symbol s . It is argued t hat there are no pre- ex is t ing mind-independent and objecti ve stru c t u res to w h i ch our concepts must con form . Rather, i t is the cogni t i ve agent i t self who gi ves an ontology to i t s ex periences w i t h the external world by i nstan t i ating symbols. In other words, cognition works by creating struct ures in t he worl d , and not by adapting to some preexisting ones . Cassirer, as I acknowledged in Chapter 4 [§4.3], was a cha m p io n of t h i s v ie w .
bayne,
p oi n t e d o u t t h at metaphor is the primary p rocess by w h i ch created in the external world. In o t h e r words, it is met ap hor that makes a correspondence between the symbols and p a rts of the world, t hereby creat ing struct u res in the world that the cognitive agent sees. Thus, metaphor becomes the k ey to cognition. From 'all k nowledge is inherently symbolic' and ' symbols are ne c es sar i l y i n t e rp reted by metaphor,' one arrives at the conclusion: ' al l knowledge is necessarily metaphori cal . '
Then,
it
is
structures are
This t hesis, however, raises an interesti ng metaphysical problem. If all our knowledge i s met aphorical, how can we ever be aware of it? If the only mode of interaction with the external wor l d available to us is by using symbols that are created by u s , what d iffe rence does i t m ake i f we ass u m e those s y mbols to be rooted in the structure of the external world?
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Implications
An answer to t hese questions i s prov i ded by Turbayne i n his fasci n at i ng essay Th e Myth of Metaphor. He argues , w i t h a very elaborate example, t hat the external worl d i s i n accessible to us, and we can only view i t t h rough some metaphor. Yet , we can view it t h rough diffe1·ent metaphors, and only by doi n g so can we gai n awareness of t he metaphori cal n at u re of our k nowledge. Moreover, in refu s i n g to do so, and in tak i ng the structure of one's concept u al system to be a reflect ion of the struct u re of the external wor l d , the metaphor turns i n to a myt h . ( Turbayne's sense of the term ' myt h ' here m ay be better understood as 'one- t rack m i nd . ' ) Obviously, t h i s version o f the strong t hesis i s ful l y i ncorporated i n my framework . Reca l l that in Ch apter 5, I emphasized repeatedly how the on tology of the external worl d is determi ned by the cogn i t i ve agen t via i t s per ceptual and cog n i t i ve apparat u s . The process, w h i ch I refer to as proj ection , works by the cog n i t i ve agent grou p i n g parts of the envi ronment together and associating them w i t h concept s . Later, in C hapter 7 [ § 7 . 2], I also argued t h at metaphor i s not h i n g but proj ect ion . Thus, we can say that all knowledge i s metaphorical i n that t h e ontology o f the external worl d-and any form of knowledge pres u pposes an ontology of some k i n d-i s not predetermi ned , but i s estab l i shed by the cog n i t i ve agent t h rough metaphor. Of cou rse, the p rojection m i ght be partially or f u l l y encoded b iologically t he cog n i t i ve agent, and the strong t hesis-t h i s version of i t-loses i t s force when the cogni t i ve agen t h as no freedom in carry i n g out the proj ect ion . S i n ce i f the proj ect ion i s ful ly encoded biologi cally, then as far as the cog n i t i ve agent is con cerned, the ontology of i t s worl d i s fixed by i t s b iological n at ure, and i t can never be aware of the metaphori cal nat u re of its k nowledge: The ontology of its worl d coul d not be otherwise. in
In my account of human cogn ition , the worl d view of a cogn i t i ve agen t i s first determ i ned b y i t s p e rc ept u a l ap p ar at u s i nter ac t i ng w i t h real i t y ( t he Kan t i an t hings-in-themselves), resulting in the sensorimotor data set. The sensori motor data set is then fu rther reorganized, one m i gh t say 'si mplified,' by the h i gher perceptual layers and the cognitive l ayers . V iewed through a con cept network i n a h i gher ( more abstract ) cogn i t i ve l ayer , what the cog n i t i ve agent sees in reality i s an i somorph i c copy of the concept network. T h i s is made possible by the mechanism of projection wor k i n g through all t he lower cogni t i ve and perceptual l aye rs- a process w h i ch also u n derlies metaphor . Moreover, by proj ecti ng d i fferent concept networks, the cogni t i ve agent can see d i fferent structures i n reali ty, and t hereby become aware of the metap horical n at u re of i ts knowledge.
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Version 2: All Thought 1s C omparative
Let us now exam i ne anot her version of t he strong t hesi s , perhaps best sum marized by Richards [1 936] : " Thought i s metaphoric, and p roceeds by com par iso n , and the metaphors of l anguage derive therefrom. " ( From p. 51 i n Johnson [1 98la] . ) A s i m i l ar thought i s echoed by Bl ack [1 979] . The sug gestion here i s t h at metaphor i s fu n d amental to thought p rocesses , an d the com p arative aspect of metaphor u nderl ies all cogn i t i o n , with the term 'com parati ve' not merely referi ng to notici n g pre-ex i sti ng s i m i l ar i t i es , but also to the creation of s i m ilarities. This version of t h e strong t hesis i s somew h at vaguely stated, but i t can be art i cu l ated w i t h i n my fram ework so t h at i t capt u res t h e essence of what Rich ards and Black m ay have had i n m i n d . Recall t hat i n Chapter 7 [§ 7.4.2], I poi nted out how cogn i t i on typical ly i n d uces grou p i n gs w h i ch leads to a loss of i nform ation . I n a p u rely accom modat i ng cogn i t i ve system-one i n which t h e p roj ection mechan i s m i s fu lly encoded biologically o r cu l t ur ally thi s i n formation loss i s permanent and irrecoverable. The worl ds lost are lost forever. I also argued t here how proj ect i ve metaphors m ake i t possible for the c og n iti ve agent to recover so m e of the lost worlds. The process works by projecting a different concept ne t w o r k onto the environment (different than the one t h at•is conventionally used w ith t h at envi ron ment ) . Or, to use a metaphor from Turbayne, i f we are always view i n g t h e worl d t h rough a pair of green glasses, our perception i s very much bi ased . However, w i t h i n the con straint t hat we can view the world not with the n aked eye but o n ly t h rough a pai r of glasses , the capab i l ity of putti ng on d i fferent colored gl asses ex tends o u r cog n iti ve abi l i t ies a great deal . It is precisely in this sense th at our a b i l i t ie s to create a n d un ders ta n d m e t a p hor s arc an i nvaluable asset to cogni tion . I a l so noted ( i n §7.4.2) that in p ro j e ct i ng a source concept network on to a t arget realm, the cognitive agent i s, i n effect, reaJizing the potential s i m i larities bet ween the source and target realm s . T h i s process can be t hought of a s if the cogn i t i ve agent were comparing the source real m w i t h the tar get realm . The 'as i f' part is emp has iz e d because the real m s are not always d i rect l y accessi ble fo r c om pari s on . When t he sou rce and target realms are actual ob j ec t s in the external worlds, then we c an not com pare the two ob j ects because they belong to the w o rl d of th i ngs- i n-themselves t hat is not accessible. However, i n projecting t h e c o n cep t network t h at is the conven t i on al descri p t i on of one obj ect onto the other o b j ec t , w e are partially get t i ng some i nformat ion about their ' comparati ve aspects.' T h i s is t h e comparative
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aspect of metaphor t h at is responsible for creat ing new i nsights about the target realm, and for making metaphor a key player i n cognition. I believe it is t h i s comparati ve aspect of metaphor to which Black and Richards were all u d i n g. A n analogy can be draw n here w i t h the functioning of our perceptual system . In p ast years , research into the physiology of our sensory system has establ ished beyond doubt t h at our senses are geared towards detecting dif ferences rat her than absol ute levels . For instance, the eye i s more sens i t i ve to cont rasts an d to changes i n i l l u m i n ation levels , than to absolute i l l u m i n at ion levels . I conj ect u re t h at this very same principle i s also the bas i s of cogni t i on, and metaphor is a man i festation of t h i s principle in cogn ition. ( See B ateson [ 1 979] also for a d i scussion of the role p l ayed by ' d i fferences ' in cogn i t ion . ) 8. 2 . 3
Version 3 : All C onventional Meanings Arise By Way of Met aphor
The t h i rd sense of t he strong t hesi s-which can be d i scerned in Arbib & Hesse [1986] , Cassi rer [1955] , Ricoeur [1976] and Wegener [1885]-is derived from an empirical fac t . Linguists h ave known for a long t i me t hat metaphors play a key role in the process of mean i n g change. (I am us i ng the t erm ' metaphor' in my sense here to refer to non-conventional i nterpretat ions.) Metaphors t hat are considered novel at one t i me, lose thei r novelty through frequent usage and become a part of the convent ional language. M ac Cormac [1 985, p . 59] ci tes ' war ' as an example. The current d i ctionary mean i n g of the w o r d i n c l udes ' m e n t al h ost i l i ty,' whi ch was a b se n t from Samuel Joh n son's A Dictiona1'Y of the English L anguage
in 1775. Lakoff [1987a] offers many o t h e r
examples to show th at this process of meaning change caused by m etapho r s takes place in several stages. For in st a n c e , the origin of the word 'pedigree' can be traced back to pie de grue of Old French, meaning 'foot of a crane ' I n i t i al ly, t h i s ter m was metaphorical, evok i ng the i m age of a crane's foot to refer to a fami l y-tree diagram . However, now the use of ' p ed igree' does not evoke any such i m age in most people. They might not even be aware that it has any t h i n g to do with a crane's foot , t hough the New Col lege Edition ( 1 975 ) of The American Heritage Diction ary of the English Language st i l l records the origi n of t he term. One m i ght say that, when one now uses the word ' pe d i gree ' t o refer to one's ancestry, i t i s being used conventionally, or even l i terall y. O n the other hand, the use of 'fight' in "The presidential candi dates fought bi tterly i n the debate" m ay st i l l evoke t h e i mage of ' war' in some people, even though the dictionary mean i ng of ' fight ' now includes
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' a verbal d isagreement.' G i ven that some convent i onal mean i ngs origi nate as metaphors , t h i s ver sion of the strong thesis generali zes it to concl ude t h at all convention al mean ings must h ave been metaphorical once. Even w i t h t h i s clari fication, i t i s possible to misi nterpret t h i s version of the strong t hes i s . O ne m ight t ake it to mean t h at it i s i m possible to h ave a concept network ( system of symbols ) , ever, t hat h as a con ven tional i nterpretation right from the start . Taken i n this sense, this version of the strong thesis i s easily refuted. Consi der the process of m ak i n g a scale model of a s h i p . One starts by choosing an appropri ate scale and what aspect s of the s h i p are being modeled . For i n stance, the feat ures inc l u ded in a model to be u sed by a travel agent for show i ng prospect i ve travelers the types of avai l able accommodations w i l l be different from t hose i ncl uded in a m arine engineer's model to test the s h i p 's seaworth i ness . O n ce t hese choi ces are made, i t i s the structure of t he ship t h at determi nes the structure of t he model. (A co h e r e n t cogni t i ve relation i s bei ng formed by accommodation h e re . ) When th e model is completed , t here is only one i ntended i n terpretat ion of it t h at allows it to refer to the ship modeled . This i nterpret ation i s conventional right from the start.
Several other examples can be suggeste d along this line. In developing a mathemati cal t heory of electri city that uses otherwise meani ngless symbols l i ke R for resistance, I for current , etc . , and exp l a i n s the rel ationshi p between t hese symbols by mathemat i cal equations, there is no i n i t i al metaphorical i nterpretation of the theory. B asi cal ly, any cog n i t i ve relat ion that i s b eing formed by ac c om m oda t ion w i l l have a conventional i n terpretation right from the start . This i s b ec ause i n an a c co m mod ati n g cog n i ti ve relation, the con cepts of the concept network are given a m e a n i ng befoJ-e the concept network is given
a
structure.
However, the interesting t h i n g is that in all su ch exam ples, the system b e i n g modeled or studied i s gi ven an initial ontology by u s i n g other concepts and concept networks t hat have conventional interpretations. For instance, i n dec i ding what aspects of t he s h i p are being modeled , one bas to use con cept s l i ke ' cab i n , ' ' deck, ' ' h u l l , ' and so on . Before study i n g the rel a tio n s h i p between resi s t ance a n d c urrent , one must descri be w h at 'resistance' i s and what ' c u rren t ' is, and these descriptions (wh i ch m ust include t h e ways i n which currents and resi stances m igh t be measured) make use of other con cept s t h at h ave conventi onal i nterpretations.
Thu s , i f t here are already concepts with conventional meanings, i t i s cer tainly poss i b le to define ot her concepts and generate concept networks that
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292
start out wit h conventional mean i ngs. But t his is not what the t h i rd version of t he strong t hesis is trying to say. Its m ain t hrust is that a system of sym bols that is not 1·oo t ed in pre-existing conventional symbols always starts out as a metaphor.
I shou l d emphasize t h at what is meant by 'metaphor ' here i s the process of giving a n ew ontology to the environment . The p urport of t h i s version of the strong thesis is t h at what we t ake to be the convent ional description of the world is actually brought about by a process t hat was alive and vibrant once; a process t hat also m akes metaphors meani ngfu l . Thus, t h i s version is act ually quite close to the first version of the strong t hesis, in spite of the fact that the term ' m etaphor' is used with different meanings in the t wo version s . There are t wo lines o f argument supporting t his version of the strong thesis . One comes from ant hropology by considering different st ages through w h i ch symbols evol ve in a c u l t ure. These arguments are best articulated by Cassirer [ 1 955] . (See also my brief discussion of Cassirer' s t hree types of symbols in § 4 . 3 . ) The ot her line of argument comes from considering the development of concept s in a child. Though Piaget did not exp l i c i t l y address the strong t hesis of metaphor , h i s numerous experi ments w i t h children to demonstrate h i s constructivism [§4.4] provide i n d i rect support to t his version of the strong t h esi s . (See, for i nstance, Piaget [1945] and P i aget [197.5].) I find t his version of the strong thesis quite appealing, t hough , techni call y speaking, m y accou n t of metaphor i s neutral wi t h respect to it, because I do not take sides on how the conventional interpretations come abou t . The arguments of Cassirer and P i aget convince m e t h at all that w e r eg ard as conventional and literal was once as v i brant as the meta.phors of Boland and S pender; and you need not study other l anguages and cultures in order to convi nce yourse l f of t h i s , but only need to remember your chi ldhood experi ences a n d joy of figur i n g out w h at a word means . 8.2 .4
Lakoff- Mac C ormac D ebat e
As I noted before , the strong thesis of metap hor has been criticized by Lakoff and his col leagues , and by Mac Cormac . S i nce I endorse each of th e three version s of strong thesi s , it woul d only be appropri ate to address the points raised in both t heir cri t i c i s m s . However, before doi ng that , I woul d like to discuss M ac Cormac's criti cism of Lakoff, and Lakoff's reb uttal to Mac Cor m ac , for t wo reasons. One is to demonstrate how using the term 'metaphor' in different senses can create a needless cont roversy. I feel t hat t h i s issue must be brought out , since each of t hem is an influential scholar . The second
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293
i s t h a t in d i s c u s s i n g t h e i r crit icism of each other first, m y t as k of re fu t i n g the arguments rai sed by each of them agai n s t t he s t ro n g thes i s of metaphor w i l l be m ade short , s i n ce each exposes the w ea k n e ss e s of other's arguments rat h er well . Lakoff and Joh nson [ 1 980] put fort h the fol l o w i n g t h eses t o suggest that most of our convent ional language i s i n herentl y metaphorica l : LJ l :
M any of o u r everyday concepts are metaphorical i n t h e sen se t h at they organi ze one t h i n g in terms of another: ' l ove as a jou rney, ' a r g u m e nts as war , ' and so o n . '
LJ 2 :
Even the c o n ceptual organ izations t h at we t ake for granted and use in our day to day l i ves reveal b i dden metaphors . ( For example, ' t i me i s money. ' ) S ince the metaphorical nature of these con cepts i s t aken for granted , t h ese might be t h ou ght of as l i teral or con ven tional metaphors.
LJ 3 :
If one assu mes an 'objecti ve theory of mean i n g , ' implying t h at words and p h r ases corres p o n d to some ' n at u ral ' c a t eg o r i e s o f real i t y, and i f o n e provides no mechan i s ms for violating t h i s correspondence, then se ver a l c h a r a c t e r i s t i c o f m e taph or can n o t b e e x p l a.i ned , i n c l u d i ng h ow so m any of our concepts h ap p e n to be metap h o r i c a l ly s t r u c t u red i n terms of another concept .
LJ 4 :
O u r conceptual struct u re does not reflect some n a t ural s t ruct u r e of reali ty.
LJ 5 : M a n y
of ou r
c on c ep t s we
concepts
a r e metaphorically
s t r u c t u red i n
terms of the
acq u i re from ' d i rect bod i l y experi e n ce . ' T h e term ' d i rect
bod i l y experience'
does not
c e r t ai n body, b u t a l s o
cultural and soci al
mere!
refe r
i ncludes the b i as
to the
fact of o u r hav i ng a
of our experience
d ue
to o u r
backgro u n d .
Mac Corm ac [ 1 985, C h a p 3] raised
several o b j e c t i o n s to Lakoff and Johnson's and arg u e d for m ai n t ai n i ng a l i t eral m e t a p h o r i c a l d i s t i nction . The m a i n points of his counterat t ack are s u m m a r i zed below : .
t heses ,
Ml:
-
The characterization o f m et aphor as e xpe ri e n c i n g u n d e r s t a n d i ng , a n d o r g a n i z i n g o n e t h i n g i n te r m s of anot her i s too l os e and fi t s any s e m a n t i c process i nvo l v i n g s y m b o l s and their mean i ngs. ,
t he examples pre ented b y Lakoff and Jo h n s o n are so called ' dead metaphors , ' t h at i s , met a p ho r s t hat have fa d e d i nto polysemy
M 2 : Most of
294
Part Iff: The Implications t hrough frequent usage. ( M ac Cormac cites the example of ' war' men tioned above. ) Thus, he argues, Lakoff and Johnson are merely re defi n i ng the terms l i teral and metaphorical to be l iteral metaphor and figu rat i ve met aphor .
M3:
While i t cannot be denied that met aphors give rise to l i teral meanings for as the use of a metaphor becomes more frequent , its novelty wears off and it gradually acqui res the status of l iteral meani ng-th i s recogni t ion does not necessarily force one to accept the conclusion that all l anguage is metaphorical .
M4:
I f one takes l i teral mean i ngs as given, and ass umes t hey correspond to some natuml categories of the external wor l d , it does not necessar ily p recl ude any theory that allows category violations u n der certain con d i t ions. I n fact , M ac Cormac's theory attempts to do j ust that .
M5:
There are several problems w i t h Lakoff and Johnson 's account o f how many of our concepts are structured in terms of the concepts acq u i red from ' d i rect bodily experience . ' The most weighty obj ection is that La koff and J o h n son do not clearl y e xp l ai n how the ' d i rectly a c qui re d con c e p t s ' are formed . For i n s tance, ci t i n g Lakoff an d J o h n so n ' s own example of fron t back orientation w h i ch some cultures express u s i ng ' i n front of ' a n d others express w i t h ' i n back of, ' he writes, "If some spatial concepts vary from cult ure to culture, how can we have any certainty that spat i al concepts emerge d i rectly?" [Mac Cormac 1 985, p . 68.] -
the empirical research of B e r l i n a n d Kay [ 1 969] that shows how color tern1s i n va r i o u s l a n g u age s share a common structure. T h i s shows t hat t here are certai n nat u ral b oun d a r i e s i n t he external worl d t h at a l l co n c e p t u a l systems reflect .
M 6 : T he r e i s
M 7 : C o n c l u s i on : T h e d i st i nct i on
between t h e l i teral a n d the metaphorical i s prerequisite to any t heory of met aphor , t hough t h e boundary between the two is not a sharp one but fuzzy.
Lakoff responded to these obj ections by poi nti ng out that there are no less than fou r d i fferen t senses of ' l i teral ' [Lakoff 1 986] and no less than fou r d i f ferent senses of ' dead metaphor' [Lakoff 1 987a] . Lakoff and Turner [ 1 989, p p . 1 1 4 - 1 3 1 ] also a rgued that the ' l i teral mean i ng theory' and the ' dead metaphor t h eory ' are i n consistent w i t h t h e e m p i r i cal fi n d i n g s . Let us focus h e r e on Lakoff 's object ion to what he called t he l iteral meani ng theory, which i s based on d i s t i n g u i s h i n g between t h e fo l l o w i n g four senses of ' l i teral ' :
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Refers to conventional l i tera l i ty, as opposed to poet i c language, exaggeration, i rony, i n d i rect speech acts, etc.
l i t e r al l :
Refers to the language ordi narily used to talk about some subject matter . Thus, when one normally tal ks abou t i deas as plants [Lakoff and Johnson 1 980, p. 47], as in "Her ideas fi n al ly came to fru i t , " it i s seen a s l iteral usage i n t h i s sense.
l i t e ral 2 :
Refers to the usage of language t h at i s d i rectly mean i ngfu l : that i s , i t does not p resent one t h i ng as someth i n g else. Thus, "Her i deas fi n ally came to fruit" would not be l i teral in t h i s sense, whereas "The car moved forward" would be consi dered l iteral .
l i t e r al 3 :
Refers to the language capable of describ i n g the obj ective world, and t herefore capable of being objec t i vely true or false.
l i t e r al 4 :
B ased o n t h i s d i s t i nction , Lakoff argued t h at M ac Cormac's arguments are i ll-founded since t hey muddle the fou r senses . In parti cu l ar, Lakoff clai med , Mac Cor · :tac has com bined lit e m / 1 , lit e ral2, an d lit e m l3 i n h i s use of the term ' l i t e r a l , ' t hereby i n t roducing "an i mportant theoreti cal ass u m p tio n an assumption t h at h as , as a conseq u e n ce , the conclusion that con ventional metap h or c anno t exist . " [Lakoff 1 986, p. 2 96.] ( T h i s i s because only lit e m /3 i s defined i n contrast w i t h the metaphori cal, and metaphori cal i s consistent w i t h lit e ra / 1 and w i t h lit e m /2. ) I n t heir later elaboration, Lakoff and Turner [ 1 989, p p . 1 1 4-1 28] , ch arac terize the ' l i teral mean i n g t heory ' as hav i ng the fol lowing ch a r a c t e r i t i cs : •
"If an expression of a language i s ( 1 ) conventional and ord i n ary, then i t ( 2 ) semantically auton omous a n d ( 3 ) capab l e of m a k i n g referen ce to object i ve reality.
i s also
a li n g u i st i c ex pr es s i on is c a l led ' l i teral , '
•
" Such
•
"No metaphors are l i teral . " [Lakoff & Turner 1 989,
pp
1 1 4- 1 1 5] .
They refute t h i s t heory by empirically show i ng t hat i t i s possi ble t o have con ( 1 ) b u t not (2)-conventional expressions m i ght not be semant ically autonomous , as in " Her i deas came to fru i t ," and t h at it is possible to h ave condi ti o n ( 1 ) and not (3)-conventional language does not reflect t he obj ec tive reali ty. In fact , L a koff an d h i s co l l e agu es h ave consistently argued t h at t here i s no n a t u ra l structure i n reali ty t hat our concepts must reflect; t hat i s , cond i tion ( 3 ) i s not sat i sfied by any expression, l i teral or metaphori cal . d i t i on
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This debate reveal s a great deal of confusion and m i s u n derstanding of each other's pos i t i ons, and clouds what are the essent i al points of differences between t hem . In fac t , once the fog is l i fted, it turns out t hat the two schools of t hought are closer t h an eit her one m ight be w i l l i ng to admi t , for t hey both take the same side on an i mportant i ssue, and that i ssue i s not the strong t hesis of metaphor. To see al l t h i s , Jet us analyze the poi nt s raised by each cam p . The main obj ect i ve of Lakoff and Joh n son 's study was to show t h at metaphor i s a powerful tool i n shaping t he cogn i t i ve worl d t hat we experience. For t h i s ob j ec t i ve, conventional metaphors, even ' dead ' metaphors , are q u i te i mportan t , si nce t hey b r i n g evidence t h at even what w e t ake to be t h e conven t i on al and ord i n ary description of the world i s actually brought about by a metaphor, even though the metaphor m ight not be ali ve and v ibrant today. I t i s the con vent i on al metaphors t h at demonst rate t h at metaphors are not somet h i n g that o c c u r o n l y i n the domai n s o f poet ry, art , and flowery language, b u t are an i nd ispensable part o f everyday language an d concepts. G i ven that , i t seems q u i t e logical that La koff and Johnson wou l d i n cl u de convent ional metaphors under the rubric of ' metaphor. ' M ac Cormac's criti cism of La.koff and Joh n son ut terly fail s to app reciate t h i s i m portan t poi n t . He regards metaphors to be non-conventional use of language t h a t res u l t s i n new m ea n i ng s , and , from this point of view, he is vehement ly argu i n g that what Lakoff and Johnson are cal l i n g metaphors are not metaphors at al l . I n teres t i n gly, however , M ac Cormac's use of the term ' metaphor' i s quite reason able for what he i s t ry i n g to achi eve in h i s theory. H e i s i nterested in showi ng how novel metaph ors derive their meani ngs. He woul d agree w i t h t hesis LJ3 as it i s . H owever, he correc tly emphasized in M 4 that in a theory t h at ass umes l i teral mean i ngs as give n and predeter m i ned , i t i s not necessari ly true t hat n o m ech a n ism can eve·r be pro vided for violat i ng the categori cal struct u re i m posed on the world by the li t eral meanings. His ow n theory starts from s u c h a n assum p t ion a n d t hen provides mech a n i s m s by w h i ch metaphori cal mean i ngs are created . I n fac t , he i s not the only one; others have tried i n t he si m i l ar vei n . [ Lev i n 1 977; Searle 1 979.] These theories at tempt to explain metaphor as a. process of relax i n g seman t i c constrai nts on l i t eral-conventional mean i ngs . Now one m ight di sagree whet her t h i s is the r i g ht way to for m u l ate a. theory o f met aphor, b u t t he enterprise certai n ly makes sense. T h e proponents of t h i s approach, i ncluding Mac Cormac , argue that when we understand a . new metaphor , we are already fam i l i ar w i t h the conventional mean ings of the words a n d phrases . Therefore, i t seems
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reasonable that a theory of metaphor should try to do the same: take the conventional meani ngs as gi ven , and explain how new mean i ngs are deri ved from the convention al meanings. With this object i ve in m i n d , one can see w hy conventional metaphors and l iteral usage is l u m ped together under the banner of ' non-metaphori cal . ' Lakoff 's crit i ci s m of M ac Cormac, i n t u rn , completely disregards al l t hese points. In characterizing the four senses of l i terals , and poi nting out that only one of t hem i s defined i n contrast to metaphorical , Lakoff i s ass u m i ng that the meani n g of ' metaphori cal ' i tself is u nequivocal . The same implicit assumption u nderlies L akoff 's four senses of ' dead metaphor , ' w here i t i s further assu med t h at b e i n g ' dead ' refers to a certai n fi xed characteristic of metaphor. This assumption finds its way unscathed i nto Lakoff and Turner's l ater rebuttals of the l i t eral mean i n g theory and the dead metaphor theory. T h at t he b asis of this debate is a m i sunderstan d i n g of the word 'metaphor' i s clearly seen in how each of t hem defines metaphor. Lakoff takes ' metaphor' to mean "understan d i ng and experiencing one kind of t h i ng in terms of an other . " [ Lakoff & J ohnson 1 980, p. 5.] M ac Cormac , on the other han d , defines a metaphor to be "a cogni t i ve process b y w h i ch n e w concepts are expressed and suggested [and a] cult ur al process by w h i ch l an g u age i t self changes . " [ Mac C o r m a c 1 9 8 5 , pp. 5-6 . ] As long as we use their intended sense of ' metaphor' i n i nterpreti ng the arguments from each cam p , there i s no problem , for each l i ne o f argu ment seems quite reason able-they do not contrad i ct at all . The unnecessary controversy i n their debate stems from the i mp l i cit as s u m ption each of them m akes that h i s is the correct u sage of t he term metaphor. In mak i n g al l t hei r arguments, nei ther of them ever questions his own defi n i t ion of 'metaphor. ' Lakoff, w h i le he distingu ishes four senses of l i ter al does not consi d er even once the possi b i l i ty t h at someone e l sf' might use t he term 'met aphor' d ifferently from h i m . ,
T h e f a c t i s t h at two senses o f m et a pho r can be clearly d i st i ngui shed in common usage. One of t hem, let us say m e t aph o d , appl ies only to novel metaphors . I noted in C hapter 1 that one of the reviewers of t h i s manuscrip t obj ected to m y characterizing " T h e chairperson o f t h e meeti n g plowed through t h e agenda" a s a metaphor. This was a convent ional usage o f ' plow , ' a s far a s s h e was concerned , and , t herefore, n o t a metaphor. Though I am not aware of any such study, T conj ec t u re that if one were to p resent a n umber of what Lakof[ call s conventional metaphors together w i t h some poetic metaphors and some ex am ple s of what L akoff cal l s lit e m /3 to a group o f subjects ( without giv i n g t hem any defi n i tion of metaphor ) , and were to '
'
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ask t hem to sort out t he examples i nto metaphors and non- metaphors , m any of the convent ional metaphors, such as ' t i me i s money, ' would be classified as non-metaphors. This merely reflects t he conventional way in w h i ch people use the word ' metaphor. ' The second sense o f metaphor, let u s call i t m e t aph o r2, corresponds to Lakoff' s defi n i tion of ' metaphor' and i n c ludes conventional metaphors. It is m e t aplw r2 t h at is defined in cont rast with lil e ra/3, but it i s not the only sense of metaphor. I n fact , the concept of m e taph o r2 i s somewhat problemat i c , and t h i s i s w here M ac Cormac's cri t icism o f Lakoff i s most effect i ve. For i nstance, M ac Cormac i s right in poi n t i n g out [M l ] t h at any symbol i c p rocess can be characteri zed as experien cing one k i n d of t h i n g in terms of another. ( More persuas i ve arguments support i n g t h i s clai m can be fou n d i n Cassirer [ 1 955] , who argued t hat i t i s the process of forming a symbol i t self t h at gi ves an experiential ontology to t he environment , and t he symbol essen t i al l y works by represent i ng the experience as someth i ng else. ) And, t herefore, Lakoff's defi n i t ion seems to lead to t he conclusion that all language i s metap hori cal . Lakoff, of course, vehemently denies t h i s , and points out t h at cert ai n c on cepts are non-metaphori cal i n t h at t hey are u n derstood ' d i rectly, ' t h at i s , not as somet h i n g else. Th i s separat ion of m etaphor2 w i t h /it e ra /3 i s also not w i t hout problems-! al ready mentioned some in Chapter 4 [§4 .5] . For i n st an ce, consider the point raised by M ac Cormac i n t hesis M 5 : Why i s i t t h at t h e front- back orientation i s consi dered a non-met aphori cal concept when i t i s real ly a res u lt of projecti ng a conceptual system ? When the very same si t uat ion is experienced as " t he ball is i n front of t he rock" by one person and as "the rock is in back of the bal l " by another perso n, coul d we not say t h at one of t hem i s experiencing i t i n terms of ' i n front of' and t h e other i n terms of ' i n back of' ? Bu t i n each case, t hey are experiencing the s i tuation as s o m e t h ing els e . Or , consi der when someone decides to ' save' time by bei ng more organ ized . W hy is she experiencing the t i me as somet h i n g else? If the person grew u p i n a culture where t he ' t ime i s money' metaphor (m e t aph o r·2) i s prevalen t , t h i s m ight well be her d i rect experience of t i me. I n m any of the conventional metaphors c i ted by Lakoff, i t i s questionable how many of t hem really fit the category "experi enci n g one k i n d of t h i n g as another . " A l l t h i s reveal s i s t h at t h e concept of metaphor2 i s n o t a s st raightforward · a s Lakoff takes it to be. Lakoff 's cri ticism of Mac Cormac i s most effective against t heses [ M 4 ] and [ M 6] , where M ac Cormac at tem pts to identify the l i teral ( l i teral 2 ) meani ngs w i t h n at ur a l boundaries in the external wor l d . In fact , in the at tempt to
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refute t h e ' l iteral mean i n g t heory, ' i t i s only t hese t heses t h at Lakoff succeeds i n refu t i ng, once the two senses of metaphor are clari fied . ( For, i n refu t i n g t h at all conventional language i s n o t seman t i cal ly autonomous , t h e term 'seman t i cal l y au tonomous' is used in contrast with m et a p lwr2, which faces all the p roblems mentioned above. For i nstance, why is i t that ' t i me is money ' i s not seman t i cally autonomous, i f that i s how one experiences t i me? ) H owever, taking conventional meani ngs a.s gi ven , a n d regard i ng t hem as non-metaphori cal does not necessari ly lead one to ass u m e that the conven t ional mean i ngs correspond to some natu ral preex i s t i n g bou ndaries in reali ty. Mac Cormac t akes t h i s posi t i on , but K i t tay [ 1 987] , who also uses the term metaphor in the sense of m e t aphorl , and art i c u l ates a theory of metaphor t h at explai n s the emergence of new metaphori cal m ea n i ngs as a fu nction of already exist i n g l i teral-conventional mean i ngs, does not . It i s perfectly rea sonable to maintai n , as I have been doi ng t h roughout my framework , that convent i onal meani ngs are also a res u lt of projec t i o n , so t h at t hey do not re flect some transcendental structure in reali ty. Thus, the 'objec t i ve mean i ng' con d i t ion in Lakoff's characterization of the l i teral mean i ng theory i s not a necessary con d i t ion of u s i n g the term metaphor i n t h e sense of m e t aphorl . Let us now exami ne Lakoff and M ac Cormac 's argu ments as far as they c on s t i t u t e a rej e c t i o n of the strong t hes i s of m e t a p h o r . M ac Cormac clearly stands in oppos i t ion to the strong t hesis-al l t h r ee versions of i t . T h i s r e sults from h i s wan t i ng to maintain that t here are nat u ral categories in the wor l d t h at ou r l i teral - conventional concepts reflect . T here i s no evi dence for t h i s t hough . The Berli n and K ay studies ci ted by M ac Cormac i s quite troublesome, as I h ave d i scussed earlier i u C h a p t e r 4 [§4 . 2 . 4] . Given that, M ac Cormac's arguments do not const i t ute a serious th reat to the strong thes i s . G i ven my clarification o f t he d i fferent senses i n w h i ch the term ' m etaphor' bel i ev e t h at Lakoff wou l d agree w i t h Ver s i o n l . Ile m i ght not agree w i t h Version 3 though , and m i g h t c o n t i n u e t o maintai n t h at cer t a i n concep t s are u n derstood ' d i rect ly. ' B u t m y d i sc u s s i o n i n th i s secti o n , taking note o f Mac Cormac's criticism o f Lakoff, s hows that Lakoff h as not convi n c i ngly demonst rated t h at t hese ' d i rect ' concepts are not un derstood as anyth i n g else. So, Lakoff's argu ments d o no t p o s e a ser i o u s challenge to t he strong the s i s e i t h er . i s u sed i n t h e st rong thes i s , I
I ro n i c a l ly, Lakoff 's i ns i stence on maintai n i n g t h at ce r t a i n concepts are un derstood d i rectly puts h i m and M ac C o r m a c on t he same s i d e of an i m p ortan t issue. Noti ce that i n Lakoff 's cha racterization of a metaphor as e x p e r ien c i n g one kind of t h i n g i n terms of anot her, t h er e is an i m p l i c i t a ss u m p t i on that
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t h i ngs can be sorted out i n to d i fferent ' k i nd s , ' bejo1'e being con cep tualized. Otherwise, what makes ' t i me' a d i fferent k i n d of t h i ng t h an ' money ' ? W h at makes ' l i fe' a d i fferent k i n d of t h i ng than 'j ourney ' ? I f no categorization exists prior to concept u a l i zat ion , as Lakoff staunchly maintai n s , t hen how do we know that somet h i ng i s bei ng experienced as someth i n g else? To h ave h i s cake a n d eat i t t o o , Lakoff i m p l ies a t other p laces t h at o n e c a n sort o u t d iffer ent experien t i al domai ns i nto k i n d s before concept ualizat ion. For instance, Lakoff and Turner argue: " [ M] etaphor can prov i de structur e and at t r i b utes not i nherent in t he target domai n , as , for exam ple, when dying is u nderstood as depart ure to a final desti nation or deat h i s u nderstood as a reaper. Th e ph e n o m e n o n o f death is n o t o bject ively similar to a reaper." [Lakoff & Turner 1 989, p . 1 23 ; emphasis m i ne. ] How can one conclude that the p henomenon of deat h i s not obj ec t i vely s i m i lar to a reaper u n less t here exist some obj ect i ve natuml ki nds. B u t t hen t h i s can be considered the n a t u m l structure of t he p re-concept u al world i n the sense of M ac Cormac. There i s another way in w h i ch Lakoff 's ' d i rectly emergent concepts' nudge h i m c loser to M ac Cormac . In clai mi ng t h at some of t hese concepts are deri ved from our having bodies of certai n sort s , it fol lows t hat t hese concepts ought to be the same for all those with s i m i lar bodies . ( Th i s i s a point I emphasized earlier i n C h apter 4 [§4 .5] as a weak ness of t he Lakoffian approach to cogn i t i o n . ) However, t h i s i m med i ately gi ves such concepts the status of ' u n i versal s . ' Then , the only d i fference between Lakoff and M ac Cormac seems to be that Lakoff would mai ntai n that the source of t hese ' u n i versal s ' is i n our bodies, and Mac Cormac wou ld argue that i t i s i n the structure o f reali ty. Of course, t hey m ight both be correct to a certai n extent . It cannot be deni ed t hat all humans have certai n physiologi cal and anatomi cal featu res i n com mon . We all have certai n sensory and motor organs that share many char acteristics. It is also true t hat we i n habi t a world w i t h an autonomous struc t u re that, whi le ex h i b i t i n g wide variations from one geograph i cal location to another, nevert heless has many feat u res that do not change. For i nstance, the cycle of l i ght and darkness rec urs with great stubbornness, though thei r relat i ve lengths vary a great deal depen d i ng on the lat i t ude, t i me of the year , a n d the at mospheric cond i t ions. W i t h so much common grou n d , i t i s cer t ai n ly possi ble in princi ple that w i dely d i fFerent cultures might s hare certain conceptual struct ures . However, the complex i ty of the h u m an brai n , w h i ch defies a s i m ple- m i nded way of root i ng t he source of our conce pt ual structures i nto the p hysiological struct u re of the brain [§4 . 2 . 4] , and the creat i v i ty of the hu man m i n d , w h i ch keeps com i ng u p with newer ways of concept ualizing even the m os t m u n dane objects and experiences , makes me qui te sceptical of w hether any such ' u n i versal ' st ructures w i l l ever be empirically fou n d to
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lend su p port to either Lakoff's or M ac Cormac's hypothesi s.
8.3
Metaphor and Correct ness
So far I h ave ch aracteri zed metaphor as a ' mean i n gfu l i nterpretation . ' Obvi ously, t hough , an i nterpretation can be mean i ngfu l , and yet be deemed ' false' or ' i ncorrect . ' For i n stance, on a bright an d s u n ny day, i f someone says "The sky is cry ing," you woul d u n derstand the statement , but wou l d con sider it false. Then , of course, a l i teral - m i n ded person m ight consider the statement false even if the sky were grey and it were rai n i ng , but s t i l l maintain t h at she u n derstands i t . Consider agai n the exam p le t hat was i n t rod uced at the be gi n n i ng of the chapter : " i xon is a h alo surrou n d i n g a vacu u m . " An ad m i rer of the former U n i tes States presi dent , and an ardent cri t i c of N i xo n , both m i gh t u nderstand wh at i s meant by t he statement, t hough b i tterly d isagree on whet her t he statement is correct or i ncorrect . Moreover, each of t hem cou l d q u i te reasonably argue t hat the correct ness (or i n correct ness ) of the metaphor i s a m atter of h i stori cal fact, somet h i n g t hat cou l d be obj ect i vely verified . To add to the confusion , a l i teral- m i n ded person cou l d agai n claim t h at the statement i s i n correct obj ecti vely s p ea k i ng . T hese examples raise a number of i m portant quest ions w i t h w h i c h any comp rehen s i ve theory of metaphor must grapple. W h at does it mean for somet h i n g to be correct ? W h at is the d i fference between correctness and truth? W hat i s the d i fference between understan d i n g and correctness? What i s the difference b e t ween l i teral ( conven t ional ) and metaphori cal correc t ne s s ? l n t h i s section I add ress t hese quest ions w i t h i n my framework of metaphor and cogni tion . 8.3.1
C orrect ness , Trut h and C o herency
I n the example of t he scale model of a ship t h at l i nt roduced in the previous section , t here is a n obvious cri terion to determine whether or not the model i s correct . The correspondence between t he parts of the model ( concept network ) and the parts of the s h i p i s fixed and can not be varied . For t hi s reason , one merely needs to a s k i f t he struct u re of the m odel res pects t he structure of the obj ect bei ng modeled i n order to deter m i n e the conectness of t he model . However, t h i s ch arac t erist i c is cal led ' coherency ' in my framework . T h i s suggests t h at correct ness c a n be identi fied w i t h coheren cy. Let u s
look
at another exam ple. Say t h at someone is learn i ng t o do para!-
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lei parking. The person h as some feel for d ri v i ng and the maneuvers necessary for parallel parki ng. She carries out the maneuvers , and h i t s the curb. Obvi ously, one woul d say, the maneuvers were ' i n correct . ' Now from the point of view of the person attempting the t as k , she was carryi ng out ' actions' that s h e t h o ugh t wou ld m ake the car end up i n the desired posi t ion. However, on actually carrying out the act ions, she d i scovered t h at the car did not end u p i n the desi red pos i t i o n . We coul d say that t h e result of act ually carrying out the action correspon d i ng to the ' mental acti on ' (operator in my framework ) d i d not result i n the s it uation ( parallel parked car) t hat corresponds t o the ' mental i m age' ( symbol ) that the ' mental action' predicted . I n other words, the environment d i d not respect the actions of the driver as she expected , based on her concept network. I n short , the cogni t i ve relat ion between the driver's mental concept network of parallel parki n g and the envi ronment was i n coherent . T here are many other examples as wel l . Consi der skiing, s w i m m i ng , or any other act i v i ty t hat requi res coordi nat ion and plan n i ng. Come to t h i n k of i t , all ac t1 vities, even wal k i n g and s i t t i ng , requi re coordi nat ion and plan n i ng, except t hat we are so habi tuated to some of t hem t h at w e are n o t consciously aware of it. I n each of t hese cases , i t can easily be seen t h at the notions of correct ness and coherency coi ncide. It must be emphasized here that coherency here i n vari ably means local coh e re n cy. In the example of parallel parking, i f the dri ver managed to do a perfect maneuver we cannot say t hat her concept network of d r i v i ng i s correct for al l s i t uations and a t a l l t i mes . I n fact , the question of correct ness can be raised w i t h respect to any description. You m i ght recall from C h ap ter 5 [§5 . 7.3] t h at the term ' descri ption ' appli es to any obj ect or situat ion in the env i ronment via i t s rep resentat ion in the concept network. I n the context of the paral lel parki ng example, the situation of a. paral lel parked car is rep resented i n ternally in t he driver's concept network of d r i v i n g , and any sequence of operat ions that resul t s in t h i s representation is a description of parallel park i ng . However, i n i nterpret i n g t h i s d e s c r i p t i o n i n the envi ron ment. , by act ually performing the actions correspond i n g to the operators, i t might reveal i ncoheren cy. I n t hat case w e woul d say t h at t he descri ption was i n correc t . Ot herwise, if the i nterpretat ion of the description d i d result in the obj ect described, we would say that the descri ption was correc t , i rrespecti ve of whether the i nterpretation of the rest of the concept network is coherent or not .
So i f coherency i s correct ness, what i s truth? Observe that h ad I defined my concept networks in terms of relations, i nstead of operators , coherency
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woul d h ave come out as the Tarskian model t heoret ic notion of truth as correspondence. This suggests that tr uth is to relations as co 1Tecl n ess is to o p e ra t i o n s . I n other words, if the u nderlying algebrai c structure of a cogni t i ve system i s a boolean algebra, t hen a ' descri ption ' becomes a 'statemen t , ' and ' coherency' is ' t r ut h . ' As with correctness, I mean local coherency here also. T h at is, we can ask w hether a statement i s true or not , w i t hout considering whether t he i n terpretation of the w hole concept network i s coherent . Several i nteresti n g observat ions can b e made here. F i rstly, not i ce t h at the concept of correctness i s more fu n damental than the concept of truth i n that t h e concept o f truth does not apply, o r becomes mean i n gless , i n many s i t u ations w here correctness is st i l l app l i cable. For i n s tance, in the example of the scale mode l , or that of paral lel parking, one can not say that the model is false or the d r i ver's parallel park i n g maneuvers were fal se, w i t hout unduly stretching t he mean i n g of false. O n the other han d , the use of "The sky is cryi ng" to describe a clear sunny day cou ld be descri bed e i t her as false or i n correct. Cons i derations such as these have led some other researchers , i nclu d i ng Hesse [ 1 97 4 , 2 . I V . 3 , p p . 56-6 1 ] and B l ack [ 1 979, p . 4 1 ] , to argue t hat the con cept of correct ness i s broader , more u sefu l , and encompasses t he n arrower concept of truth ; and therefore, when t alk i n g abou t cogn i t i on , one shoul d use t he terms correct and i n correct rat her t h an true and false. T h i s con c lusion , i n t he l i ght of the analogy ' t r u t h i s to rel ations a s correct ness is to operations , ' rei nforces my P i aget i an assumpt ion that in cogn i t i on , the noti o n of operations is more fun d amental t h an the notion of relat ions. [ P i aget 1 953.] Secondly, i t must be emphasi zed here t h at coherency i n my accou nt does mean inte rn a l consist e n c y of a syst e m of symbols . I n fact, my n ot ion o f coherency is defined only for cogn i t i ve relations, and not for systems of s y mbols ( concept networks ) . This i s to say that my coherency invariably i n vol ves a correspondence bet ween el ements of t h e c o n c e p t network and parts of the e n v i r o n men t . I t is only an i n t er p r e t ati o n of a concept network i n au environment that c a n be coheren t or i n co h ere nt The concept c a n n ot be app l i ed to a concept network by i t self. For t h i s reason , my use of the term ' coherency ' i s more along the l i nes of Hesse [ 1 974 , Ch ap 2] , and not at all as M ac Cormac [ 1 985 , p p . 2 1 1 -2 1 2] views i t . not
.
.
F i n al ly, t h ough my view o f t r u t h also i n volves a correspondence w i t h parts of the environmen t , t here is a key d ifference between it and the Tarskian model t h eoret i c view of t r u t h based on correspondence. I n the model t heo retic view of trut h , though t h e symbols are al lowed to be i n t e 7'p re t ed d i fferent l y i n d ee d , t h e classi cal m o d el t heory was developed expressly to study t h e -
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characteristics of systems of symbols u n der d i fferent i nterpretations-the p ro cess of carrying out t he i nterpretat ion is not taken into consideration at all . T h i s , i n m y opinion, i s t he major factor beh i n d the i n adequacies o f all the at tempts m ade so far to come u p with a complete and satisfactory theory of tr u t h and reference that start out w i t h a Tarsk i an model t heoreti c approach . T h i s , of course, i s not to faul t the model t heory-i t was developed for a d i f ferent pu rpose and has a d i fferent role to p lay-but only i t s use i n cogni t i ve t heories of reference and truth . I n my accou n t , on the other han d , the p rocess of making a correspon dence between th e concept n etwork a n d the e n viro n m e n t is seen as a n a c t of cogn ition itself. Th is difference has two very i mp ortant consequen ces . O ne i s that every mean i n gful statement i s capable of being obj ect i vely correct or i n correct . This i s a point I shall elaborate upon in a momen t . The other consequence i s t hat the referent of any concept cannot be determi ned w i t h out changing the meaning of t he concept i n the process. For i nstance, i n deter m i n i ng the referent of ' water' the cogni t i ve agent must make causal connections w i t h cert ai n stuff in the envi ronment based on t he avai lable de scription of water. S i nce some of this stuff that tastes and feel s l i ke water m i ght later t u rn out to have a d i fferent chemi cal com posi tion , the mean i n g ' water ' h as been changed , unbeknownst to the cogni t i ve agent , i n determi n i ng i t s referent . ( See I n d u rkhya [ i n preparation] for elaboration of t h i s point . ) It i s i nteresting t o point out that the concept of 'truth' i tself does not h ave an unequi vocal meani ng in everyday language, as the fasci n at i ng study by S weetser [ 1 987] c learly demonstrates . She i n vesti gated t he concept of ' l ie' which, one m i ght s im ply say, means a false statement-only to d iscover t he complex of one's cult ural backgroun d , concept networks of i n format ion and com munication , concept networks of morali ty, etc . , t h at u n derlie its use i n normal everyday discourse. ( For instance, is i t ' lying' t o tell t he host how won derfu l the d i n ner was , even if one t hought it was aw fu l ? ) T h is accentu ates the fact that t here is no fixed correspondence b e t w ee n our concepts and the external wor l d , based on w h i ch all coherency ( an d trut h ) must be deter m i ned. A framework such as mi ne i s more eager to i ncorporate S weetser's observat ions by noting that truth depends on the correspondence between parts of the concept network and parts of the envi ronment , and t h i s corre spondence is determ ined by the cogni t i ve agent i t self, which woul d naturally reflect its cultur a l and i n d i v i d ual background.
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Underst anding vs . C orrectness
The d i fference between u nderstan d i n g a descri ption ( or a statement ) and j udgi n g it as correct or i n correct is easily settled . R ecal l t h at i n Section 2, I ar t iculated the view t h at to understand a descri ption i s to i m agine an experience in the i n termed i ate cogn i t i ve layers to w h i ch the description could h ave been applied. Moreover, the cog n i t i ve rel at ion formed i n u nderstanding a descr i p t ion respect s t h e autonomous struct u re of t h e i n termed iate layer ( wh i c h reflects the cogni t i ve agent 's past perceptual ex periences )-that i s , the cogni t i ve relation i s coherent . ( O t herwise, the descri pt ion i s dubbed anomalou s . ) When the experience i s no l onger i magi n ary but real , then t he notions of u nderstan d i n g an d correct ness begi n to coi ncide. I n other words, i f t h e p rocess of i nterpretat ion does not stop a.t a.n i ntermedi ate cogni t i ve l ayer , b u t goes all t h e way to the envi ron ment t h rough the sensori motor data set , then in understan d i ng a descri p t i on , we are act ual l y determ i n i ng i t s correctness. Consider i n g some exam p les will eluci date t h e d i fference bet ween under stan d i ng and correct ness . Take the statement " I t is snow i n g outside '' To u nderstand th is s t atem ent , you might i m agine a scenario of snowy weat her. To say t h at it i s correct , however , you wou l d need to look outside, and see if th e statement descri bes the s t i m u l i you are recei v i ng from the environmen t . Not i ce t h at t he correctness i s n o t estab l i shed b y m atch i ng t h e i m agi ned scene again s t the s t imul i . You might h ave i m agi ned a b l i zzard , whereas t here i s only a l i gh t snow a n d no w i nd outside. S o , the process o f i n terpretat ion must begi n all over, taking i nto account t h e i n formation bei ng recei ved from t he env i ronment, i n deter m i n i ng the correct ness of a descri ption . Take another example now. In understan d i ng " T h e sky is crying," you m ight i magine a percep t ual experience t hat cou l d h ave been d esc r i b e d by t h e statemen t , giving an u nconventional i n t erpretat i o n t o t h e c o n ce p t ' c ry ' i n t h e process. However, i n determ i n i ng whether the statement is correct o r not , you look out of the w i ndow , and see if the descript ion can be applied to t he s t i m u l i recei ved from the environment . A gai n , t h e concept 'cry' must be i nterpreted u nconvent ionally. A l i teral - m i nded person , on t he other han d , u n w i l l i n g to i nterpret 'crying' unconventional ly, m i g h t dec l a re th e statement anomalous; or she might fantasize a. real m i n w h i ch the sky i s l i teral ly cry i ng, and thus ' u nderstan d ' the statement , b u t , look i n g out the w i ndow when i t i s g rey a n d rai n i n g outside, decl are i t i n correct . T h i s ac c o u n t of determi n i ng correctness i s somewh at s i m p l i s t i c . M any of we t ake to be ' correct ' are not based on d i r ec t observat ion, as I i m p l ied above. �or i nstance, you m i ght correc t l y k now t h at i t i s rai n i n g outthe t h i ngs
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side because someone j ust came t h rough the door w i t h a dri pping umbrella. M uch of our k nowledge comes i n d i rectly from books, newspapers , and other media. This feat ure can be i ncorporated i nto my account by noti cing that cer tain real m s in an i ntermedi ate l ayer can be dubbed ' correct . ' We read a descri ption , say i n a newspaper story, a h i stori c accoun t , or an encyclopedia, and u nderstand it by creat i n g a derived realm i n an intermedi ate cogni t i ve l ayer . This deri ved real m can then be l abeled ' correct , ' i f we h ave reasons to believe t h at the aut hor of the descri ption h as verified the descript ions in the environment. Now any i nterpretation t h at i s coherent in this realm woul d be consi dered correct , as i f i t were coherent w i t h respect to the environment . 8. 3 . 3
C o nve nt io nal and Met aphorical C orrect ness
With the d i fference between u nderstanding and correct ness cleared away, let me recap i t u l ate what it means to say t h at a description or a statement , l i teral- conventional or metaphori cal , i s correct or i n correct . A part of the concept network that contai n s the description i s i nterpreted i n the realm via all the i ntermedi ate l ayers. This i n terpretat i on can be li teral- conventional or metaphori cal ; t h i s i s not crucial . O n ce the i nterpretation h as been decided on, t hen one can test to see w hether the description i s coherent w i t h respect to the i nterpretat ion or not . This i s what determines the correctness . S i m p l e as t h i s account of correctness is, i t i n corporates many of the obser vations m ade on the nat u re of truth and correctness, both literal- conventional and metaphorical , by previous scholars. I woul d l i ke to note a few i mportan t connections here . My view o f correctness, and we h ave seen t hat t r u t h i s a speci al case of correc tness, sees t h e same mechanism u n d erlying l i ter a l - c on v e nt ion al and metaphorical descriptions. In t h i s respect I am i n com plete agreement with B i n kley [1974] , Goodman [ 1 976, p . 79] , Lakoff & Johnson [ 1 980, C h . 24] , and H i n t i k ka & S an d u [ 1 990, p . 72) . A s this i s also a m aj or point of difference between my view and that of m any other scholars , such as M ac Cormac, it woul d be useful to elaborate upon it some more .
Notions of truth and correctness presuppose an on t o logy. Something can be t ru e or false, correct or in correc t , only w i t h respect to some perspective. And t h i s perspecti ve is determi ned by the c og n i t i ve agent i n establishing a c or re s p o n d e n c e between parts of the concept network and parts of the environment , t h ere by giving an ontology to the environmen t . This corre spondence might be composed of only the conventional inter p retations that
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the cogn i t i ve agent is h ab i t u ated to ( as in i nterpret i n g "It is snowing out s i de," ) only the novel metaphorical i nterpretations that are deri ved by using the mechanisms descri bed i n Chapter 7 [§7.4] ( as i n i nterpreti ng the Mon drian ) , or some conventional and some metaphorical i nterpretat ions ( as in interpreti ng Boland's and Spender's poem s ) . A description or statement is made refe rential in m ak i n g such a correspondence. And it is only after mak ing a descr iption referent ial that we can determine whether it is correct or not . However, once the correspondence i s estab l i shed , by whatever means, the mechani s m for determi n i ng coherency does not depend on w hether the i n terpretation i s conventional or metaphori cal . l n other words, the mechanism for determi n i ng correctness i s t he same for metaphorical descri ptions as for conventional descr ipt ions, echoing the thoughts of B i n k ley : " [ I ] t is necessary to keep separate the two different act i v i t ies of estab l i s h i ng the truth and es tablishing the mean i ng of an expression . A l t hough l i teral and metaphori cal sentences h ave d ifferent types of meaning, when they are used to make claims t h ose c l a i m s can be t r u e or fal se i n rough ly t h e s a m e way, i .e . , without t he mediat i o n of an addit ional expression of thei r mean i n g . " ( From p. 1 50 i n Johnson [ 1 98 1 a] . ) O f course, i n i nterpret i ng a concept network metaphori cal ly i n a n envi ronment , since t here i s no generally acc e pt e d i nterpretat ion of the concept network in that env i ronment-i t wou l d not be metap h ori cal otherwi se-t here i s p lenty of room for vagueness and wide vari at ions among i n d i v i d u al i n terpretations. It i s t h i s characteristic that ca.uses metaphors somet i mes t o miscommuni cate a n d t h e i r mean i ngs to be vague. However, t h i s happens t o l iteral i nterpretat ions a s wel l . ( See K am p [ 1 98 1 ] a n d Scheffler [ 1 979] for a di s cussion of some i ssues surrou n d i n g ' vagu e n ess ' in l i teral u se of the language. ) T h e r efore , any attempt to d i s t i nguish the l i teral from the met a p h ori cal on the b asis of vagu en ess-and I a m a l l u d i n g to M ac Corm ac ' s u s e of fu 'lzy set t h eory to characterize metaphors here-i s not l i ke l y t o be very fr u i t fu l .
T h e final point t o be highlighted here is that i n m y account a l l meani ng ful statements are capable of o bject ively bei ng correct or i n correct-or true or false, i f one i s w o r k i ng w i t h a concept network h av i n g a rel at i on al s t r u c t ure . Here, by the term 'obj ect i ve ' I mean referri ng to the external world somet h i n g t h a t cou l d b e ver i fied i n tersubj ect i vely. O f cou rse, the cor r ec t nes s must be d e c i ded w i t h respect to t h e ontology c r e a t e d by i nstantiat i ng t h e t h eory or t h e concept n e t w o r k i t se l f. For i n s t a n c e , Gentner and Gentner [1 983] s t u d i e d two models, t eeming crowd and _flo wing w a t e r, t h a t people use to u n derstand and reason abo u t e l e c t r i c i ty. They noted that the t eem i n g
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crowd model is correct for mak i n g certai n pred i ctions about electri cal sys tems, and the flowing water model i s correct for some other predictions. Of course, t here are characteri s t i cs of electricity t hat both models p redict cor rect ly and characterist i cs that neither one does . However, t h i s correct ness or i n correct ness is an objective matter. It is the autonomous structure of the external wor l d , m ade visi ble by giving i t an ontology w i t h the concept networ k , that m akes the model i n correc t , if it does not respect the struct ure of the concept network. Thus, my sense of 'objec t i ve' here i s d i fferent from the way Lakoff uses it i n liteml4 and i n h i s characterization o f the l i teral mean i n g t heory ( Section 2. 4 ) .
Lakoff i s using i t t o mean not j ust 'being able t o be verified i ntersubj ecti vely' but to also i nc lude ' t he one and only correct way to describe real i t y. ' For i nstance, he used the exam ple from Gent ner & Gent ner [ 1 983] to argue t h at these two models are not capable of being obj ecti vely true or false: " [ B] ecause we have no obj ec t i ve way of knowing w h at elect r i c i ty ' real l y i s , ' t hey are not l i teral 4 . I n fac t , the fluid metaphor and the crowd metaphor h av e i n consistent ontologies. Both m e taph o r s cou l d not both be o b j ec t i vely t r u e , because fl u i d s are cont inuous and crowds are i n d i vid uated . " [Lakoff 1 986, p . 295] I, on t he other hand, woul d argue t hat both the models a.re capable of objec t i vely being t rue or false. Th i s , of course, i s merely a termi nologi c a l d i fference, for La. k off woul d quite agree w i t h me on the objecti vity of metap hors-wi t h the term 'obj ect i ve' being used in my sense. S t i l l , I feel t hat i t is i m portant to clarify t h i s point , lest a needless cont roversy l i ke the l iteral- metaphori cal d i chotomy ensue. From t h i s
p e r s p ec t i ve , i t i s easy to see h o w t w o persons m i g ht d i sagree
about whet her " N i xon is a halo s ur r o u n d i n g a vacuu m " is c o rre ct or not , w i t h each maintai n i ng that the m atter i s an objecti v e one. ( A n d each of t h em wou l d be u n derstan d i ng the statement m e t a p h o r i c a l l y , s i n ce declari ng it i ncorrect based on a l i teral understandi ng of it woul d be explai ned as in t h e previous sect ion . ) The difference between t he t wo l i e s i n t h e ontology g i ve n to N ixon 's actions during h i s pol i t i cal career by group i ng them in order of their sign i fi cance. To one. theses actions are all i nsignificant , so she sees a vac u u m t here. To the o t h e r person , many of h i s act ions were q u i te significan t , so, alt hough she u n derstands t h e vac u u m m e ta p h o r , it does not agree w i t h what she s ee s a s t h e actual s t ate of the environmen t . Both persons ar e objec t i vely correct , and t here is no cont radiction there, because eac h of t h e m i s v i e w i n g the worl d with a . d i fferent ontology, even i f t h ey use the same wor.d - p e r h a p s
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not u n l i ke Lakoff a n d M ac Cormac. I n d eed , i t is o n l y when one forgets t hat words do not have an intrinsic mean i ng t h a t they become tyran ni cal , as C h ase [ 1 938] h as argued so wel l .
8.4
Aptness ( Q uality) of Metaphor
There is anot her characteristic of metaphor-variou sly referred to as aptness, compel l i ngness, or qu al i ty-th at characteri zes the fact t h at certai n m e t a p hors seem more compell i n g than ot h ers . In the begi n n i ng of the chapter, I mentioned Q u i n n ' s example of t h e i c e cream m et a phor for m arri age (you can eat it all at once, or m ake it last a long ti me) t h at is m e a n i ngf u l ( m ight even b e cons idered correct ) but wou l d be consi dered a very poor metaphor by most people. \;\Th at m akes a metaphor more compell i n g t h an another? Many psychol ogists h ave studied t h i s question empirical ly, and h ave com e up with differ e n t ways of characterizing metaphoric quali ty. For i n stance, O rtony [ 1 979; 1 979a] ch arac t e r i zed metaphoric q u ali t y i n terms of the sal ience of the at tributes t ra n s ferred from t h e source t o the t arge t : a good metaph o r uses h i ghly s a l i en t att r i b utes of the source to h i gh l i ght l e s s sal i e n t att r i b u tes of the t arget . Johnson and Malgady [ 1 980] con c l u ded t h at a m etaphor is j udged good when it is easily i n terpretable and when t h ere are m any interpretations. T hough I co n s i d er the quality of metaphor essen t i al l y a p ragm at i c issue whether a metaphor i s j u dged good or bad depen ds on w h a t the i n t e n t of t h e metaphor i s , I woul d l i ke to make some general observat ions regard ing how d i fferent factors affect the qual i ty of a. metaphor in my accou n t , and how these factors are rel ated t o others ' ch aracteri zat i o n s of aptness . Before un dertaking this t as k , I must poi n t o u t t h at t h e q u al i ty of a m etaphor h as n o t h i n g to do w i t h w h e t her the m e t a p h o r i s co r r e ct (or t r u e ) o r not. The i ce cream metaphor for m a rr i age m ay well b e correct u n d e r a certai n i n t e r p retat i o n , but i t still remai ns a poor metaphor . O n t h e o t h e r h an d , a n ad m i rer of N i xon m i g ht g i ve hi g h m ark s fo r t h e q u a l i t y of " N i xon is a h al o s u r r o u n d i n g a vacuum" metaphor ( t h e i dea t h at a p e r son can be ' a. h a l o s u r rou n d i n g a vac uu m ' i s certai n l y q u i t e i nteres t i ng and n ovel ) , b ut sti l l deny that the metaphori cal descr i p t i o n app l ies correctly to R i ch ard N i xon . Let me now 1.
l i s t some factors
t h at
can
affect t h e q u a.l i ty
of
a
m e t a. p h o r :
Th e d egree of co n v e n t i o n a li t y of the in t e rp re t a /. io n : I h ave characterized me t a p hor as an u n conventional i nterpretat ion of a con c e p t network i n a. real m . C learly, if the i n t e rpr et at i o n is conve n t i o n al , i t i s not m et aphor-
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2 . Th e degree to which the target is m a de t o look sim ilar b y the s o u rce: C learly, a metaphor i s much better i f a l arger part of the source concept network can be i nterpreted in the t arget real m . A s any interpretation res ul ts in mak i n g the t arget real m look s i m i lar to the source, it means t hat the more the s i m i l arit ies t here are between the source and the t arget ( t hese are s i m i lari ties aft e r the m e taph o r has been u n d e rstood) the better the metaphor . While t h i s role of s i m i l ar i t ies i n affect i n g metaphori c qual i ty h as been demonst rated by many scholars (see Malgady & Johnson [ 1 980] ; Mc Cabe [ 1 983] ; and ' w i t h i n-domai n ' s i m i larity criterion of Tourangeau and Sternberg [ 1 982] ) , most of t hese s t u d i e s do not d i s t i ng u i s h b et we e n s i m i larities before an d after the m e t ap h or. I n fact , with the exception of McCabe, t hey all t ake a stat i c view of metaphor i n t h at the given representations of the source and the t arget never change as a result of understan d i ng the metaphor. Not surprisingly then, such studies con e ! ude that the source and the target ( concept networ k s ) must be s i m i l ar prior to the metaphor, i n order for the metaphor to be compelling. McCabe, who did make a disti nction between s i m ilari t ies before and af ter the metaphor, fou n d t h at when metaphors are p resented i n i solated for m u l a i c c o n te x t s ( w h i ch i s how most o t her s t u d i e s p res en t e d meta phors ) , t h e n t h e q ual i ty of metap hor is s i g n i fican l l y related to ' before s i m i larit ies ' be t wee n the sou rce and the t arget . However, w hen m e t a phors were p rese n t ed i n an extended context ( i ncluded i n a l arger body of te x t ) , there was l i t t l e or no correl ation between ' before s i m i l ar i t ies ' a n d metaphoric quali ty. ( See also the discussion in Chapter 2 [§2.3] . ) 3 . Th e degree of difficulty in inte7'p 7·eting the m e t aphor: I t has been p ro p osed t h at the easier it is to interpret the metaphor , the better t he metaphor. [John son & M a lg a d y 1 980; K at z , Paivio & Marschark 1 985.] However, w hat m akes a metaphor easier to i n terpret ? O r, to use my term inology, when i s a c o n ce p t network easy to i n t e rpre t in a real m ? There a r e two t h ings that c a n affect the ease o f interpretation . O n e i s t h at i f the target realm i s such t hat no m atter how i t i s descri bed ,
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and how its ontology i s changed , i t j ust does not fi t t h e struct u re of the source concept network , t hen the metap h o r will be d i ffi c u l t to i nterpret . ( Recal l t hat the target real m has i t s own auto n o m o us structure. ) S uch m ight be the case w i t h Johnson and M alga. d y 's exam ples l i ke "Hair is a ship." T h e other t h i ng affecti ng the ease of i nterpretation i s t h a t , assum ing t h at d i fferent p a rts of the source concept network have d i fferent saliences, and t h at the cogn i t i ve agent starts out by trying to i nte r pret the h i gh l y salient parts first , i t fol lows t hat i f the h i g h l y salient parts of the concept network are getting i nterpreted , t h en the metaphor is easier to i nterp r et . Thus, the " B i l l boards are warts" m et a pho r ends up being easier to i n terpret ( ugl i n e ss b ei n g a h ighly salient property of wart s ) , than "The h ighway is a r ope " ( w i t h t he i n te n ded m e a n i ng t h at the w i n d i ng h i ghway i s l i ke a coi le d rope ) , for b e i ng coiled is a less salient property of the rope. ( See O r tony [ 1 979; 1 9 79a] ; and the 'extreme val ue of the t ransferred attri bute of the veh icle' cri terion of Tou r a n g e au & S t e r n b erg [ 1 982] . )
4 . Th e ope n - e n dedn ess of the meta p hor: A m e t ap h or is c o n s i dered more com p el l i ng, if it can be i n terp reted i n more t h a n one way ( as in t h e metaphor of Bo l and ) . A n d when t here i s an u n am biguous core i nter p retat ion of the metaphor ( as in "The sky i s c r yi n g " ) , then a metaphor is more compel l i n g i f t here i s am ple roo m fo r e xt e n d i n g the core i nter p re t a tio n by subject i vely i n t e r p r e t i n g other parts of the concept net work in various ways. This is because d i fferent people h ave d i fferent perceptual e x perien c es w i t h the t arget , and c h oo s in g a concep t network t h at allows different people to i nterpret the co n cept network in t hei r own ways heightens t h e emot i o n al a n d personal val ue of t h e metaphor . Moreover, i f t h e same pf'rson can i nterpret t h e melaphor i n d i ffe re n t way s , t hen t h e mean i n g of t h e metaphor i s e n r i ched , for l h e m e t a.phor s e e m s to be s ay i n g all t h o s e different t h i n gs at once. If t he t arget realm i s not M o n d r i an ' s p a i n t i n g ) ,
ex p l i c i t ly
suppl ied
by
then t h e m e t a p h o r b e c o m e s
the
metaphor
( as
in
even more appeal i n g
( i f i t i s u n de r s t o o d at a l l ) , since now d i fferent p eo p l e can choose thei r own real ms, and i n t e r pre t t h e meta p h o r i n t hes e real m s i n the i r own way (or t he same person can interpret the me t a phor in d i fferent r e a l m s i n different ways ) . Thus, the more i n terp ret at i o n s a. metaphor h as, t he b ett e r i t seems. [Johnson & Malgady 1 9 8 0 . ]
5.
Th e s t m c l u ra l rich n ess
of tha t part o f
is i n t e rp re t e d b y th e m e t aph o r:
I n ot ed
t h e s o n 1'Ce
i n t h e l as t
t n e t wo rk tha t a p t e r [§7.4. 1 ] that
co n ce p ch
312
Part III: The Implications a syntacti c metaphor allows t he cogni t i ve agent to reason about the less fami l i ar target realm by using the more fami l i ar source concept network ( as in analyzing the mechanical systems as electr ical circui t s ) . S i nce i t i s t he operational structure of a concept network that provi des an abi l ity to reason and m ake predictions about the environment , t h i s suggests that the more structural l y r i c h the source concept network i s ( actually, t h e part o f i t that i s i nterpreted i n t h e target real m ) , the better the metaphor. [Gentner 1 983.] Here I am strictly referri ng to t he role of metaphor i n w h i ch one al ready has sufficient knowledge of t he target real m in t he target concept network , for it is t h i s k nowledge that i s used in ascertai n i ng which part of t he sou rce concept network can be successfully applied to the t arget realm . ( T h i s knowledge, of course, m ight resi de i n t he teacher, who deci des to explai n a new concept to the students by using an analogy from a concept fam i l i ar to the student . )
6 . Th e cognitive information g e n e ra t ed b y the m etaphor: The most i m por tant role of metaphor in cogn ition m ight well be to reclai m ( part i ally, of course ) some of the i n format i on t h at was lost in c o gni t i z a t i o n ( i n reduc ing the detailed world of sensori motor data set to a handfu l of concepts and categories ) . From this perspec t i ve, it seems that t he more new i n format ion generated b y t he metaphor, t he better t h e metaphor . Thus, ' pai nting as pumpi ng' i s a better metaphor than ' painting i s a m asking surface. ' Or 'j acki n g mechan i s m as the Indian rope trick' i s a better metaphor than 'j acki ng mechan i s m as a biologi cal system . ' [§2.6] Even when the metaphor does not generate any new i nformation about the target ( as in s y nt ac t ic m e t a phors) , it can still h ave cog n i t i ve val u e i n highlighti ng subtle feat ures of the target real m ( features that are, nevertheless, i n cluded in the t arget concept network ) . For i n s t ance , O rtony [ 1 979; 1 979 a] noted that a m e t a p h or works by highlighti ng less s a l i e n t at t r i b u tes of the t arget , as in " H i gh w ays are snakes ." If the at tribute of t he target highlighted by the metaphor is a l r eady highly salient , as in "Encyclopedi as are d i ct ionaries ," t hen t he statement be comes what Ortony referred to as ' l iteral comparison . ' Tou rangeau and Sternberg [ 1 982] have also suggested a related factor, cal led t he ' between- domai n s ' s i m i larity between the source and the tar get , t hat is i n versely related to the quality of a meta p hor. Between domai ns s i m ilarity is taken to be a measure of how semantically dis tant the domai ns are. The more d istant the domai n s , the better the metaphor. Thus, "The shark is the hawk among fish" would be con s i d-
Chapt er
8:
Metaphor-Related Issues
313
ered a less compell i n g metaphor than " N i xon is the su bmarine o f world leaders ," because the domains of ' b i rds' and ' fis h ' are less distant than the domai ns of ' world leaders ' and 'ocean vessels . ' On e can view the between-domai ns distance between the domai n s as the semantic di s t ance created by our cogni t i ve apparatus i n categorizi n g the environ ment . When a . metaphor successfu l l y l i n k s two d i sta.n t domai n s , then i t effect i vely amounts t o sugges t ing a n alternate semantic metric i n which the t wo domains are act ually quite close. T h u s , the m o re d i stant the t wo domai n s , the more i s the surprise in real i z i n g that they cou ld be represented as much closer, and the more i s the cogni t i ve information generated by the metaphor. A point must be emphasized with respect to the l ast factor l isted above n amely that w h at ( an d how much ) cogni t i ve i n formation is generated by a metaphor ( an d hence the quality of the metap hor) can be determ i ned only afte r th e m etaphor has been assimi lated . There i s no way to tel l from look i ng at the source and the t arget concept networks before the metaphor is p re sen t e d whether t h e m e t ap h o r w i l l come out as i ns ightful or mun dane. A n u m be r of scholars combi ne t h i s fac tor affect i n g rnel a p h o r i c q u a l i ty with the one p receding it ( s t r u c t u ral richness of the source ) , lead i n g t hem to conclude t hat if a metaphor t ransfers structurally ri cher parts of the source concept network to the t arget concept network , then it i s also more l i kely to prov i de new cogni t i ve i n formation about the target real m . [Gent ner 1 983.] This i m mediately t u rns metaphor i nto what l h ave termed pred i c t i ve analogy [ § 1 . 6 . 2] . While I d i scuss predict i ve analogy at length in Chapter 9, I must, once more, emphas ize that my notion of metaphor does not cover pred i c t i ve analogy i n any way, an d , t herefore, T do not need to address the p r edic t i v e abi li t y that some scholars i m p u t e to metaphors. A s a p aren t h et i c remar k , let me add t h at my framework of c og ni t i o n does i n clude a notion of p red i c t a b i l i t y, which should not be confused w i t h predictive an alogy. Tf y ou put t w o marbles i n a box , a n d t hen put i n t h ree more, then you can predict that t here are five marbles i n the box wi thout actually emptying out t he box and coun t i ng the m a r b l e s . I t i s the opera t ional struct u re of a concept network , the natural n u m ber system with the operation of add i ti on i n this case , t h a.t m akes i t po s si b l e to m ake this predic tion u nder a certai n i n t erpre t at i o n . Of c ou r s e , t h e pred i c t i o n m i ght or might no t turn out to b e t r u e -i t m i g ht be a magi cian 's box w i t h a false bottom d e p e n d i n g on whether the autonomous s t r u c t u re of t h e e n v i ronment respects t h e s t ruct ure of t h e concept network or not , a property t h at f h ave been cal l i ng ' coh e ren c y. ' T h i s sense of pred i c t ab i l i ty, however, is quite di fferent from
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the way predi c t i ve power is i mputed to metaphors in predi c t i ve analogy. For , a s I show i n Chapter 9, i n predi c t i ve analogy, a certain characteri s t i c of con cept networks-namely, t hat the source and the target concept networks are struct urally s i m i l ar-is tied to the structure of the environmen t , someth i ng that blatantly violates the structural autonomy of the env i ronment t h at I have been emphasizing throughout my account. Thus, as far as prov i d i ng an answer to the question "Why do certain metaphors provide il l u m inat ing i nsights while others do not ?" in terms of the characteristics of the source and the t arget concept networks, I must essentially concur with Black : "There is, in general , no simple 'groun d ' for the necessary shifts of meani ng-no blan ket reason why some metaphors work and others fai l . " [ B l ack 1 962, p. 45] Metaphor mus t , t herefore, remai n to us a remi n der of t he l i m i t s of cogn i t ion w i t h our finite m i nds in an i nfini tely complex world.
Chapter 9 O n Pred ictive Analogy and Ind uction
9.1
Introduction
In Chapter l [§ 1 . 6 . 2] , I i denti fied a sense of ' an al ogy ' t hat i s used to refer to t he process of predicting further s imilarit i es bet ween two objects or sit u ations, given some exi s t i n g s i m i l arities. I h ave been cal l i n g t h i s mode of analogy p redictive a n a logy, bu t it is also known as a n a logical reason ing, a n a logical infe re n ce , and argu m e n t b y a n alogy. Fo r instance, given that one h as j ust bought a 1 987 Toyota Celi ca for $6000, on hear i ng that a close friend i s consi derin g b u y i n g a 1 987 Toyota Celica also, pred i c t i ve analogy leads h e r to expect t h at the friend will spend around $6000. Or, on finding out that the p lanet Venus has several characteri s t i cs in common with Earth , predi c t i ve analogy woul d suggest t h at Venu s is i n habited also . In each of the above examples , pred i c l i ve analogy i m ports fca.t. u rt's from a more fam i l i ar o bj e c t or s i t u ati o n , usu al l y referred to a s the soune, to a l e s s fami l i ar one, u sually referred to as t h e target. I n t h e fi r s t e x am p l e , the subj ect 's own automobi le is t he source, the automobi le t h at the friend i s c ons i d er i n g to buy i s the target , and the feature i mported from the source to the target is the cos t . S i m i larly, in the second example, Earth is the source, Venus is the target, and the state of being i n h ab i ted is the i mported feat ure.
ought to be clarified from t he outset t h a t a conclusion drawn from is seen as justified a n d not necessari l y t r ue . That i s , in some p sy c h o log i ca l sense or p ro b a b i l i st i c sense a c o n c l u s i on from analogy is c o n s i d ered more rat i on al or more l i kely. J u st i ficat ion is i n dependent of It
p r e d i c t i ve an al o gy
315
316
Part III: The Implications
t ruth-a true statement can be u nj ust ified an d a j ustified statement can be fal se-and the two should not be confused with each other. All through this chapter, I am only concerned w i t h the j ustification of predictive analogy ( an d i n d uction ) , a n d n o t a t a l l w i t h its truth . Notice t h at a con clusion derived from predictive analogy is not a logical i n ference. I n other words , an argument from predictive analogy cannot be logi cally dedu ced from the existing knowledge of the source and the t arget . Thus, pred i c t i ve analogy makes possi ble n e w k nowledge beyond the logical l i m i ts of the exi s t i n g knowledge, and t herei n lies the l u re of predictive anal ogy. I ndeed , phi losophers, cogn i t i ve psychologists and artificial i ntell igence re searchers have all taken the bai t of predictive analogy. Philosophers have t ried to formulate elaborate m athematical systems to show why an i n ference from pred i c t i ve analogy is more p robable. Cogni t i ve psychologists h ave tried to provi de empi rical evi dence to show how predictive analogy i s a valuable p roblem-solv i n g heuri s t i c . Some art ificial i ntelligence researchers have em b raced pred i c t i ve analogy w hole- heartedly by design i n g c o mp u t at i on al sys t e m s that , on encou ntering a new problem , work by r e c al l i n g some fam i l i ar problem ( t he sol ution of w h i ch i s know n ) t h at is similar to the new prob lem , and then applyi ng the solution of the familiar problem , as it is or in a modified for m, to the new problem . G i ven the promi nence enj oyed by p redictive analogy, and given my re peated emphasis t h at my characterization of metaphor does not cover p re d i c t i ve analogy in any way, it is necessary now to analyze p redictive analogy in more detai l , so tha.t my reasons for disti nguishing it from metaphor can become clear. This i s my mai n obj ect i ve in this chapter. I
be g i n , i n Sect ion
2,
by articulating i n
more detai l exact ly how predic
modes of metaphor [§7.4] . I here t hat i t i s the process of s u ggest i ve (open-ended ) metaphor that comes closest to p redi c t i ve analogy, but t here is o ne b ig difference: predi c t i ve a nalogy carries the aura of 'j ustification , ' whereas suggest i ve metaphor does not . I argue at the end of this section that this difference is quite significant because it is t he 'j ustificat ion ' t hat adds luster to predictive analogy, and m a. k es it an attract i ve problem-sol ving heuristic. ti ve a n a l o gy d i ffer s from each of t h e d i ffere n t
s how
The next problem then i s to provide some grounds for the j usti fication of pred i cti ve analogy. This p roblem h as been at t ac k e d o n two fronts . One has been to prov i d e s o m e logical j u s t i fic at io n for predictive analogy by show i ng t h a t an i n ference from predictive analogy is m o re probable than, say, a random i n ference. The ot her has been t o s h ow empirically t hat predic-
Chapt er 9: Predictive Analogy and In duction
317
t i ve analogy plays a significant role i n creati ve problem sol ving, i n cluding scienti fi c break t h roughs . In Sections 3 and 4, I take a crit i cal look at both t hese l ines of research , and show that neit her one bas succeeded i n validat i ng pred i c t i ve analogy. As the believers in predi ctive analogy only present those examples where an inference from p redictive analogy is j ustified ( for some other reason ) , the ' dark ' s i de of predictive analogy is rarely seen . To put predictive analogy and i t s role i n cogni t ion i n proper perspecti ve, i t is necessary that the dark side of pred i ctive analogy be exposed also. I m ake an attempt to do so i n Section 5 b y p resent i ng some arguments from pred i ct i ve analogy that might seem psychologically compell i ng but are not rationally j ustified. H av i ng seen both si des of predictive analogy, I present , i n Sect ion 6, w h at I consi der a balan ced perspecti ve on predi ct i ve analogy and i ts role in cognition. I argue here that p redictive analogy i s best seen as a cogni t i ve p rocess t h at i s as l i kely to lead to i l lu m i nat i ng i nsights as i t i s to ' close' our minds by blocking crucial i n formation com i n g from the environ ment; and that it is as l ikely to b e a l i ab i l i ty as an asset to cogni t i on . The b i g brother of pred i c t i ve analogy i s the process o f i n d u c t io n . O n having encountered a certain regularity i n the environment o n numerous past occasions, i n d u ction allows one to j ustifiably conclude t hat the regul arity w i l l also be observed on all fut ure occasions. I ndeed , m any schol ars see predictive analogy as not h i ng but a part i cular man i festation of t h e more gen e r a l process of induction. The sign i fi cance of the role played by predictive analogy i n cogn i tion i s overshadowed b y t h e significance o f i n duction . Theories that have attempted to provide a j ustification for predictive analogy h ave been far fewer than theories of i nduction . Moreover, many t heories of an alogy are, in fact , corol l aries to more com p rehens i ve t heo r i e s of i n d uction .
The close con n e c t i o n b etween pred i c t i ve a n a l ogy a n d i n d u ct i on i s , how e ve r , a two-way street . lf it can b e u sed to apply t h eo r i es of i n d u c t ion to t h e problem of j u s t i fication of pred i c t i ve analogy, i t can also be used i n t h e reverse d i rect ion-to e x t e n d t h e i n s i ghts i nto p re d ic t i ve a n a l ogy to the pro cess of i nduction . This is exactly what I set out to a c h i eve i n t he rest of t h i s chapter.
To begi n w i t h , I bri e fly discuss the background to the problem of i nduc Section 7 . In the section fo l l owi n g t h at , I argue t h at a n y a t t e m p t to provide a fou n d at i on for i nduction by u s i n g probab i l i ty theory i s v u l n er ab l e to a generalized ve r s i o n of G oodman 's ' gruc' p a r ad ox . T h e n , i n Section 9, I present some exam ples of w h at I co n si d e r to be u nj usti fied u ses of i n d u c t i on , to show that i n d u c t ion , like p red i c t i ve a n a l o gy, can also be abused . Finally,
tion in
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Part III: The Implications
in Section 1 0 , I extend my perspect i ve on predictive analogy that was l ai d out i n Section 6 , to t h e process o f i nduction .
9.2
Predict ive A nalogy and Metap hor
Before we can compare predictive analogy with my modes of metaphor, it i s necessary to reformulate t h e p rocess o f predictive analogy i n t h e context of my framework . This t as k i s somewhat non-trivial because, with the exception of Holland e t a l . [ 1 986, Chap . 1 0] , nowhere, i n all the l iteratu re on predictive analogy I h ave seen, i s a dist i n ction m ade between an object ( environment ) and i t s representation ( concept network ) . A s this distinction lies at the heart of my framework , in order to relate metaphor with predictive analogy we must first decide whether the ' source' in predictive analogy refers to a concept network or an environment , and the same for the t arget . Recal l that i n pred i ct i ve analogy, one notices that the source and the t ar get have some properties i n common and t hat the source has some addi tional properties; and from t h i s one concludes that t h e t arget h as t hese ad d i t i o n al propert ies as well . Keeping i n mind t hat , i n my framework , an environment is not accessi ble to the cogn i t i ve agent except via some concept network , i t becomes obvious that the source could not possibly b e a n environment . S i n ce the cont ribut ion of t he source to the process of predictive analogy is to supply properties , it must necessarily be the ' source concept networ k . ' The t arget , however, i s another matter . I t supplies properties t o establi sh t he precondit ions of predictive analogy, a n d t hen ' recei ves addi tional prop erties' from the source. Though the former role must necessarily be played by t h e concept networ k , t h e latter fun c t i o n can equally well be c arried out by
the conce p t network or the environment .
A n example m ight be hel pful here. Consider the source as army m aneu vers to capture a fortress , and the target as use of electromagnetic radiation to dest roy a tumor: an example from G i ck & Holyoak [ 1 980] that I i ntroduced in C hapter 7 [ §7. 4 . 1 ] . The p recond ition of predictive analogy-existing similari t ies between army maneuvers to capture a fortress and use of electromagneti c rays t o d e s t r oy a t u mor-is es t a b l i s h e d b y co m p ar i n g the respective concept networks. One notices t hat in approachi ng the tumor by electromagnetic rad i at i o n , a c o n t a c t w i t h t h e su rrou n d i n g heal t h y tissue should b e avoided, j ust as i n approaching the fortress the army s h o u l d avo i d any contact with land-mines . This simi lari ty can be comprehended by examining t he two con cept networks, si nce the relevant fact s m u s t b e t here if t h e cogn i t i ve agen t
Chapter 9: Predictive Analogy an d In du ction
319
t h at i s reasoning from predictive analogy knows them a t all . Note t h at there are similarit ies as well as dissimi l ari ties. The healthy t i ssue surrou n d i ng the t u mor m u s t be p rese1·ved, but the m i nes surrounding the fortress are to be destroyed or neutral i zed. However, i t is the simi l ari ties t h at m ake the process of predictive analogy applicable. Once the p rocess of predictive analogy i s evoked , based on the observed simil arities between the source and the t arget concept networks, the cogni t i ve agent concludes (or hypothesi zes ) t h at the source a n d the target might be similar in other respects as wel l . In the example above, the cogni t i ve agent m i gh t conclude that given t h at t he army can be d i v i ded i nto several small u n i t s and be m ade to converge on the fort ress simul taneously i n order to capture i t , the same approach might also be used to destroy a tumor with electromagneti c rad iation. A ny property of the sou rce t h at the cognitive agent selects to apply to the t arget must agai n be a part of the source concept network, since otherwise the cogni t i ve agent cannot be said to h ave known the property at all . I n applying t h e add i t ional source property t o t he t arget , there are two possibilities. The fi rs t i s to merely check t h at t h at the property i ndeed holds in the t arget by exam i n i ng one's know ledge of the t arget environ ment ; that i s , by checking to see i f the property is either already i mplied by the tar get concept network or definitely contradi ct s i t . In the above example, the source concept network suggests t h at i t is possible to send decoys to detonate m i nes, after which the army can proceed to capture the fortress. However , the existing struct ure of the t arget concept network rules out transferring this property-t he healthy tissue needs to be preserved and ought not to be d es t royed . Notice that when the additional property of the source concept n et work i s m erel y app lied to the t arget c o n c e p t networ k , t h e process p r o d u ces n o th i n g new b eyond what is already i n c l u d e d in the t ar get concept networ k . For t h i s reason , it can h ar dly b e said to b e ' p re d i c t i ve . ' The second-and more i nteresti ng-case i s when it cannot be es tab l i s h e d by j ust looking at the t arget concept network whet her the add itional property from the source concept network i s d efi n i te l y present t h ere , or definitely contradicts some k nown fact in the t arget concept network . In other words, t he property t ran s fe r r ed from t h e source concept network i s consistent with, but not i mplied by, the structure of the t arget concept n e t work . In this case, t h i s p r o p ert y from t h e source con cept n et wor k must be op e r at i on a lly tested i n the t a r ge t environmen t , w h i c h , by virt ue of its au to nomou s s t r u c t u r e , can accept or rej ect t h e property. In s i t u at ions like t hese, the add i t ional property gives us a new p rediction about the t arge t e n v i ronmen t . I t i s preci sely t hese
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Part III: The Implications
cases t h at for m i nstan ces of predic t ive analogy. We can sum up the above d iscussion i n the follow i n g defi n i tion of p re d i c t i ve analogy : it is the p rocess by which, based on the knowledge that the source concept network and the t arget concept network h ave certai n proper t ies in common , it i s concluded t h at some add i tional properties of the source concept network , t h at are not already in c lu ded in or contradicted by the t ar get concept network , can also be applied to the t arget environment . (This formulation of p red i ctive analogy fully agrees with the ' an alogy as a second order Q- morp h i s m ' view of Holland e t al. [ 1 986, p p . 1 96-300]-the only other theory to m ake a d i s t inction between representations and object s . )
Let u s now see how predic t ive analogy differs from metaphor. I carry out this task by considering each mode of metaphor [§7.4] in turn , and not i ng s i m i larit ies and points of difference between i t and predictive an alogy. Consi der proj ect i ve ( s i m i l ari ty-creati ng) metaphor first. One can easily see t h at proj ecti ve metaphor d i ffers from pred i c t i ve analogy i n two i mportant respects. Firstly, predictive analogy i s a process less often applicable t han proj ect i ve metaphor s i n ce i t ( p redic t ive analogy ) requi res as a preconditio n t h at t here be some s i m i l a r i t i es b e t ween t he source and the target concept networks. But proj ect i ve metaphor, as I argued in [ § 7 . 4 . 2] , p l aces no such req u i rements. I t works by d i rectly i nterpret i n g the source concept network in the t arget envi ronment and often produces deep i nsights i nto s i tuations when t here were no existi ng s i m i lari t i es between the source and the t arget concept networks before the metaphor. Second ly, p red i c t i ve analogy carries more force . I t co n cludes t h at the addit ional p roperties of the source concept network are also app l icable to the t arget. env i ronmen t . P roj ecti ve metaphor merely interprets t h e source concept network in the t arget envi ronment coherent ly. What is the d i fference b e t w ee n i n t e rp re ting a concept n e t work in an en v i ro n m e n t and con cluding t h at the properties of a con c ep t network are ap plic able t o an envi ronment ? Wel l , i n interpret i ng a concept network, one i s free to carve up t h e envi ronment i n any poss ible way s o l o ng a s coherency is maintai ned . I n other words , t h e ontology of t h e e n v i ronment i s not pre determined and can be adj usted to suit the concept network . I n concluding from predictive analogy, on the other h an d , the conclusion is made with re spect to the exis t i n g ontology of the t arget envi ronment as seen from t h e target concept networ k. Thus, p roje c t i ve metaphor and pred i c t i ve analogy are two e n t i rely different p rocesses . The s i t u a t i on i s somewhat d i fferent w i t h syntactic a nd sugge s t i v e meta phors [§7.4. 1 ] . Bei ng s i m i l arity-based, both types of m etap h o rs are t r i gge r ed
Chapter 9: Predictive Analogy and Ind u ction
32 1
by the exi s t i ng s i m i larities between the source and the t arget concept net works, j ust as predictive analogies. But syntactic metaphor says not h i ng new about the target environmen t . ( Recall that i n a syntact ic metaphor, the source concept network i s i nterpreted only by comparing i t w i t h the existing concept ualization of the target environment i n the target concept networ k , a n d t here i s no open-endedness to i t . ) lts useful ness l i e s exclusively i n making i t easier for the cogni t i ve agent to reason about the t arget environment by using a more fami l i ar concept network (even t hough the cogn itive agent can reason w i t h the target concept networ k ) and i n highlighting and downplay i ng parts of the target environment ( that are already i ncluded in the target concept networ k ) . It is hardly predictive at all . That leaves u s w i t h suggestive met aphor . I n deed , s uggestive metaphor can be considered a close cousin of predictive analogy. They are both t rig gered by the existing s i m ilarities between the source and the target concept networks. They both m ake hypotheses about how add i tional structure can be i mported from the source concept network to the t arget envi ronment structure t h at is not already present i n the target concept network. Moreover, this i mported struct ure i s with respect to the existing ontology of the t arget environment as seen from the target concept network . Yet , t here i s a seemi ngly small but crucial difference. In suggestive metaphor, given t hat a part of the source concept network h as been mean i ngfu l l y interpreted in the t arget envi ronment by using the ontology given to i t by t he t arget concept networ k , there i s no promise, no j ustificat ion, t h at some add i tional struct ure can also be so i nterpreted by using the same ontology. The process m ight or m ight not succeed . Predictive analogy, on the other h an d , carries exactly such a j ustifi cation wi t h it. H s u gges ts t hat if the source and the target concept networks are structurally s i mi l ar in certain way s , it is very likely t hat some other s t. r u d. ur al featu res of t he source concept network-those that are consi stent w i t h the struct ure of the target concept network-might al so be fou nd i n the target environmen t . T h u s , suggestive metaphor i s essentially predictive a n a l o gy m inus the j ustification . Or , to p u t it the other way, when a suggestion from suggestive metaphor i s seen as ' forceful' i n any way, then i t turns into predictive analogy. If t h i s j ustificat ion business seems to be j ust a techni cal poi n t , let me p o i nt out t h at w ithout i t , predictive analogy l oses all its force as it problem-solving heuristic. G i ven a target envi ronment on wh i ch one is t r y i ng to g e t some new i nsight ( for problem s olv i n g, or any other reason ) , the fact that some metaphors can be open-ended does not tell you w h i ch source w i l l bring i n t he
322
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III:
The
Implications
i nterest i ng i nsights. On t he other h an d , p redictive a nalogy, i n connecti n g the existing s i m i larit ies with woul d be s i m il arities, i m mediately suggests t h at the source that i s most s i m i lar i s also the most l ikely one to lead to the sought after i nsights . Thus, j us t i fi cation i s very much t he l i feblood of predictive analogy. T h i s shoul d also be obvious from the amount of effort various scholars have spent in trying to provide some logical or empirical grounds for this j us t i fication . It is t hese efforts t hat I discuss nex t .
9.3
The S earch for Log i cal Just ificat ion of P red i ct ive Analogy
S u ppose t hat two objects S and T have a set of properties ¢> in common . I n add i t i on , suppose S has a set o f propert ies '1/J about w h i ch i t i s n o t known w hether T h as t hem or not . W h at j ustification i s t here, i f any, in assu m i ng t hat T h as p roperties '1/J als o ? This i s the logical problem of j ust ification of pred i c t i ve analogy i n i t s essence. T here are , of course, vari at ions. It might be known t h at S a n d T are dissi m ilar in some respects also-say, S h as some p roperties, a, t h at T does not h ave, and T has properties, (3 , t h at are absent from S'. W h at effect , i f any, do the dissi m i l ar i t ies h ave on the j ustifi cation t h at T has '1/J also? Then t here is the question of degree of sim ila rity. For i nstance, suppose t h at t here i s another object S' that has properties ¢>' i n common w i t h T such t hat properties ¢> are i ncluded i n ¢>' ( ¢> C ¢>' ) . B u t S'' does not h ave properti es '1/J . I n stead , i t h as the p ro pert i e s '1/J ' t h at are d i sj o i nt from '1/J ( '1/J n '1/J ' 0 ) , and of w h ich it i s a l s o not k n o w n whether T has them or not . Then are we more j ustified in ass u m i n g t h at T h as '1/J ' t h an we are assu m i n g t h at T h as '1/J? And i f so, why? I l e av e such variations for you to muse upon ( see also Hesse [ 1 966] , p p . 1 0 1 -1 29 ) and focus exclusively on t he central problem of the j ustification of predictive analogy, which i s p roblemat i c enough as i t is. In the p ast t h i rty years or so, many t heories h ave been suggested t h at p urported t o s how why the i n ference from pred i c t i ve an alogy-n amely that T h as '1/J also-is j us t i fied . N eedless to s ay, the j us t i fication i s provided i n a. p robab i l i s t i c sense, since t he i n ference from predictive analogy i s not c o nsi dered true, but only =
ve1·y likely. T here are
basically t h ree approaches t h at h ave
been t aken t o provide
Chapter 9: Predictive A na.logy an d In du ction j ustification for the i nference from p redi c t i ve analogy. tu r n now . 9.3.1
T
d iscuss them each i n
P redict ive Analogy as a n Induct ive P ro cess
A number of theories of predictive analogy see i t essen t i ally as a form of i nductive reasoning. Recall that i n d u ction i s the p rocess w h i ch al lows us to j ustifiably i nfer, on h aving noti ced some regularity several t i mes in the past , t h at the same regularity w i l l be observed i n the fut u re as well . I n the case of pred i c t i ve analogy, the ' regu larity' i s the set of s i m i l arit ies between the source S and the t arget T. A l l t he properties t hat are i nc l uded in rjJ ' confi r m ' t h i s regulari ty. From t h i s , o n e i nductively i n fers t h at the s i m i l arity w i l l extend t o the p roperties i nc luded i n 'lj; a s well . T h u s , the p roblem of th e j u stification o f pred i c t i ve analogy is eas ily sol ved b y embedding i t i n a theory of i n d uction . H arrod [ 1 95 6 , p p . 1 23-1 27] , for i nstance, used t he sam p l i ng principle to j us t i fy analogic a l reasoning. The sampling principle, eas i l y demonstrated by using simple c omb i n ator i c s , asserts that if a ra ndom sample is dr awn from a pop u l at i on then the probab i l i ty t h at the popu l ati on h as the same characteristics as the sample i s very high , p rovi ded that the sample i s l arge enough . S i n ce the known properties of an object can be considered a sample of all of i t s properties-known as well as u nknown-H arrod argued that i f i t i s k nown t h at two objects S and T h ave some propert ies i n common t hen it i s highly probable that they w i l l h ave other properti es in common as well . I n t u i t i vely, the argument proceeds as fol lows . Suppose that S and T have fifteen properties i n common , and furt her, S h as ten other properti es of w h i ch w e do not know i f T h as them or not . Now if S and T had e x a ctl y fifteen properties in c o m m o n , nnd no more , i t i s highly i mp robable lhal we wou l d get to know o n l y t hose fifteen p roperties of T . In other word s , i f the p ropert i es of T t h a t are k n own to us are c o n s i d er e d a sample of all the pr o p e r t i e s of T then the probab i l i ty of T s h aring other properties w it h S i s much h i gher than the probab i l i ty of T not shar i ng any other properties- beyond the k nown fifteen-w i t h S . Thus, H arrod c o n c l u d e d , " [T]he arg u m e n t by an alogy h as the fun damental characteristic of a sam p l i n g argu men t . " [ H a rro d 1 95 6 , p . 1 27] . I n H arrod 's framework , each known s i m i l ari ty between t h e source S a n d t he t arget T prov i d es a separate i nstance to confirm the hypothesis t hat S a n d T are alike. Thus , the m o re the known s i m i l ar i t y between S and T , t he h igh e r i s t h e probab i l i ty t h at S an d T arc ali ke and , consequent ly, t h e more j ustified is the i n ference from predictive analogy. fo l l o wi n g t h i s re a s o n i n g ,
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Part III: The Implications
H arrod wrote: " A rgument by analogy h as been shown not to be, as Keynes, for i nstance, supposed , an arm of empirical reason i ng i n dependent of, and to be contrasted w i t h , i n d u ct ion by s i mple enumerat i o n . Its principles are to be deri ved from the more fundamental princi p les of i n d uction by simple enumerat ion . " [ H arrod 1 956, p . 255] . H arrod's t h eory, si nce i t consi ders the source and the target i solated fro m their context , c an be easily shown to lead to a paradox , w h i ch I do a b i t l a t er . A m i nor flaw i n i t i s t hat merely coun t i ng properties to l e n d strength to an argu ment from pred i c t i ve analogy does not seem satisfactory. Carnap [ 1 962] , for example, noted t h at , based on t he evidence t hat b an d c h ave some properties in common and that, further, b h as an additional property; some difficulty i s i nvolved in j ustifying t he hypothesis t hat c has t hat property too. "It seems plausible to assume t h at the probab i l i ty of the hypothesis is the h igher t he more properties b and c are known to have i n common; o n t he other hand , i t i s fel t that t hese common properties should not be simply be counted b u t weighted i n some way." [Carnap 1 962, p . 569] . One obvious reason for t h i s i s t h at i f a property p subsumes ( i mplies ) another property q ( as being a ' bachelor' subsumes being a ' male ' ) then we should not count p and q twice. Even i f two properties are i n dependent i n t he sense that nei t her o f them subsumes t h e other, they m ight sti l l m ake different cont ributions to t he argument from analogy because of their d i ffer ent logical width; where the logical width of a property measures , i n t u i t i vely, the number of logi cally i n dependent properties subsumed by i t : the more the subsumed properties the logically narrower the predicate. ( See Carnap [ 1 962] , p p . 1 24- 1 30 for the formal defi n i t ion of t he logical w i d t h of a pred i cate. ) Thus, if being red , bei ng triangular, and h av i ng a smooth texture a re all all logically independent properties , t h e n t h e p roperty of bein g a r e d t ri angle is logical ly wider t h a n the property of bei n g a smooth red t riangle. I f a p r o p e r t y subsumes another property, t he n the former is logically nar rower than the latter-the property of being red i s logi cal l y n arrower t h an the property of bei n g colored. Now gi ven objects S and T such that ifJ is the conj unction of all t he properties S and T are k nown to s hare, the width of ifJ i s x , ifJ 1\ 1/; i s the conj u nction of all known properties of S , and the width of ifJ 1\ 1/; i s y , the probab i l i ty that the object T w i l l have p r o p e r t i e s 1\ 1/; as well i s given in Carnap 's system by [Carnap 1 962, pp. 569-70) : y+ l x + l
Obviously, s i nce ¢
1\
1j; subsumes ¢,
y
i s less t han
1: .
Therefore, Carnap 's
Chapter 9: Predictive Analogy an d Ind u ction
325
system captures the i ntuition t hat the more propert ies 5 and T are known to have in common, the more con fidence can be p l aced in the i n ference by analogy ( th at T h as propert ies 'ljJ as wel l ) . M oreover, the relati ve increase i n t he confidence factor, as more shared propert ies are discovered between 5 and T-or as x approaches y, i s very small and Carnap poi nts out that " [ T]his i s i n agreement with the general conception accordin g to w h i ch reasoning by analogy, although adm i ssible, can usually yield only rat her weak results." [Carnap 1 962, p. 569] . Criticisms and revi sions of Carnap 's system cont inued fu rther i n Achin stei n [ 1 963] , Carnap [ 1 963] , and Hesse [ 1 964] . However , one major charac teri stic of h i s origi n al system , which was also p resent in H arrod 's fra mework t h at u sed t he sam p l ing princi ple, remained u ntouched in al l t hese revisions: namely t h at the source and the t arget are considered i n isolat ion-devoid of any context . That is , i f a less fami l i ar object T i s bein g compared w ith a more fami l i ar object 5 , and many of the k nown propert ies of T are possessed by 5, formal systems a Ia Carnap or H arrod would p redict w i t h a high prob abil i ty t h at the object T has other properties of 5 as well . In t h i s prediction only the overl ap between properties of 5 and T i s consi dered . The knowledge of other objects and thei r properties has no bearing on t h i s predi ction . This, however, i mmediately leads to a paradox . For i nstance, suppose t hat the objects 51 and 52 are exactly alike except t hat 51 h as the color red and 52 is black . Now, gi ven a less fam i l i ar object T such that i t s color is not k nown and all of i t s known properties are possessed by both 51 and 52 , contrad i ctory pred ictions are made of T's color depend i n g on whether i t i s compared w i t h 5 1 or 52 . This p o i n t was made astutely b y Agassi [ 1 964] who argued t h at analogies are either generali zations or are completely ad hoc. 9.3.2
P re d ict ive A nalogy as a F irst O rder
G e neralizat ion
A number of t heories of pred i c t i ve analogy see i t as a fi rst order generaliza tion . That is, given t h at 5 and T h ave properti es
326
Pari III: The Implications
opposed to a second order one, w i l l become c lear in the next section. From t h i s viewpoi n t , the knowledge t h at t here i s some object S' that has p ropert i es 1/J depen d i n g o n the scopes of i t s antecedent ( ¢ ) a n d consequent ( 1/J ) . In the second part , he s howed how t h i s a priori probability i s affected by t h e number of i nstan ces confirming the general ization. It is the first part of h i s framework t h at is of relevance h ere. Keynes' notion of the scope of a pr o pos i t i on is an a l o g ou s to Carnap ' s notion of t h e w i d t h o f a predi cate. I nt u i t i vely, i f a proposition f1 i m p l ies another p roposi tion h , then the former h as a scope smaller t han or equal to t h at of the latter. B ased on t h i s defi n i tion, Keynes showed t hat the p robabi l i ty of a generali zat ion
1/J i s in d irect p ro p o r t i on to the scope of its consequent ( 1/J ) and in i n verse proportion to the scope of its a n t ec e d e n t ( ¢>) ; an d therefore "some general i zations stand initially i n a stronger position t h a n others ." [Keynes 1 92 1 , p. 225.] Thus, if fewer add i t ional p rop erti es are i n ferred abou t the target based on a l arge n umber of properti es t h at the
Chapter 9: Predictive Analogy and In duction
327
source and t he target have i n com mon , then the i n ference i s more j u s t i fied ; i f more addition al properties are i n ferred based on fewer ex isting s i m i l ari t ies , t hen t he i n ference h as less j ustificat ion . A very s i m ilar approach was taken by von Wright [ 1 965, p p . 1 34- 1 36] who argued t hat reasoning from analogy depend s , "for its logical force, on s i m p le i deas concerning the proportional i ty of scope and probab i l i ty i n gen eralizations . " [ p . 1 36] .
The second-and fatal-problem w i t h the ' pred ictive analogy as a first order general i zat ion ' approach i s t hat i t makes the exi stence of the sou rce superfluous. S i n ce the i n i ti al probab i li ty of the general i zat ion 'all objects t hat have ¢> have 7/J as wel l ' is only dependent on the scopes of ¢> and 7/J , we can m ake the i n ference ' t he target T has 7/J , gi ven t h at T has
P re d ic t ive Analogy as a S econd O rder G eneralizat ion
A l l t hese shortcomings o f the e x i s t i n g approaches l ed We itze n fe l d [ 1 984] t o view t h e process of predictive analogy i n a d i ffere n t l i gh t . Fi rst of al l , h e saw pre d i c t i ve a n a l ogy as a seco n d order general i z ati o n -an d not a fi rs t order one. Secondly, he arg u e d that i t is a deduct i ve p rocess-i n t h e logical s e n se of the word-but one based on a n assu med prem i se of the secon d order generalizat ion .
Let u s first c l a r i fy t h e d i ffe re n ce between first order generalizat ions a n d second o r d e r ones. A first o r d e r generalization h as t h e fo r m : " I f an automo bile h as the m ake Toyota, model Celica, and was b u i l t i n 1 9 8 7 , then i t c o s t s about $6000 . " A second or d er general i z at i o n , o n t h e o t h e r h an d , s ay s : " i f two a u t o m o b i l es h ave the s a m e make, same model , and were b u i l l i n t h e same year , then they cost about the same . " Though t he existence of t h e so u r ce i s
Part
328
III:
The Implications
superfl uous w i t h respect to a first order generalizat i on, save for p roviding a si ngle confi r m i n g i n stance, i t is very crucial for a second order generalization . G i ven t he above second order general i zation , and a 1 987 Toyota Celi ca, the cost of w h i ch i s not k nown , not h i ng w h at soever can be i nfer red about i t s cost w i t hout an appropri ate sou rce. Weitzenfeld referred t o the secon d order generali zations as
d e t e rmin ing
sl ntclu 1·es-t he relat ions and propert ies in the antecedent are seen as d e t e nnin ing the relat ions and properties i n the consequent . The source and
the t arget , w h i ch are i nstances of a second order generalization , he called h o meomorphs.
( Weitzenfeld also di scussed para m o rphs, w h i ch are determi n i ng structures t h at are assu med to be i somorph i c . I do not d iscuss t hem here because t hey do not p rovide any add i t ional perspective on the logical problem of j ustification of pred i c t i ve ana logy beyond the one p rovi ded by homeomorph s . ) T he secon d novel ty i n Wei tzenfeld ' s approach to predictive analogy l ay i n h e saw i t as a deductive process t h at ass u m es t he premi se of the second order general izat i o n . The 'ext ra- logi cal ' force of t he i n ference from predictive analogy comes from t h i s assumed premise, s i n ce i t can n o t be deduced from the background k nowledge. t h at
Now t h i s might seem to be a mere tech n icali ty. I certainly symp at h i ze i f you fai l to see any real d i fference between Wei t zenfeld's approach and t he t radi t ional view, w h i ch puts the 'extra-logi cal ' force i n t he p mcess of deriv ing an an alogi cal i n ference from logically t rue premi ses (existing s i m ilarities bet ween the source and the target ) . Yet t h i s techn i cali ty underlies a signif i cant point of d i vergen ce. I n the t radi tional view , the p rocess of p redictive analogy is g i ven
the
e x i s t i n g s i m i l ar i t i es bet ween t h e sou rce and t h e t arget .
From t h i s , t h e p rocess i n fers t h at
i t is very l i kely t h a t t here w i l l be other s i m i l ar i t i e s as wel l . Thus, the exi s t i n g s i m i l arities alone are seen as j u st i fying the analogical i n ference. Though no one h as yet been ab le t o exp lai n s a t i s fac t o r i l y what t h i s j ust i fi c a t i o n i s , I h av e already d i s c ussed t he short comi ngs of some of the attempts. I n Wei tzenfel d ' s approach , on the other h an d , pred i c t i ve analogy i s merely a deductive p rocess t hat i s given the exist i ng s i m ilar i ties between the source and t h e t arget , and the second order generalization . Now the existing sim i l ar i t ies a r e l og i c a l l y true, b u t t he second order general i z at i o n is not . The problem of the j u s t i ficat ion of predi c t i ve analogy, t he n , becomes t h e pr obl e m of j u st ify i ng t h e s e c ond order gener a li z a t io n from one's back g round knowl e d g e . T h i s latter pr o bl e m is e s s e n t i all y a cogni t i v e one, and t h e a r e n a for tackl i ng it is wide open . The m a i n t h i ng i s that t h e e x i sti n g s i m i l a r i t i e s
Chapter 9: Predictive Analogy an d In duction
329
between t he source and the t arget are no l o n g e r the only factor--or even a factor-affecti n g t h i s j ustification process.
Thus, though Wei tzen feld does not sol ve the logical proble m of j ustifica tion of predi c t i ve a n al og y per s e , h e present s i t i n a d i fferen t p er s pe c t i ve- a p e r s p ec t i ve that i s more l i kely to lead towards the reso l ut ion of the p r oblem t h an the t rad i t i onal view, as I will show sh o r t l y . B e fore doing so it w i l l b e i l l u m i n at i ng to review the attem pts t h at have been m ade to j u s t i fy predictive a n a logy on e m p iri c al g r ound s .
The S earch for Empirical Just ificat ion of P redict ive Analogy
9.4
Various r e s ea r c h e r s , mo s t ly p s yc h ologi s t s , h ave t r i e d to j u s t i fy p r edi c t i v e an al o gy on e m p i r i c a l gro u nd s . These attem pts essentially provide s u p porting evi dence for pred i ctive an a.l ogy in two d i fferent ways. One set of s u p por t i n g evidence comes from numerous classroom experi ments t h at have been done to demonstrate that people do use p r ed i ct i ve analogy to s u c c e s sfu l l y solve problems and reason about an unfami l i ar t arget domai n . The other set of s u p po r t i n g eviden ce i s provi ded by analyzing real- world p r oblem solv ing act i v i t ies t h at i n clude s ci e n t i fi c and t ech n o logi c a l break t h rough s . Let us cons i der each s et of s u p po rt i n g ev idence i n t u r n , an d s ee if i t does , i ndee d , provide a j u st i fi cation for pred i ct i ve analogy. 9 .4 . 1
Evidence fro m C lassro o m Experiment s
A number
of
psyclwlog i s l s h a.ve t r i ed t o ahow t h at
pred i c t i ve
a n a. l ogy
1s a
u s efu l p r o b l e m so l v i n g heuri s t i c by con d u c t i n g cl assroom ex pe r i m e n t s i n a s o m e w h at ar t i fi c i al se t t i n g . ( S e e C le m e n t & G e n t n e r [ 1 99 1 ] ; Gentner [ 1 989] ; G i ck & Holyoak [ 1 980; 1 983] . ) For i n st a n c e , i n G i ck and H olyoak 's [ 1 9 0] s t ud y , five d i fferent experiments w er e co n d u c ted t o i n v est i g a t e how exactly people use a n al o g y i n p ro b l e m sol v i ng . O u e of t h e p r o b l e m s t h at was u s ed i n t h ei r e xp e r i m e n t al set up was the rad i a t i o n p ro b l e m t h at r h ave d i scussed earlier [§7.4 . 1 ] . ( Yo u might r e c a l l that the p roblem in t h i s d o m ai n was t o co m e u p w i t h some way to us e electromagnetic r a d i a t i o n t o dest roy a t u mor w i t h o u t destroy i ng t h e surrou n d i n g h e a l t h y t i ssue. )
In
one of G i ck and H o l yoak 's
g i v e n an an alog source ( army
way ( d i ffe r e n t
for each
g rou p )
experi ments, t h re e groups of s u bjects we re to cap t u re an e n e m y fo r t re ss ) and a solve t h e a n a l o g o u s prob l e m i n the source,
m a n e u vers
to
330
Part III: The Implications
while a fourth group was supplied w i t h no such source. The results i n d icated t h at for the t hree groups who were given the analog source, the given solu ti o n to the source problem h ad a marked i nfluence in t hei r proposed solution to the target problem. Moreover, the fourth group d i d rather poorly: about half of the subjects ended up suggesting that the pat ient be operated upon to clear a pat h for the electromagnet i c rays. None of t he subj ects in t h i s group suggested what was consi dered to be t he most creat i ve solution: that weak electromagneti c rays be sent from d i fferent d i rections so as to converge on the tumor. The experiment was conducted both with the experi menter i nteract i ng w i t h the subjects during problem sol v i ng, and w i thout such i nteraction , w h i ch was found to have no significant effect on t he results, except that more i n complete solut ions were generated in the non-interactive version of the ex peri ment . This, accord ing to G i ck and Holyoak , clearly demonstrated the power of pred i c t i ve analogy i n sol ving a n u n fam i l i ar problem . In another experimen t , i t was found t h at even when the solution to the source problem was not expl ici tly given , and the subjects were allowed to develop their own solution to i t , t hey were s t i l l able to use the sol ution of the source problem to solve the target p roblem . This is purported to show that even when the subject does not already k now the sol ut ion of a s i m ilar problem in t he source, making the analogy i s s t i l l helpfu l because the subject can p roceed by fi rst solving t he analogous source problem ( wh i ch ought to be easier, as the subject i s more fami l i ar with it) and t hen t ransferring the solution to the target . In yet another experi ment, the subjects were d i v i ded i nto two grou p s . B o t h groups were presented w i t h t h ree stories, o n e o f w h i ch was a potential sou rce analog for the target proble m. Then e ach group was given the t arget problem to solve. The su bjects i n one grou p were told t h at one of the stories p re s e n t e d earlier could provide a h i n t in sol ving the prob lem . The results of this e x p e r i m e n t were t h at t h e a l a r ge fraction ( 92%) of s ubj e ct s in the grou p t h at was given the h i n t were able to fi n d the ri g h t source and apply it successfully to solve the t arget problem , w h ere as only a small fraction ( 20% ) of subjects i n t h e 'no- h i n t ' gro u p were a b l e to solve the problem at all . This showed t h at predictive an alogy i s not an a ut o mati c p r o b l e m - s ol v i n g strategy, but needs to be consciously appl ied . Before a n al y z i n g to see i f these experi ments do i ndeed p rovide an empir i c a l j usti fication for predictive an alogy, let us review one more set of experi ments t h at w as p u b li sh ed more recent ly [ C lement & Gent ner 1 99 1 ]. I n t h e i r experiments, Clement and Gentner m ade up a scenario about some hypo t hetical creat u res called ' Tams' as the potent i al source ( r efe rr e d to as ' b ase'
33 1
Cl1ap t er 9: Predictive Analogy and In d u ct ion
by Clement and Gentner ) . The scenario had two di fferent causal struct u res in it that explained why Tams , w h i ch h ab i t ually gri n d and con sum e m i ner als t h rough t hei r underbellies, somet i mes stop usi n g thei r u nderbel lies, an d w hy t hey cannot work on a new terrai n . One causal stru c t u re explai ned that when the m ineral i n one spot is all exhausted then Tams stop using thei r u n derbellies. The other causal structure explai ned t h at the u n derbelly of a Tam gets spec i alized to the tex t u re of a particu l ar rock t h rough adaptation , and so i t i s u n able to fu nction on a rock w i t h a. d i fferent texture. The subjects were gi ven two d i fferent versions of a. target scen ario in volv i ng robots t h at gather data on planets using probes . l n one version , the subjects were told t h at when robots exhaust data from one place, they must move to another place; and that the robots are designed wi t h del i cate probes t h at cannot survive fl ight to another planet . In the other version , t he subjects were told that when t he robots gat her a lot of data, t hei r i nternal computers overheat ; and that the probes adapt and become specialized to one p l anet . Then the subjects were asked to make pred i ctions about t h e target sce nario. Clement and Gentner argued that there are two potent ial predict ions with respect to each version of the target . For i n stance, with respect to the first version, it might be p red i cted t h at the robots wou ld stop using the probes at some point ( when the data. is exhausted ) or that the robots can not function on another planet ( s i n ce they h ave del icate probes that can not survive flight to another planet ) . Only one of t hese pred i ctions ( the first one) fits the systemat i ci ty model of Gent ner [ 1 983] , w h i ch was shown to be the most favored prediction in the experimen t . T h u s , C lement and Gentner not only clai med to h ave demonst rated t h at people u se pred i ct i ve analogy for m ak i n g pred i ct i o n s , b u t t h at t h e pred i c t i o n s are d e r i ved from
a
' sy s t e m
( wh i ch m e a n s a m ap p i n g that i n c l udes h i gher o r d e r rel at i o n s a n d not the a t t r i b u t e s ) between the sou rce and the t ar get a r c more l i kely ot occur . at i c ' m ap p i n g
L e t us now see i f any o f t hese experiments do provide an empiri cal j ust i ft cat ion for pred ic tive analogy. F i r s t c o n s i d e r G i ck a n d H o l yoak ' s ex p e r i m e n t s . I nterestingly, one con d i t ion t h at was t rue i n al l of t h e i r e x p er i m e n t s , an d not men t i o n ed e x p l i c i t l y at al l hy t h e m , was th at t h e a n a log so 1.t 1'Ce did lead t o the s o l u t i o n o f t h e t a rg e t p m b le m . Even w hen two o t h e r seem i ngly i r rel evant sources were i n c l u ded , t h ose two sou r ces were n o t a n a l ogo u s to t h e t arget problem . I n other word s , t h at p red i ct i ve an al ogy wou l d w o r k i n this example was satisfied a p r i o r i . W h at t h e ex pe r i m e n t d i d c o n fi r m w a s t h at whenever t h at is t h e c ase ( t hat it i s k n o w n a p r i o r i t hat predi ctive analogy
Part ITI: The Implications
332
woul d work ) , t hen the subjects were capabl e of using predi c t i ve analogy to arrive at the sol ut ion ( as long as i t was expl i c i t l y h i nted ) . To val idate p red i c t i ve analogy as a problem-sol ving heuristic, a n i ssue must be add ressed t h at G i ck and Holyoak 's experiments i gnore altoget her: How to select the sou rce domai n ? To appreciate t h i s , cons i der a real- world problem-so l v i n g s i t uation . There i s a problem t hat no one k nows how to solve. Now i f some source ( s i m i lar to the target ) provides a sol u t ion to the prob lem , t hen ap p l y i ng pred i ct i ve analogy with t h at source wou l d lead u s to i t (and we will k now afterwards t hat t h e source i s , i n fac t , t he correct one ) . H owever, t here are a l arge n umber o f poten t i al sources ; how d o w e decide which one to use? There is no oracle here to point us to the correct sou rce. P red i c t i ve analogy pu rports to fi l l t h i s gap by suggesti n g t h at a source t h at is s i m i l ar i n cert ain respects ( accordi ng to systemat i c i ty or some other such cri terion ) i s more l i kely to be the correct one. B u t t hen i t must be empirically demonst rated t h at this i s the case, somet hi ng t h at G i ck and Holyoak ' s study fai l s to do. C lement and Gentner's study i s even weaker in prov i d i n g an empi rical j us t i fi cat ion for pred i c t i ve analogy. The target dom ain is quite art i fi c i al , and t here i s no ' real ' problem about i t . What i t does manage to show i s t h at people tend to favor certai n k i n d s of pred i ctions based on analogy to certai n ot hers . B u t t here i s no correlation between what people m i ght predi c t and t he sol u t i o n of a real- world problem . I f the subjects i n C lement and Gentner's study were to sol ve a real- worl d problem , and t here was no oracle to gi ve t hem the ' righ t ' source, t hen i t i s not clear whether the k i n d of predi cti ons t hey m ade i n the experi ments wou l d be usefu l a t al l . 9.4.2
Evidence fro m Real- World P roblem- S o lving Act ivit ies
I fau l ted G i ck and H olyoak's study above in i t s i nabi l i ty to provide an em pirical j ustification for pred i c t i ve analogy on t h e grounds that t h e s u c c e s s i n their c l assroom experiments does not t ranslate i nto s u c cess w i t h real worl d problem sol vi ng. This suggests t hat i f one were to look at rea.l-world problem-so l vi n g s i t uations, and i f i t coul d be shown t hat predi c t i ve an a logy is responsible for lead i ng to the s ol u t i o n s of even some of these si t u at ions, then pred i c t i ve a n a l ogy woul d h ave recei ved some empi r ical j ustification .
P roblem sol v i ng i n t he real world h as n o t been extensively s t u d i e d ; but the few stu dies that have been done [Gordon 1 96 1 ; Schon 1 963] poi nt away from pred i c t i ve analogy by revea l i n g t h at most creative i ns i ghts are gene r ate d
Chapt er 9: Predictive Analogy an d Induct ion
333
by using a source t h at is very d i ss im i lar to the t arget-so m uch t h at the j ux t ap os i tion of t he source and t he t arget seems bi zarre i n i t i ally-a process that Gordon very aptly names making the fa m ilim- strange. I h ave al ready discussed t h i s point at length in Chapter 2 [§2 . 5 . 2] . I t must b e emphas ized wi t h respect t o t hese studies t hat when a 'st range' source i s used to get a new perspecti ve on the t arget, the process ends up ' creati ng s i m i l ar i ti es between the source and t h e target . Th at i s , t here are always s i m il ar i t i es between the source and the target ajle1· lhe fa ct. Some scholars, not m ak i n g any d i s t i nction between before- t he- fact and after-t he fact states of affairs, cite t hese same studies as if they provide emp i ri cal j us t ification for p red i c t i ve anal ogy, when , in fact , t hey do not . Th ere are, nevertheless, a few exam ples of real- world problem solvin g studies t hat do p rov i de some s u p port for pred i c t i ve analogy. There are th e studies t h at I revi ewed i n [§2 . 5 . 1 ] where the sou rce t h at i s used to sol ve the p roblem about a target i s i n i tially s i m i lar to i t . ( See, for i n stance, Gordon 's [ 1 96 1 , p p . 42-45] ' d i rect analogy. ' ) Researchers who study creat i ve problem sol v i n g , however, are caut ious, and do not t h row their weight beh i n d p re d i c t i ve analogy for several reasons . One is that t he i n sights obtained by the s i m i larity- based approach are not always deep or i n s i g h t fu l . For i n stance, Carnot ' s hypothes i s "The rate of heat-Row i s proport ional to the tem pera t u re d i fference between two bodies , " i f i t was deri ved as descri bed i n Gentner and Jeziorski [ 1 989] , seems rat her obvious. O n the con t rary, i n Schon's ex ample of the ' paintbrush as a p u m p ' metaphor, the hypothesis t h at how the fi bers of a paint brush bend in the p rocess of pai n t i n g affects the appearance of t he pai nted surface contai ns a deep i nsight. Or, com pare a theorem that i s deri ved by p r ed i c t i ve analogy from a s i m i lar known theorem about grou ps with Cantor's t h eorem t h a t t h e re il.re more re a l n u mbers than i n tegers.
p eo p l e w h o h ave h ad a first-hand experien ce w i t h c reat i ve i n the real world real ize t h at t r u l y c reat i ve i n sights req u i re completely new and revol u t i o n a ry perspec t i ve s . T h ey are unw i l l i n g to su gge s t t h at w hen there i s a p roblem about a t arget domai n , one's best bet is to go look i n g for a s i m i lar s o u r c e a n d t h e m ore s i m i l a r the source t h e better it i s , w h ich is exactly how pred i ct i ve analogy i s viewed i n m u c h of c og n i t i ve science and arti ficial i ntel l i gence. lf pred i c t i ve analogy i s u c h a u sefu l p r o b l e m solving h e u ri s t i c as i t i s clai med t o b e , m o s t of o u r eco n o m i c , soc i al , and scientifi c problem should b e eas i ly s o l v a b l e a l l we n eed to do i s to find t he most s i m i l ar sou rce. B u t t h e exi s t i ng stat e of h u m an i t y see m s to bf' q u i te fa r from such a b l i s s fu l s t a t e . Secondly,
most
p roblem solvi n g
,
-
F i n al ly, schol ars who have s t ud i e d
creat i ve
problem
sol v i n g h a v e
a
dee p
Part III: The Implications
334
respect for the autonomous structure of the real wor l d , w h i ch does not de pend on the part ic ular forms of our representat ions ( concept networks ) . I n part icular, most o f t hem never say that , i n applying a s i m i l ar source to solve a p roblem about a target , s i m ilarit ies ( wh i ch are properties of representa tions ) are more i mportant i n certai n respects ( such as structural s i m ilarities ) t h an s i m i lariti es i n certai n other respects. Nor do t hey i mpute any sort of 'j ustification ' relat ion between s i m ilari ties t hat are seen and s i m i l arities that m i ght be lurking around the corner. For real-world problems, some sources work, and others do not , and the success and fai l u re of a source j ust cannot be related to wh atever s i m i l arities that source m i ght h ave to the problemat i c s i tuat ion . To summarize t h i s d i scussion, we see t h at the only empirical evidence for pred i c t i ve analogy from problem sol ving i n t he real worl d i s that occasional l y u s i ng a source that i s s i m i l ar to the target c a n lead to a successfu l solution t o the t arget problem . Moreover, t he solution to the target problem suggested by p red i c t i v e anal ogy in t hese cases is usually not a particularly deep or i nsi ghtful one. G i ven that , for real- world problems, deep i nsights come from using 'strange' sources that do not seem s i m ilar to t he t arget at all , a system t hat puts its fai t h in pred i c t i ve analogy as a problem-solv i ng strategy i s sure to m i ss most such i nsights. Consequently, predictive analogy i s not such a wonderfu l problem-solving heu ri st i c as i t i s purported to be.
9.5
The 'Dark S ide'
of
Predict i ve
A nalogy
G i ven t h at no one has been able to provide a reasonable j ustificat ion for pred i c t ive analogy, eit her logi cally or empiri cally, one wonders if t here are
any examples of ' unj ust i fied ' instan ces of pred i c t i ve analogy. Perha p s not surprisi n gly, all the research on predictive analogy only ci tes what one m i ght con sider a s reasonable exam p l es of p r e di c tiv e analogy. I n fac t , most of the pred i c t i ve analogy examples used in the l i terat ure make correct predictions about t hei r targets , and their sources a r e q u i t e u seful in u n derstan d i n g the u n fam i l i ar targets. This only shows the careful attention t hese researchers give i n selecting (or mak i ng u p ) thei r exam p les, so as to p resent predi c t i ve analogy i n the best possible l ight . The ' dark side' of predictive analogy, w h i c h contai ns i nstan ces when an i n ference from predictive analogy is n o t justified, and when pred i c t i ve analogy becomes a h i n drance rather than an aid to cogn i tion , i s never seen at all . To fi l l t h i s vac u u m , I provide some examples below t hat provide a gli m pse of the dark side of pred i c t i ve analogy. For each example, I argue why the
335
Chap t er 9: Predictive Analogy an d In duction
suggestion from predictive analogy is not j usti fied , or w hy predic tive analogy becomes an obstacle to cogni t ion by block i n g the i n formation that m ight otherwise be recei ved from the environment. •
S uppose you are i n a j ury. The case bei n g tried i n vol ves an accident between a Ford Escort and a Toyota pick-up. The drivers of both vehi cles gi ve completely contrad i ctory a. c counts, p u t t i n g each other at faul t . T h e accounts given b y both drivers are consistent w i t h t h e known facts. The pictures of the scene of the accident taken by the pol i ce are no hel p i n i denti fy i ng who i s at faul t . There are n o eyew i t n esses eit her. How ever, you recal l that several months ago you w i t nessed a very simi lar accident at an i ntersect ion s i mi lar to the one at w h i ch t h i s acci dent took place. ( There are many rel at ional and causal [' systemat i c '] sim i lari ties i nvolved here . ) Is i t j us t i fiable for you to p redict from this analogy t hat the faul t for t h e acci dent t h af is being tried l ies with the Toyota driver? I woul d say that t here i s no such j u st i fication there. The pred iction m i gh t well be correct , but based on the avai lable i n formation, nothing w h at soever c an be sa i d about who was a t fau l t i n the accident being tried. All the ' systemat i c ' similarities i t m i ght h ave with the accident you saw before are completely i rrelevant .
•
I n a study o f first-t i me users o f com puter text-ed itors, A l l wood and Eliasson [ 1 987] found that many of t hei r diffi c u l t ies emanate from the fact t h at t hey use t he typewriter analogy to u n derstand text-edi tors . 1 The subjects were fam i l i ar w i t h using a typewriter, and they automat i call y form u l ated an an a l ogy between i t and the tex t-edi tor ( t here a r e m any struct ural s i m i l ari t i es b e t wee n the two ) . T hey t hen proceeded to apply this a n al o gy to u n derstand the t e x t - e d i t or . Unfort u n ate ly, as d o c u m e n t e d b y All wood and Eliasson , this analogy became a s t u mb l i n g b l o c k to t heir u n derstan d i n g . In part i c u l a r , i t led to a . n umber of errors ( keepi n g a key pressed too long so t h at mu l t i ple instances of a com m and were i ss u e d ) and i nefficiences ( moving the c u rsor chara.c t e r w i sc wh e n i t wou l d h ave been m or e efficient to move word wise) i n t h ei r use of the text-editor. ( See also H alasz & M oran [ 1 982] for difficulties of using analogical m o d e l s i n e x p l ai n i ng some computer-related concept s . ) Here the fa. c t that predi c t i ve an al ogy m a.y h i n d er cog n i t i o n is c l ea r ly seen . If i t w er e n o t for analogy, t hese subject s wou ld be op e n - m i n d e d
1 1 am gratefu l to D r . Erica Melis for b r i n g i n g l h i s wo r k t.o
my
attention .
336
Part III: The Implications about learning t he text-edi tor. As it i s , they rush i nto it t h i n k i ng t h at t hey u n derstand i t t h rough predictive analogy, and fail to realize the i m portant di fferences and t he vastly superior power of text-edi tors. •
Gentner and Jeziorski [ 1 989] prov i de some exam ples of alchemists' use of an alogies . For i nstance, they cite Stil lman [ 1 924] who noted that egg was used as a source of many analogies. In one such analogy, " [T]he shel l , ski n , w h i te, and yolk of the egg were thought to be analogou s to the fou r metals i nvolved i n t ransmutations-copper, t i n , lead , and i ron-although the pairings cou l d vary between the components and the metal . " [Gentner & Jeziorski 1 989, p . 3 1 3 .] S uch an alogies amou nt to no more t han fancifu l whims that are not 'j ustified ' in any sense of the word . In fact , t hey often h i n der the t rue objective of scientific i n q u i ry by mak i n g i r rational arguments that refuse to acknowledge facts w hen the fact s do not fit t hese whimsi cal analogies . ( See, for i n stance, Francesco Sizzi 's arguments against Ga. l i leo's discovery of the satel l i tes of J u p i ter that I cite i n Sect ion 9 . )
•
O n J anuary 1 4 , 1 9 9 1 , as the multi national force allied agai nst Iraq and led by the U n i ted States stood poised for at tacki ng Iraq in a bid to l iberate K uwai t , an art i cle appeared in the Wall Street Jo urnal [Rob b i n s 1 9 9 1 ] that made an analogy between t he arguments used by the representati ves of the U . S . congress during the debate to authorize the President t h e use of force agai nst I raq, and the arguments used in the congress d u r i ng a simi lar debate in 1 939, when Europe was standing on the brink of what was to become World War I I . Besides a. t h ree sentence i n troduction, the art i cle contained not h i n g else t h an pairs of quotations; one quotation of every pai r was taken from the 1 939 d e bate and the o t h e r from the 1 99 1 debate, w i t h an appropriate heading fo r each pair. Both arguments i n each pai r made essen t i ally the same poin t . For i n stance, under the head ing "To save democracy?" Senator Charles Tubey was q uoted as arguing in 1 939, "[This is] a war not to save democracy but to preserve terri tori al powers of certain Europen n ations." And Representat i ve W i l l i am Gray was q uoted as arguing i n 1 99 1 , " I s [our policy] to d efe n d democracy? Hardly! Kuwait i s no democracy, nei t her i s Sau d i A rab i a or Syria. " Thus, thet:e i s a. c lear analogy between the debate of 1 939 and the debate of 1 99 1 . ( A n d s ince the arguments i nvolve causal struct u re and h i gher order r e l a tio n s there is an obvious ' system aticity' in the analogy. )
,
What i s the poi n t of analogy? Taken as i t is ( i n the sense of what l re fer to as syntactic metaphor ) , i t merely shows that congress i s cautious
337
Chapter 9: Predictive Analogy an d In d u c t ion
about rush i ng i nto war and com m i t t i n g billions of dol lars and putting l i ves of hundreds of t housands of people i n j eopardy when the security of the country i s not d i rectly t hreatened . B u t the author seems to be i mplying someth i ng more. In one of the t h ree sentences p reced i ng the quotations , the author claims t hat "The s i m i larity is more t h an super ficial ," but no further explanation was offered as to how. Of cou rse , i f o n e uses predictive analogy, a number o f other hypot heses are a t once suggested . For instance, one might con c l u de t h at i f we did not go to war right away, a World War woul d ensue with significantly great er loss of l i fe, or t h at I raqi war machinery was as formidable as Germany 's was i n 1 939, or that a l l reservations put forward i n the 1 99 1 debate are mean i n gless because t hey t u rned out to be not vali d in 1 939. One can go on and on here. Perhaps the aut hor, using pred i c t i ve analogy as a psy chological sleight of h an d , meant people to d raw all ( or some ) of these conclusions subconsciously. God forbid , if art ificial i ntell igence systems t hat used the ' systemat i c i ty ' principle to m ake predictions about the fut ure had ever a n y t h i n g to do with pol i t i c a l dec ision maki ng, they would be easy prey to such sleight of han d . A n alogies l i ke t hese are q u i t e common i n pol i t i cal rhetori c . They essen t i ally work by h i d i n g what i s significantly d i fferent about two s i t u ations, and by p resenting a distorted p i c t ure so t h at people m ay draw the con clusion that the politician wishes them to draw . Si nce the conclusion is not always stated explicitly ( as in t h i s exam p l e ) , it seems al l the more convincing. ( Everyone t h i n k s t h at t hey arrived at it themselves ! ) By not quest ioning the basis of pred i c t i ve analogy, we o n l y m a ke ou rsel ves more vul nerable to such m an i p u l a t i on . •
A nother example i n t h e same vei n is p r ov i d e d by Eleanor Clift 's criti cism of President Georg e Bush's h a n d l i ng of the U . S . economy. She was qu o t e d as sayi ng, "The rhyt h m m e t h o d is a b o u t as good in e c o n o m i c planning as i t i s i n fam i l y p l a n n i n g . " 2 ( The com ment was a response to P resident Bush's remark on wai t i n g i n the ' n at u ral cycle' of the e c onomy as a strategy to combat the recession . ) T h i s a n alogy m akes a com p l e t e l y i r relevant com parison to s u p p o r t a c o n c l u s i o n . O f course, the conclusion ( th at wai t i ng in the ' nat u ral cycle' of t h e economy is n ot a successful strategy to combat recession ) c a n b e i ndepen dent ly analyze d , and o n e can argue for or aga.i n s t it. B u t t h e a n a lo gy t r i es to gi v e an aura of j u s t i fi c at ion to the concl usion w i t hout bri ng i ng i n a
2 This appeared in "Quotes of Notes," ( p . 27)
ber 30, 1 99 1 .
in
the
B o s t o n Globe
on
Saturday .
ovem
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sh red of evidence or considering a si ngle fact about the economy. •
F i n al ly, a h i storical example where predictive analogy, j ustified or not , woul d h ave been a grave l i ab i l i ty. D u r i ng the French revolution , the pol i t i cal situation was in such a state of flux t h at what was 'politically correc t ' at one point in t i me woul d become the reason for sen d i n g some one to the gui l lotine a l ittle l ater. How predictive analogy wou l d h ave led to di saster in t h i s period might be best app reciated from Shurk i n ' s [ 1 984] description o f a computer simulation o f t h e French revolution designed by h istorian M i chael Carter: "Students at Dartmout h can . . . play a game that simulates the French revolution . The student assumes the role of a J a cob i n who undergoes pol i t i cal i nterrogation . He or she must answer the questions according to the party line at a certain t i me d u r i ng the revolution or be swept off to the guillotine. G i ven a second chance at the questions, t hey frequently find t h at what was right before i s fatally wrong now ; the rules have been changed and they are s t i l l doomed. A n umber of real J acobi n s died t h at way. " [Shurkin 1 984 , p. 3 1 7 . ] Pol i t i cal revol utions provide an excellent source of examp l es where a cogni t i ve agent reason i n g from p redictive analogy i s doomed. Consider the recent fai led coup in the Soviet U nion . During the coup , the r ules changed as to what was considered right . When the coup was over t h row n , the rules changed again to the other extreme. In fact, even s i t t i ng on the fence in not opposing the coup was also p u n ished in var ious ways. A l l this shows t h at p r e d i c t i ve analogy is not such a great asset t o cogni t i on as i t is pu rported to be, and an art i fi c i al system t h a. t uses it as a source of heuristic is not going to survive any revolutions.
I hope all t hese examples give you at least a cause for concern about p re d i c t i ve analogy : t h at an i n ference from predict i ve analogy ( w het her ' systemat i c ' or not ) i s n o t always j ustified, a n d is n o t always u seful to c o gn i t ion O n t h e contrary, pred i c t i ve analogy c a n become a major stumbling block to one's abil i ty to be object i ve and see t h ings as t hey are, with possibly fatal consequences . .
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Pred i ct i ve Analogy and Cogn i t i on
Now t h at we h ave seen the dark side of predictive analogy, we can analyze it more objecti vely. Clearly, and this i s what the psychologi cal studies of Gentner and Holyoak have effectively demonstrated , people find arguments from p red i c t i ve analogy psychologically compel l i ng. I h ave no problem un derstan d i ng this poi n t . A lso, from this point of view, predictive analogy seems an i m p ortant cogn i t i ve phenomenon t h at ought to be researched, so t h at we can u n derstand it better, and become aware of the pitfal ls it creates i n cogn i t ion . B u t t h i s h as not been the spirit of the cog n i t i ve science re search on p red i c t i ve analogy, where the att i t ude towards pred i c t i ve analogy h as been nothing short of awe and reverence: P red ict i ve analogy is good . P red i c t i ve analogy works most of the t i me. P red i c t i ve analogy is the key to learning and problem sol ving. Predictive analogy i s a key i ngredient of i ntel l i gence. P redictive analogy must be i n corporated i n com putational models of i ntel l i gence. And so on. A l most no effort has been spent to exam i ne t he negati ve effects of predi ct i ve analogy i n cogn i t i o n . The fact t h at an i n ference from p redi c t i ve analogy appears psychologically conv i n c i n g often prevents a person from seeing t h ings as they are, some exam ples of w h i ch I presented above. In fact , my examples show only the t i p of the i ceberg. Once you become aware of the potenti al abuses of pred i c t i ve analogy, you wou ld be surprised to find how much more pred i ct i ve analogy i s abused t h an i t is u sed . But the abuses are rarely, if at all , d iscussed in the l i terature about pred i c t i ve analogy. T h i s , what is essen tially a negati ve contribut ion of pre d i c t i ve analogy to cogn i tion, raises serious doubts as to w hether it is useful to i n corporate predictive analogy in an artificial intel l i gence system at al l . T h i s poi n t can be better u nderstood b y an an alogy ( u sed i n rtn explan a tory ' syntacti c ' sense and not i n a p red i c t i ve sense ) . Consider o u r vi sual system . Its structure makes i t useful to us i n certai n ways, but also gi ves rise to certai n h al l u ci n at ions a n d p ar a doxes . ( See Favreau & Corbal l i s ( 1 976] ; G i llam [ 1 980] ; K an i zsa [ 1 9 76] ; Sekuler & Lev i n son [ 1 977] ; and Siegel [ 1 977] . ) Now one can study these paradoxes so as t o get a better u n derst a n d i n g of how our v isual system is struct u red . But it wou ld be q u i t e silly to i nsist t h at in order to design and build a smart mach i n e vision system , we must somehow i n corporate these paradoxes in the design . B u t t h is is precisely the approach t aken by much of artificial i ntel l i gence research w i t h respect to p r e dictive analogy. Looking at predictive analogy as a cogni t i ve p rocess , somet imes successfu l b u t often m i s leading, some observat ions c a n be made here. O n e i s t h at t here
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i s no correl ation bet ween the exi s t i n g s i m i lari t i es between t h e source and t h e t arget concept networks, a n d the l i keli hood o f fi n d i ng some add i t i on al struc t u re of the source concept network i n the target environment . I n deed , i f t h i s correl at ion were a s assumed to be i n predi c t i ve analogy, t h e n m o s t problems ( w hether t hey be proving a t heore m, developi n g a new product , comi n g up w i t h a new physi cal theory, or set t l i ng a pol i t i cal crisis ) woul d be solved by merely fi n d i n g a s i m i lar source. On the cont rary, we find t hat i n real worl d s i t uations, pred i c t i ve analogy often leads to mundane a n d t ri te observations. The key to creat i v i ty lies i n bringing i n a fresh perspective, in creating s i m i l ari ties w here none existed before, a n d i n not i c i n g t h i ngs t hat are h i dden by the usual categories formed by our cogn i t i ve apparat u s . A l l of t h i s is accom p l i shed by t ry i n g to i nterpret a source concept network t h at i s very dissim ila r to t he t arget concept network i n the t arget environmen t . H owever, t here i s no correl a t ion here eit her between the di ss i m i l ari t i es between the sou rce and t he t arget concept n etwork, and what fresh perspect i ve, if any at al l , wou ld be provided b y i nterpret i n g the source concept network i n the target envi ron ment . G i ven a problemat i c target , many dissi m i l ar sources fai l to create any i nsights at al l , let alone useful ones . Thus, the fact remains t h at some source concept networks work-i n terms of creat i n g a useful perspec t i ve on the t arget environment t h at results in gett i ng the problem solved-whereas m any ot hers do not , and t h i s d i fference can not be explai ned on the bas i s of the exi s t i ng s i m i lari ties between the source and the target concept networks This con clusion can be better appreci ated in my framework , as I all uded in Section 2 . The t hesis t h at an argument deri ved solely from som e existing s i m i l ar i t i es between the source and t he t arget concept networks i s j ustified , es s en t i a l l y says t h at i f parts of the s o u rce concept network h ave been mean i ngfu l ly i n t e r p r e t e d in the t a rg e t e n v i ron ment , t hen other parts can also be so i nterpreted w i t h respect t o the same ontology. T h i s , in t u rn , a m o u n t s t o say i n g t h at the cogn i t i ve agent can determine the ontology of the envi ron ment a n d i t s structure. B u t I h ave e m p h as i zed i n C h ap t e r 5 t h at t he cogn i t i ve agent can determ i ne e i t her t he ontology of the e n vi ro n me n t , ( as i n accommodation , when the envi ron ment constrai n s the s t r u c t u re ) , or the cogn i t i ve agent can opt to i mpose the structu re of a concept n e t wo r k on an environment , ( as in projection , when the environment constrai ns the pos s i b le ontologies ) , but cannot do bot h . I n other words, predictive analogy e ffect i v ely denies the fact t h at an e n v i ronment i s a u t o n o m o us and external to lh e cogn itive age n t-t h ere by r e ve r t i n g to an extreme form of subjecti v i s m . The second observat i o n i s t h a t even t hough an i n fere n c e from predictive analogy does not h ave an i n c re a s e d l i keli hood of s u cce s s i n t he envi ronment , one could s t i l l use the term 'j u s t i fied ' i n a ps y c h o l o gi ca l sense to distinguish
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reasonable i n ferences based on predictive analogy (such as i n ferri n g the cost of an automob i l e from the cost of anot her automob i l e w i t h the same m ake, model , year, and mileage) from u nreason able ones ( such as the exam ples p resented above ) . This i s where Wei t zenfel d ' s [ 1 984] approach is most i llu m i n at i ng . You m ight recal l from Section 3 . 3 t hat he saw pred i ctive an alogy as a deductive p rocess t h at ass u m es a second order general ization a.s a premise: and , in his account , the j usti fication for an argument from pred ictive analogy comes from the assumed second order generalization . At t h at t i me it might h ave seemed a tech n i cali ty, but now we can appreci ate th e fu l l sign i fi cance of Wei t zenfeld 's i nsights. Weit zenfeld 's accou n t contain s two key i nsights. O n e i s t h at i f an infer ence from predictive analogy is based only on e.'risling similm·ity between the source and the target concept networks, then t here i s absolutely no j u stifica tion for i t . I n fac t , an i n ference derived on l y from some syn t actic p roperties ( such as systematicity) of the source and the target concept networks is not j ust ified at all . However compel l i ng such an i n ference may seem , the com p el l i n gn ess i s really a resu lt of i m pl i c i tly ass u m i n g t hat an argu ment from predi c t i ve analogy is always j ustified , an assum p t ion t hat is easily refuted by t he examples of Section 5 . I t is t h i s i mp li cit but false ass u m pt ion t h at makes an argument from pred i c t i ve an alogy cast a spel l t h at is exploited in various abuses of an alogy an d suggestive metaphor. C e r t ai n s i m i l a r i t i es a r e poi n t ed out between the source and the target concept networks as a j ustification for reaching an erroneous conc l usion about the t arget en v i ron men t-a techni que al l too often employed in p ropagand a and pol i t i cal rhetoric. lt is t h i s spell w h i ch u n dermi nes the educational and exp l an atory usage of metaphor and a n a l o g y . [ M i l ler 1 976 . ] O n c e the s p e l l i s b roken , w e real i ze t h at an arg u m e n t t hat i s based only ou some exis t i ng s i m i l ar i t y between t h e source and the t ar g et concept networks, and nothing else, is ut terly u nj ustified . We l e a r n to e x e r c i se e x t reme c a u t i o n i n t r u st i n g an argu m e n t b ased s o l e ly on some ex i s t i n g s i m i l ar i t i e s . Every s u ch a rg um e n t i s a potential snare. lt must b e operat i onal l y t e s t e d in the target environment. And if t h il.t i s n o t possi b l e , o n e must fi n d s o m e other piece of k n owled ge , s o m e other fac t-bes i d es the ex i s t i n g s i m i l ar i t i e s between th e source and the target concept networks-t h at j u st i fies t he argu ment from predictive analogy. A n d if no such j u stification can be fou n d , t h e so called ar gum e n t from anal ogy o u g h t to b e properly d i scard ed . i n si g h t of Wei t zenfeld is that t h e j u s t i ficat i o n of an i n ference a n a l og y l ies in how far t he seco n d order ge n er a l i z a t i o n t h at t h e p r e d i ct i v e ana.logy i s j us t ified from t h e b ackgro u n d k n ow ! -
The second
from pred i ct i ve is assumed i n
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edge. This, however , introduces a seman t i c component to pred i c t i ve analogy ; because the j ustification to pred i c t i ve analogy comes from the background ' knowledge , ' w h i ch i s interpreted concept networks ( cogni t i ve models ) t h at are coherent ( as far as the cogni t i ve agent has been able to ascertai n ) . For i nstance, i n t he exam ple of i n ferring t he cost of an automobi le from the cost of a s i m i lar automobile, it i s the background knowledge t h at automobiles of the same make and model cost approxi mately the same in any given year, and that they depreciate at roughly the same rate with years and m i leage, that makes the i nference j ustified . I must emp h as i ze t h at I am talking about j ustification i n a psychologi cal sense here. G i ven the autonomous structure of the external world , one's background knowledge i s fall i b le, and, therefore, t here i s no guarantee, even in a probabilistic sense, that a j ustified i n ference w i l l t u rn out to be cor rect . The psychological nat u re of this j us t ification can be better appreci ated by emphasizi ng i t s subjecti v i ty. Different people can have different concep t u al systems, w i t h d i fferent types of causal l i nks and different ways of giv i ng ontologies to the worl d by i nstantiat i ng t hese concepts. Yet , all t hese con ceptual systems can q u i te reason ably be cons i dered backgroun d 'knowledge. ' For i nstance, to a believer i n ast rology, t here i s a causal relat ions h i p between the positions of the stars and the planets in the sky and certain events t ak i ng p l ace on Earth . This relationship might well be coherent w i t h the actual experiences of such a perso n . To her, the general ization that two p eople, if t hey were born when the p l anet M ars was i n the same position woul d h ave cert ain character t raits in com mon wou l d be perfect ly j us t i fied . Yet , to a non- bel iever i n astrology, t h i s i s about as j ustified as saying that two cars of the same make, model, and year are of the same color. Taken in t h i s sense, predict i ve analogy can b e more fruitfully studied along w i t h i t s j u stification . For instance, we might find out what i t is t hat makes u nj u st ified i nferences psychologi call y c o m p e l l i n g to peopl e . Is i t t h at t hey subconsciously, as in the p h enomenon of apparent motion [§4 . 2 . 1 ] , fi l l i n the requisite second order generalization needed t o make t h e i n ference from predictive a n alogy j us t i fi e d ? O r is it t h at they h ave some background knowledge that i s being made overt by the i nferen ce from predictive a n al ogy. Focusing on i ssues such as t hese is bound to increase our u n derstand i ng of predicti ve an alogy prepare us better to counter t he negati ve role i t p l ay s in cogn i tion , and heighten our awareness of its potent i al abuses so that we are less v u lnerable to i t . ,
Chapt er 9: Predictive Analogy a.n d Ind u c t ion
34.3
The Problem of Induct ion
9.7
P red i c t i ve analogy, as I menti oned i n the i ntroduct ion , i s often seen as an i n stance of the more general process of i nduction . O n h av i n g encountered a certai n regul arity i n the environment on numerous pa.st occasions, i n d uction allows one to 'j ustifiably' conclude that the regulari ty w i l l be observed i n the fut u re as well . The problem o f the j ustification o f i n d uction was fi rst d i s cussed at length by D av i d H u me, a l ead i ng eighteenth century p h i losopher, i n h i s celebrated work , A T1·eatise on Hum a n NalU1'e. A fter some del i beration , H u me concluded t h at all our observations and experien ces give us absol utely no logical basis for conclu d i n g anyt h i n g about the u nobserved . This l ater came to be known as the sceptical t hesi s about i n d uction . S i nce most, perhaps even al l , of our cogn i t i ve act i v i ty consists i n m aki ng predictions about t he fut u re based on the past experiences and observations, H ume's scepti cal thesis conveys a ch i l l i n g sen se of i n securi ty. I s t here no logical basis for any of our knowledge? Is the outcome of any event pred i cted by a scientific t heory t h at is supported by several prev ious observations no better t h an a random guess? O f course, in p ract i ce , we do conti nue t o put our fait h i n predict ions based on our past experiences; even an act as simple as wal k i n g requi res many such predictions w h i ch we i n st i n ct i vely carry out . H ume, despi t e h i s scep t i ci s m , had no problem gran t i n g t h i s . B u t t h i s prag mat i c success of i n duction i n certai n cases i s not an issue h ere-si nce even the most ardent i nductivist woul d acknowledge t h at i n d uction can , at ti mes , lead to false conclusions from true p rem i s e s . The issue i s to provide some 'logical foundat ion ' for i n duction such t h at an i n d u ct i ve i n ference is seen as r at ion a l even if o cc asion al l y fal l i b le . A n d it is p r e c i se l y t h is p roject t h at i s u n derm i n ed by t h e H u mean thesis. As you mi g h t be awar e o f , t h e re h ave been m a n y at t e m p t s s i n ce H u me to refu t e h i s s c ep t i c a l t h e s i s an d p r o v i d e a l og i ca l fou n d at i on fo r i n d u c t i o n . Most of them have t a k e n t h e form of d e s i g n i n g some m a t h e m a t i cal framework, almost a l w ay s based on prob ab i l i ty th eory, that m a d e i n d u c t i ve i n fe ren ces come out to be mo r e p robable t h a n any other i n feren ces ; an d , fu r t h e r , t he p ro ba b i l i t y of an i n d u c t i ve i n feren ce i n c r eased w i t h the n u m ber of confi r m i n g i nstances. An excel l e n t account of some of t h ese t h eor i es of i n d uction can be fou n d i n Salmon [ 1 966] . So close i s the relationship b e t w e en pred i c t i ve a n a l o gy an d i n d u ct i o n , t hat many t heories of p r ed i c t i v e analogy-i n c l u d i ng t hose of Carnap, H arrod , and Von Wright t h at I discussed earlier-are, in fac t , c o ro l l ar i e s to more com p re hensive t h e o r i e s of i nduction . However, given the pa r a do xes a n d p r ob l e m s ,
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facing these t heories of pred i c t i ve analogy, should we not expect a s i m il ar fate for the theories of i nduction? I n deed , the problem of t he j usti fication of i nduction i s r i d d led with p ara doxes . For i n stance, t here i s the Raven's paradox . Consider the hypothesis "All ravens are b l ack . " I n t u i t i vely, we expect this hypothes i s to be confi r med whenever we find a b l ack raven, strengthened as the number of observed black raven s i ncreases , and refuted whenever we find a non-black raven . F i n d i ng any other object t hat i s not a raven should h ave no effect on t h i s hypothe sis. However, t h i s hypothesis i s logically equi valent to its contraposi t i ve " A l l non-black t h i n gs are non- ravens," which is confirmed b y finding a non-black non-raven , such a.s a . w h i te handkerchief. T here are several other paradoxes a.s wel l , one of which I d i scuss in some detai l in the next section . U n d au nted by them , i n d uctivists kept on devis ing more complex t heories and coming u p w i t h newer arguments to j ustify i n d uction. One such recent attempt h as been made by Dav i d Stove i n h i s book Th e Ration ality of Indu ctio n . He a.d va.n ced very rigorous argu ments to j us t i fy i nd u c t i ve reasoni ng by presenti n g four ' p roofs ' to refute what he calls "the scep t i cal thesis about i n d uction . " However, I have shown else where [ I n d u rkhya 1 990] that none of S tove's four ' p roofs ' succeed in t h i s tas k . Th ree o f h i s proofs do n o t refu te the scepti cal thesis a t all , but a. n alto get her d i fferent thes i s . Stove's fou rt h ' p roof' uses the sampling princi ple to j ust i fy-i n a. p robab i listic sense-one particular i n d u ct i ve i n ference. H aving one j us t i fied i n d u c t i ve i n ference, of course, refutes the sceptical thesis t h at no i nd u c t i ve i n ference is j ustified. However, I hav e shown that S tove's ' p roof' makes a crucial unstated assumpt ion regard i ng the randomness of a sample. The particu lar i n d u c t i ve i n ference is not j us t i fied at al l , once t h i s u nstated ass u m p t i o n i s brought to light . S i n ce many theories of i nduct i o n seek t o j us t i fy i t by using the sam p l i n g principle, I review my cri t i que of Stove's fourth ' p roof' [Stove 1 98 6 , p p . 55-75] i n t he n e x t sec t ion .
9.8
The S a m p li n g Princi p le , Ra n do mness and t he Generalized Grue Paradox
,
The sa m p l i ng principle states t hat when a sample is d rawn randomly from a population , t he probab i l i ty that the sample i s representat i ve of the popula tio n i s very h igh p rovided t h at the samp l e is ' reasonably large . ' T h e i nterest i ng t h i ng about i t i s that ' reasonably large' i s measured on an absolute scale, and not as in ' reasonably large fraction of the total p o p u l a t i o n . In fact , t h e '
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sam p l i ng principle holds even when the sample is a very small fraction of the total pop u l at ion , as long as i t i s reasonably l arge on an absolute scale. For i nstance, as Stove showed by using simple combi n atorics, i n a pop u l at ion of one m illion ravens composed of j ust 50 percent b l ack ravens, more than 99 percent of the 3000-fold sam p l es match the blac k n ess freq uency of the popul at ion w i t h i n 3 percent . That is, of all the possi ble sam ples contai n i ng 3000 ravens t h at can be drawn from t h i s pop u l ation , more t h an 99 percent of t hem h ave a proportion of b l ack ravens between 4 7 and 53 percent. Clearly, 3000 i s a small fraction of one m i l l ion . Moreover, the proba b i l i ty that the random sample w i l l nearly m atch the distribution of the popu l ation shows an almost negligible decrease, as the size of the pop u l ation grows while t he size of the sam p l e i s kept constant . B ased on this sam pl i ng principle, S tove very carefu l l y constru cted an argument to show that from the hypotheses A and D given below , where ' Pop' stands for "the populat ion of ravens, each at least 1 00 cc in vol ume and no overlapping, on earth between 1 0,000 B . C . and A . D . 1 0 ,000," the inductive i n ference E h as a very high probab i l i ty. A:
S is a 3000-fold sample of Pop .
D:
J ust 95 percent of the raven s i n S are black.
E:
The proportion of black raven s i n Pop is near 95 per cen t .
T h e gist o f Stove's argument i s very s i m ple, though he took great pai ns t o lay d ow n each and every step very el a bo r ate l y . S i n ce by the sam p l i n g pri n c i p l e , most of the 3000-or-more-fold samples of Pop contai n nearly the same pro portion of bl ack ravens as Pop, i t fo l l ows t h at t h e p robab i l i t y t hat S c on t ai ns t he s a m e proportion of b l ack ravens a s P o p i s very h i g h . C o n s e que n t l y , the probab i l i ty of E given A and D i s al so very h i gh . A s the i n ference f r o m A and D to E i s i n d u c t i ve , Stove con c l u ded t h at t h i s amou nts to a refu tation of the s c ept i c al t hesis about i n d u ction by means of a co u n terexample. The above a1·gu m e n t s , h owever , m ake a very c r u c i al h i d d e n ass u m p t i on . t o highlight t h i s u n derlying assumption , cons ider t h e fol lowing sce n ari o . You are s t an d i ng outside a sea l e d room which is k nown to contain a large number of balls, say a m i l l i o n . The bal l s, al l o f t h e same s i ze , m aybe all black, a l l w h i t e , or any proportion in between . T h ere i s a s l o t in t h e room from w h i ch a person i n side the room passes you a b al l . You ex a m i n e the bal l , determine its color, and then ret urn it back th rough t he lot , at wh ich point the person p ass es you another ball , an d so fort h . A fter g o i n g t h r o ugh t h i s p r o ce d u re 3000 t imes and having found t h at 95 percent of the bal l s were In
order
346
Part III: The Implications
black , woul d you say confidently-or w i t h a high degree of probab i l ity-that 95 percent of the bal ls in the room are black? I clai m t h at in the absence of any other i n format ion, any rational person will be very much reluctant to make such sweepi ng general ization . For instance, t here seems to be no reason to suppose t h at the person i s giving a new ball to be exami ned each t i me, i nstead of using j ust one black and one white bal l . O n e might obj ect here that i t i s t h e p resence o f a person , a free agent , that makes al l t h e difference. B u t suppose that you rep l ace t h e person w i t h a machi ne; i n the absence o f any knowledge about h o w the m achi ne operates one would still be rel uctant to conclude any t h i ng about the balls i n the room. Even i f you were not requi red to retu rn the bal l s , h av i ng exam i ned 3000 bal l s , a n d having no knowledge whatsoever about the mechan i s m responsible for ej ect i n g balls out of the slot , 1 maintain th at a rat ional person w i l l h ave no 'grounds' to make any conclusions about the balls inside t he room. However, arguments s i m i lar to Stove's can be made for a l l t hese situ ations, lead i ng one to i n fer with a high probab i l i ty t h at 95 percent of the balls i n the room are b l ack. The fall acy i n Stove's argument , as should be apparent by now , stems from illegi t i m ately assi m i l at i ng two distinct cases . One case i s of an urn contai n i ng one m i l l ion bal l s such t h at 95 percent of the 3020 bal l s ra n domly drawn from it are black . The other situation i s that of the 3020 ravens observed so far 95 percent are black . In t he first case t here is a very h i gh probab i l i ty t h at 95 percent of the balls i n the urn are b l ack . I n the second case, in the absence of any other i nformation, not h i ng what soever can be sai d about the colors of all the ravens ( e xc ep t that 2869 o f t h e m a r e b l ack ) . ( The c on f u si o n emanating from ignoring t h e relevant distinction i n t hese two cases h as al so been noted by Keynes ( 1 92 1 ] , ch. XXIV:4, p . 284 . ) However , l e t u s concent rate o n the specifics of S tove's arguments. Stove's argument does i ndeed show t h at one can i nfer E from A a n d D w i t h high p r ob abi l i ty p rovided t hat sample S i s t aken at random . But if the s am p l e exam i ned i s not random , the inference to E from A and D h as no cred i b i l i ty. Thus, i n o r d e r to vindicate i nduction, Stove must show that i t i s possible to i n fer E from A and D w here S i s a 3020-fold sample of ravens examined so far . In order for his arguments to l ead to this end he must also show t h at t h i s sam p le S is r an d o m w i t h respect to Pop. S i n ce Pop e x t e n d s over space ( 'on Eart h ' ) as wel l as t i me ( ' between 1 0 ,000 B . C . and A . D . 1 0 ,000 ' ) , t he randomness of S m u st b e demonstrated w i t h res pe c t to space a n d t i me. F i rst consider randomness of S over space. For A an d D to j ustify E , w i t h a h i gh d e g r ee of p robab i l i ty, the sample S must be chosen randomly from t h e
Chapter 9: Predictive A nalogy an d In du ction
347
surface of Earth , or else t he hypothesis E must be restricted accordi ngly. I t i s very easy to i m agine t h at due to environmental d i fferences , raven s i n different geograph i c regions have different colors ( as i s i ndeed the case w i t h several other species-bears, for i nstance ) . Having d rawn one's sample all from Austral i a i t woul d be unreasonable to conclude t h at 95 percent of t he ravens are black all over Earth . Even when an attempt has been made to seek ravens from most places on Earth an d examine t h e i r color, a reasonable person w i l l not rule out-in the absence of any other grounds, the poss i b i l i ty of a l arge population of raven s exist i n g i n some u nderexp lored region, say the South Pole, and of predom i n antly w h i te color. The con fidence i n the randomness of 5, and consequently in the hypot hesis that i s i n d u ct i vely deri ved from i t , w i l l , and shou l d , depend a great deal on how the sample S was collected . O ne cannot rule out the poss i b i l i ty of M ot her N at u re play i ng a trick, i n spite of our best efforts to ensure t h e random ness of S . So i t seems t h at i n order for Stove 's arguments to save i n d uction 's face, t he sample S i n hypothesis A m u s t b e ran d o m ly d rawn from all over Earth. T hough t h i s criterion i s by no means easy to sat isfy, let us grant i t to Stove. But what about randomness w i t h respect to t i me? It is concei vable, agai n due to environmental differences , t h at ravens at d i fferent t i m e s pans show vari ations i n t h e i r p l u m age color. If t h i s sounds farfetched to you , consi der the following case t hat the biologists found puzz l i n g at one t i me. A round 1 850, previously u nrecorded dark forms of several species of moths were observed i n the i ndustrial areas of Man chester and B i r m ingham , Englan d . Later work by D r . H . B . D . Kettlewell showed that the change of color resul ted from the adapt ation of moth species to environmental alterations caused by i n d u s t r i alizat i o n . Vast quant i t ies o f soot , released from fa c t ories and home chi mneys, h ad deposited o n t ree trunks in t h e s u rrou n d i n g a reas and made the bark uniformly black . Moth s p ecies a d a pt e d by devel o p i n g the d ark form so that they were more effecti vely concealed on t he b l ack t ree t r u n k s from t h e p re d a to r birds.3 [ Wa l l a c e & Srb 1 964, pp. 4 0-42] . This exam p l e , of cou rse, i s presented merely to p o i n t ou t t h e p o s s i b i l i t y t h at , for re as o n s u n foreseeable at present , all the ravens after year A . D . 3000 could t u r n out to be w h i t e . Thus, i n order to co n c l u d e E j ustifiably from A and 0 , the s a m p le S must be drawn randomly over 20,000 Earth ye a r s One speci men from 5000 B . C . , another from A . D . 1 2000 , a n d so on . I n t h i s case i t i s i m po s s i bl e lo make S random u n le s s one adm i ts t he possi b i l i ty of t i m e t ravel . O n e can i n c l u d e i n S random s am p l e s of raven s from 1 0 ,000 B . C . to the present t i m e , t h ou g h some ancient ones might be h ard to fi n d . ( Here , by i n c l u d i n g a raven in s a m p l e S I .
,
31
am gratefu l to Beryl N e l so n for b r i n g i n g
this example to my a t te n t i on .
348
Part III: The Implications
do not req u i re t h at a si ngle person must go exam i ne each of t he ravens . T h i s , of course, i s i m possi ble. I t i s sufficient that someone has seen the raven and recorded its color-and that t here is no reason to suspect t h at t h i s person was color- b l i n d or was lying. ) But how would you i n cl ude samples of fut ur e ravens i n S ? T h i s i s the real problem w i t h S tove's final attempt a t v i n d i cati ng i nduc t i o n . The best we can do i s obtai n a sam ple S that i s random w i t h respect to the surface of Earth and between 1 0 ,000 B . C . and the p resen t . On the basis of such a sample, one might conclude, w i t h a high probab i l i ty, that the proportion of black ravens i n the population of ravens on Earth between 1 0 ,000 B . C . and the p resent time is 95 percen t , not w i t hstan d i n g Mother Na t u re p l aying a t r i ck . B u t as t h i s sam p le i s anyth i n g but random as far as Pop i s concerned , not h i ng whatsoever can be concluded about Pop w i t h any degree of probab i l i ty. At least to me, t h i s is what the scep t i cal thesis on i n d u ct i on is all abou t . The form o f Stove's argument , a s well a s any other t h at u ses t h e sam p l i ng prin c i ple to j us t i fy i n d uction, i s fatal l y vulnerable to Goodman 's gnte para dox . [ Good m an 1 955, p p . 72-8 1 . ] Goodman put forth a r i d d le for t heories j us t i fying i nd u ction by i nt ro d u c i n g a predicate grue. G rue is defined as fol lows: an object is grue i f, and only i f, i t i s green and i s exami ned before the year A . D . 2000 or i s b l ue an d i s not exam i ned before t he year A . D . 2000. B ased on t h i s defini t i o n , a l arge sam ple of objects of a k i n d E, say emeral d s , if all taken before the year A . D . 2000 and all green i s also all grue. Consequently, on the basis of t h i s sample, i f one feels j ustified , a Ia Stove, i n concluding t h at a l l Es are green , one shou l d also feel j ustified in concluding all Es are grue. B u t both these hypotheses lead to contrad i ctory expectat ions for Es ob se rv e d aft er t h e y e a r A . D . 2000. T h e first t h i n g to n ot i ce abou t the grue paradox i s t h at it exposes the fl aw in any argument that attem pts to j us t i fy an i n ference span n i ng all t i mes based on a sam p l e res t r i c t e d over a s m a l ler t i m e span . S i n ce , in t he absence of any fu r t h e r assnmptions, a sam p l e rest r i cted over a specific t i m e s p an (smal l or l arge ) i s not random w i t h respect to a population spanning a l a r ge r t i me span , any attem pt to j u s t i fy p r o b ab i l i s t i ca l l y a h y p o t h e s i s coveri n g the whole pop u l at i on based on the sam ple w i l l be v u l nerable to the grue paradox . The reason i s t h at if we know a priori th at the sample i s res t r i cted to a t i me span T" where the popu l ation has a t i me span 1� and Tp > T. , t hen i t i s always poss i b l e t o i nt roduce a pred i cate l i ke grue t hat app lies t o t h e objects that are exam i ned i n s i de the t i me span T. and are green; and the obj ects exami ned outside the t i m e span T" i .e. i n the t i m e span ( TP - T. ) , t h at are
Chap ter 9: Predictive A na.logy a.n d Induction
349
b l ue. As far as I am aware , the debate on t he grue paradox h as fai led to note t h i s s i mple cru c i al poi n t . ( See Barker & Achi nstei n [ 1 960] ; Good m an [ 1 9 7 2 , p p . 398-4 1 2] ; Rescher [ 1 9 76] ; B u n ch [ 1 980] ; S h i rl ey [ 1 9 8 1 ] . ) I f we ad m i t the poss i b i l i ty of t i me travel , w h i ch makes i t possi ble to h ave a sample t h at is random with respect to time span of the whole pop u l at i on , t hen an argu ment based on the sampling theorem w i l l be i rrefutable an d , moreover, i m pervious to the grue paradox . The reason the grue paradox cannot be rai sed agai nst such an argument i s that the sample, being random , i s as l i kely to contai n objects that are exami ned before the year A . D . 2000 as objects exam i ned after the year A . D . 2 0 0 0 . From here i t i s only one more step to see how the grue paradox can be general i zed so t h at i t can be used agai nst any argument that tries to j ustify a conclusion about a whole population based on a sam ple drawn from a small section of t he population . Consi der a p op u l at i o n P t h a t spans an i nterval Dp i n some dimension . The d i mension cou l d be space, t i me, or a com b i n at ion of bot h . Now let S be a sample of P , i .e. a proper subset of P , t h at s p a n s a. smal ler i nterval D s across the same d i mension . T h e problem o f i nduction i n t h i s context i s : What j usti ficat ion i s there to ad m i t a statement about t he characteristics of t he unsam pled p op u l at i on ( P - S) based on the characteri s t i cs of sam p l e S? The scepti cal thesis , of course, says ' none! . ' The non-scept i c m ight t ry t o argue that by the sam p l i ng princi ple that i f S has a certai n characteri stic R i t i s highly probable t h at P h as characteristic R as well . I am deli b erately using a. vague word 'characterist i c ' to cover a w i de range of i n d u c t i ve statements l i ke ' a l l Xs are Y s , ' ' most Xs are Y s , ' ' 9 5 percent of Xs are Ys,' etc. For our pu rpose here, let R be the st atement ' al l X s are Ys, ' where X and Y are two i n dependent p red i c ates . Now an ar gum e n t based on t h e sampl ing pri n c i p l e t o j u s t i fy i n d u c t i o n w i l l be val i d on l y when one of t h e fo l l ow i n g t wo con d i t i o n s i s sat i s fied : l.
The sample dom n ess i s
S
pp . 585-603] , pnon . 2. It
is
ran d o m
with respect to
S i n ce t h e i ssue of ran X X I V ; B u rks 1 9 7 7 , t h a t D. must n o t be k n o w a bl e a
cont roversial o n e [Keynes
a.
l e t m e s ay
least say
Cb.
the objects sat i s fy i n g pred i cates X and Y interval Dp . In t h i s case one woul d qualify t h e argument j u s t i fy i n g i n d u c t i o n b y say i n g t h at i t on ly applies to p r e d i c a t e s t h at are uniformly d i stributed . is known
a
at
Dp .
1 92 1 ,
priori t h at
are u n i fo r m l y di stri buted
If
neither o f these
s am p l i ng
con d i t i o n s
i n t he
is
princi ple can easily be
sat i sfied ,
t hen
the by i n t roducing a
t he argument b ased on
show n to be paradox i cal
Pa. r t III: The lmplica.tions
350
new predi cate Z, where Z applies to objects t h at lie i n the span G. and are Y , or t h at do not lie in the span G. and are not Y. The sample S, obviously, also h as the characteristic 'all Xs are Zs' set t i ng u p an expectation in the u nsampled population ( P - S ) t h at contradicts the one predi cted by ' al l X s are Ys . ' If the first of the above conditions is sati sfied, then the paradox cannot be raised , as G. i s not known beforehand . If the secon d con d i t ion i s t r u e , t hen agai n the paradox fail s because n o w Z i s n o t u n i formly distri buted across DP by vi rtue of its defi n i t i o n . This demonstrates that the sam p l i ng pri nci ple cannot be used to rescue i n d uction w i t hout making further assu mptions abou t randomness or uniform distribut ion .
The 'Dark S i de ' o f Induct i on
9.9
G i ven t h a t t he p roblem o f j ustification o f i nduction is a s open a s t h e problem of j ustificat ion of pred i c t i ve analogy, one wonders if i n d uction also h as a dark side, contai n i ng i n ductive i n ferences that are not j ustified. I ndeed , t here are p lenty of u nj ustified i nductive i n ferences . Some examples are presented below . •
1 i s less than 1 000, 2 i s less t h an 1 000, . . . ,999 i s less t han 1 000, t herefore all numbers are less than 1 000.
•
It has been reported that Francesco Sizzi used the following argument agai nst G al i leo's discovery of the satell ites of J u p i ter:4 "There are se v e n w i ndows in the head , two nostrils , two eyes, two ears , and a mou t h ; so in the heavens there are two fa vorable s t a r s , two u n p r o p i t i o u s two l u m i n a r i es and Mercury alone undeci ded and i n d i fferent . Fr o m which and m any ot h e r s i m i l ar phenomena of nature, s u ch as the seven metal s , etc . , which i t were t e d i ou s t o enu merate, w e gather that the nu m ber of planets i s ne ce ssar i l y seven . " ( T h i s is quoted on page 822 in Newman [ 1 956] . ) ,
,
During 1 988, which was a. presidenti al elect ion year i n the U S , I was to fi n d , in several newspapers, statistical a n alys e s of the past elect ions. Several patterns were noted by reporters and presented as sugges t i ve of this ye a r s outcome. For i n s tan c e i n one such news story, 5
•
amused
'
41
am
5 As
,
gratefu l to P rof. Peter G acs for bringing this exam ple t o my atten t i o n . I recal l , t h i s story appeared in Boston Glo be a r o u n d t h e m i d d l e of Febru ary 1 9 8 8 .
Chapter 9: Predictive Analogy and In duction
35 1
i t was noted t h at i n the past , whenever the Democrat i c party nomi nee was the one who had won the Iowa caucus ( the fi rst caucus to be hel d ) , he lost to the Rep u b l i can opponent in the main elect i on . On the other han d , whenever a Democrat i c nom i n ee was t he one who had won the New H ampshi re p ri m ary ( t he fi rst pri m ary to be hel d , w h i ch fol lows the Iowa caucus) then he won the p residential elect ion . Would t h i s j ustify an i n ference t h at the win ner of the Iowa caucus ( who was Richard Gepha. r dt ) woul d lose the pres i dential election , if nom i n ated ? Perhaps the point of i ncluding t h i s analysi s i n the new story was to weakly suggest i t , but this i s a prime exam p l e of what [ wou l d consider totally u nj ustified i n ference from i n d uction . 6 •
Sports i s another area t h at i s r i fe with analyses l i ke this. Past statistics are often p u t forward , w i t h no j ustificati on w h atsoever, suggestive of w h at might ha p p e n now . For i nstance, during the basebal l world se ries i n 1 99 1 , the two contending teams ( M i n nesota Twins and Atlanta. B r aves ) were tied 3-3 goi ng i nto the seventh and the fi n al game. The seventh game was taking place i n M i n nesota so t h at the Twins h ad the home-team advant age. Before the game, m any sportswri ters recal led a. s i m i lar situ at i on fou r years ago when M i n n esota. entered the seventh game with a 3-3 tie agai nst St. Loui s , and won the game, and the world championshi p , by beat i ng S t . Lou i s at home. P red i c t i ve analogy woul d surely s uggest that t hey woul d do the same agai n i n 1 9 9 1 . D u r i n g the telecast of the seventh game between the Twins and the B raves, the commentator poi nted out t h at in the h i story of baseball , only fi ve t imes before i t h as happened t h at i n t h e fi r s t s i x gam es of the world seri e s , the h om e team al ways won . ( Th i s wo u l d res u l t in a 3-3 tie, because t h ree of the six games a r e p layed at t h e h o m e of o n e team , and t h e rest are p l ayed a.t t he home of t h e o t h e r team . )
these
A nd i n four of
s i tu a t i o n s , t h e
home team lost the seventh game. ( The e x c e p t i o n was the 1 987 world series. ) Applying i nd u c t i ve i n ference t o t h i s d at a wou l d suggest t h at M i n nesota has a 20% chance of w i n n i ng t h e game. This cont r ad i c t s the i n ference fr o m p red i c t i ve a n a l ogy u s i n g t h e 1 987 w o r l d s e r i e s as the source. am sure t here are some of you w h o find such s t a t i s t i c s compelling would disagree, b u t I c o n s i d e r such use of i n d u ct i o n q u i t e u nj u s t i fi e d . What is the connection between the wor l d ser i e s t hat was p l aye d i n I
6 Incidentally, t h e i n ductive i n ference suggested b y t h i s analysis t u rn e d o u t t o be false . Michael Dukakis, the Democrati c nom i nee and the w i n ner of New Ham psh i re p r i m ary, lost the presidential election to G eorge Bush .
Pa.rt III: The Implications
352
1 955 ( when B rook lyn won at New York Yan kees ) and the one being p l ayed now? A nd why should any t h i n g t h at h appened in 1 955 h ave any relevan ce to what m ay happen now? ( Of course, such stat i st i cs m ight be q u i te i nteresting for i t s own sake. I am only object ing to their use in generat i n g i n d u ct i ve i n ferences . ) •
I n i nvest igat i ng the Challenger space shuttle d isaster w i t h t h e P resi dent i al com m i ssion , famous physicist and N o b e l laureate Richard Feyn m an noted the gross abuse of i n d uction as one of the factors contri but i ng to t he t ragic m i shap: " . . . [ T ] he p henomenon of accep t i ng seals t h at had shown erosion and blow by in previous flights i s very clear. The Challe nger fl ight i s an excel lent example: t here are several references to previous fl ights; the acceptance and success of t hese fl ights are taken as evi dence of safety. But erosion and blowby are not w h at the design expected . T hey are warn i ng that somet h i ng i s wrong. The equ i pment i s not operat i ng as expected , an d t herefore t here is a danger t h at i t can oper ate w i t h even w i der deviations in t h i s u nexpected and not t horoughly u nderstood way. The fact t h at this danger d i d n o t lead to a catastrophe before i s no guarantee t hat i t w i l l n o t t h e next t i me, unless i t i s completely u nderstood . W h e n p l ay i n g Russian roulette, the fact t h ai the first s h o t got off safely is of little comfort for the nex t . " ( See Feyn m an [ 1 986] . The quote here i s from p . 223 of the reprint i n Wh at do you c a re . . . .
)
T h ere are many o t h er exam p les l i ke t hese . In fac t , one can i n d u c t i vely i n fer
from t he m that i n d uction is not j usti fied . B u t , att ract i ve as t h i s t r i v i al refu t at ion of i n d uction i s , i t i s not the point here . The po in t is t h at the j us t i ficat ion for an i nd u ct i ve hypot hes i s i s not to be fou n d in the number of i n st a n c es con fi rm i n g t h e h y p o t h e s i s alone, an d a hypothes i s based solely on some regu l arity observed i n t h e past i s not j u s t i fied a t al l .
9.10
Induct ion i n Cognit ion
T here remai n two facts concerni n g i n d uction t hat can not be i gnored . Firstly, i n d u ctive i n ferences are j us t i fied , as our scient i fi c and tech n ological progress clearly attests . Secon dly, i n d uction carries a psychological force so m e
Chapter 9: Predictive Analogy an d Induction
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t h at m akes an i n ference derived from it almost com pel l i ng, even when 1 t J S not j us t i fied , as the l ast two exam p les above test i fy. A ny reasonable t heory of i n duction must be able to explai n both t hese factors. Regarding the fi rst factor, we ask : W h at j u sti fies a n i n d u c t i ve i n ference? We h ave j ust seen t hat it cannot be the number of i n stan ces encountered in the past alone. Wel l , then we need to look in some other place. B u t where? Wei t zenfeld's perspec t i ve on p red i c t i ve analogy i l l u m i n ates the way to an answer here. Recall t h at Wei t zenfeld argued t h a t it i s not the observed s i m i l ar i ties between the source and the t arget t h at p rovide a j us t i fi cat ion for an arg ument from predi c t i ve analogy, but i nstead , i t is t h e backgro un d k nowledge t h at j us t i fies (or does n o t justify ) t h e second o r der general ization w h i ch says t h at the observed s i m i larit ies determ i n e t h e i n ferred ones . I n the same spir i t , we can perh aps seek the j u sti fication for a n argument from i n d uction i n terms of background knowledge. I n deed , when we reconsi der the j us t i fied i n d u ct i ve argu ments, we fi nd t h at almost always t here i s some underlying theory t hat gi ves some expla n a tion for why fi n d i ng the confirming instan ces of t he i n d uc t i ve hypot hesi s should i ncrease one's confi dence in the hypothes is . Thus, t h e n u m ber of i n st an ces encountered in the past lends s t rength to an inductive hypothesis only when t here already exists some t heoreti cal framework p rov i d i n g t he j ust ificat ion . T h i s observat ion, trite as i t m i ght seem to some, h as several major con sequences. F i rstly, since ' t heories' are cogn i t i ve c o n st r u c t s , i t i m mediately m akes the j ustification of an i n d u ct i ve hypothesis a subject i ve not i o n . People h ave d i fferent theories an d , t h erefore, what i s a j us t i fied i n d u ct i ve argu ment for one i s h u mb u g fo r anot her. Various kinds of s u per s t i t iou s b e l i e fs , as t rology, etc . provide examples to i l l u s t r a t e t h i s poi n t . It m i g h t well be t h e c a s e t h at w h en e v e r a total l u n ar ec l i pse has occ u rred , s o m e m i sfort u n e h as b e fal l e n Joh n . This p ro v id e s co m pe l l i n g evidence to J oh n , a beli ever i n as t r o l o gy , t h at total l u n ar ecli pses cause m i s fort u n e . H oweve r to Peter , a close friend of John and an u n i magi n at i ve b u t b r i gh t aero n au t i cs e n g i n eer , t hey are merely c o i n c i de n c e s . On the other h an d , Peter h as n e ver been able to convi n ce J o h n , who h as a fear of fl y i n g , a b o u t the safety of ai r t rave l . A l l t h e evidence t,hat Peter poi nts out , John d i s m i sses w i t h a wave of h an d as coi nci dences. consequence of this observat ion i s that i t i dent i fies two i n de of the p roblem of i n d u ct i on : cogn i t i ve and m e t aphy s i cal . U n derstan d i n g t h e d i fference between them wou l d hel p a great deal to gel a bet ter perspect i ve on i n c! uction , an d to avoi d some of t h e n eed less c o n t roversy over i t . T h e seco n d
pendent
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The cog n i t i ve d i mension comes from consi dering the quest ion: How does our backgro u n d knowledge j ustify some i nd u ct i ve hypotheses b u t not others? A study of t h is p roblem can be u ndertaken w i t h i n a framework of beliefs and cog n i t i ve mechan isms that allow our beliefs to affect our perception of the world , and t h e wor ld to mod i fy our beliefs-w i t h i n frameworks such as t hose of Goodman [§4 . 3] , P i aget [§4 . 4 ] and the one developed here. For i nstance, in the framework of i nteractionism developed here, i t can be argued ( i n a very general sense, of course ) t h at i t i s the process of p rojection-or assi m i l a t i o n , to u s e t h e more general P i agetian term-that u nderlies induction. The only way we can i n teract w i t h an obj ect or a s i t u ation , and perceive i t , i s b y ass i m i lat i n g it t o a pre-existing concept network o r schema. It i s t h i s ass i m i lation that gi ves rise to certai n expectations from t h e object based on the concept network ; and i t i s t he process of h av i ng expectations abou t the obj ect , based on past experiences , t hat i s formally k nown as i n duction . If we realize t h at t h e concept networ k , to w h i ch t h e object is being ass i m i lated , i n corporates, i n some way, t h e structures of the obj ects and s i t u ations en cou ntered in the pas t , then there i s no d i ffi c u l ty in seei ng how i n duction can arise from ass i m i l ation . Thus, i n d uction i s not seen as prov i d i n g j ust ificat ion to certain cogni t i ve processes , b u t rat h er it i s v iewed as aris i n g out of cogni t i o n . That i s , i n stead of t ak i n g the posi tion t h at external real i ty is such t h at an i n d u ct i ve i n ference is j usti fied i n a probab i l i s t i c sense, we reverse our stan d , and view i n d uction as a h u man cogn i t i ve process-al l too fal l i b le. W i t h t h i s approach, the p roblem of i n d uct ion lies in s t ud y i ng t h e u n derlying cogni t i ve mechanisms, and to explai n t he characteristics of i n d uction in terms of t hese mechanisms. ( An effort i n t h i s spirit h as been carried out by Holland et a l . [ 1 986] . ) A d m i t tedly, !. h i s p r o ble m is st i l l too complex , g i ve n our existin g k n ow ledge of cognition, to be add ressed ful ly here. Yet , i t seems prom isi ng to me i n t h a t I foresee considerable p rogress bei ng m ad e towards u nraveling it i n the next few years or so. I nt eresti ngly, v i e w i n g i n duction from t h i s vant age point al so ex p l a i n s why arguments from i n d u c t i o n a p p e a r psycholog i cally compelling. This point m i ght be better appreci ated by com p ari ng i n d uct ion with some other c og n i t i ve process, say vi sion . When a dot i s flashed i n t he visual field of a person followed by anot her dot a short distance away from the first one, the person sees a con t i nuous motion-as i f one dot moved smoot hly fr o m t he posi tion of the first dot to t h e pos i t ion of the seco n d . ( See Kolers [ 1 972] , and also § 4 . 2 . 1 . ) The i m agi n at i ve m i n d seems to fill in the gaps of the perceptual data to c reate a pattern of i t s own l i k i ng. Perhaps, i n t he same way, when a re peat e d pat tern i s presented , as i n the examples above, the m i n d seems to
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fill in the t heory needed to m ake the argu ment j us t i fied . The metaphysi c a l d imension t o t h e p roblem o f i n d uction comes from con sidering the question : What i s i t about the n at u re of the external world t hat m akes some ( many? ) i n d u c t i ve i n ferences val i d , and consequently j usti fies the process of i n d uction? ( The reason I refer to it as the metaphysi cal d i mension i s because o f i t s i n t i m ate relationship to t h e quest ions l i ke : Why d o we e x i s t ? Why are w e the way w e are? W h y i s the world the way i t is? etc . , the pursui t of which i s equal ly fut i l e . ) Notice that t h i s form u l ation, b y tak ing 'j ustification' to mean ' i ncreased l i keli hood of s ucceeding i n the external worl d , ' i m medi ately pl aces the problem of j us t i fi cat ion in the structure of t he external wor l d . For t h i s very reason , however, any app roach to a d d ressi n g t h i s problem essen t i a l l y leads u s to a. dead encl . The key point of d i fference between the two d i mensions of i n d u ct i o n , and the fut i l i ty of pursuing the metaphysi cal di mension , can be better appreci ated by consi dering our vi sual system agai n . V i sual perception and cogni t ion in humans are of a com plex character with m any ' i l l u sion s ' l i ke s u bject i ve contours, apparent motion, figu ral aftereffects etc. S t udyi n g these charac teristics of v i sion from a. cogni t i ve poi nt of view amou nts to studying t hem empiri cally, and formulat in g function al and structural t heories to integrate the empirical observations in a framework . For i n stance, take the ch aracter i s t i c of the eye t h at causes it to ' fi l l i n ' the edges and contours in the visual fi el d . W h at j ustificat ion i s t here for i t ? The cogn i t i ve approach seeks j usti fi cation in the struct ure an d function of the eye . In t h i s case, i t i s explai ned from the con nections between the cell s in the lateral gen i c u l ate n u cleus and the v i s u al cor t ex . S i g n i fi cant ad van ces in o u r u n der t an d i n g o f the h u m an vi s u al s y s t e m t h at h ave been m a.cle i n t h i s cen t u ry cl ea r l y attest t o th<" s u c c e ss of this approach. ( See H u bel [ 1 988] . ) The metap hysical approach , however, b e gi n s by t a k i n g the nature of the v i s i on as given , an d as k i n g : What i s i t about t he st ruct u re of t h e external world t h at m akes our v i s u a l system succeed ? Why do we have two eyes ? W h at i s i t about the external worl d ( an d oursel ves ) such t h at o u r v i s u a l system 's characteristic of fi l l i n g t h e edges an d con tours i n the visual field i ncreases our survivab i l i ty ? The u t ter hopelessness of even tryi n g to address t hese questions should be obviou s . Of course, one cou ld par t i al l y answer these questions from an evolu t i on ary and geneti c s t a n dpo i n t , but then i nd uction can also be exp l ai ned in a . s i m i l ar way. H owever, a. n ardent i n d uctivisl , s e e k i n g the sol ution to the me t a p hy s i cal p r o b l e m , is not h a p py with tha t . For h e r , to s ay t h at i nd u ction is j u s t i fied because i t h as been su ccessful i n the past is i tself a n i n d u c t i ve argumen t . The only way to avoid c i rcu l ar i ty i s
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to show somehow why it is l i kely to be successfu l in the fut ur e as well . B u t s i n ce t h i s cannot be d o n e w i t hout violat i ng t h e autonomy o f the external wor l d : t h i s road leads nowhere . Of course, it does not p revent one from hypothesi z i ng el aborate t heories t hat j us t i fy i n duction metaphysi call y, but any such t h eory must remai n essentially a conj ecture. To s u m up, i n d uction i s a cogn i t i ve mechan i s m , and , in this respec t , no d i fferent from other cogni t i ve mechanisms l i ke vision . W h i l e t h ese cog n i t i ve mechanisms are a val uable asset to cogn i t ion , t hey can nevertheless, lead to serious j u dgmental errors . The best we can do i s to u nderstand them ful ly, and make ourselves less vu l nerable to the erroneous j u dgments caused by t hem . T h i s proj ect , however, can only be add ressed from a cogn i t i ve poi n t o f view . A s far as the metaphysi cal d i mension to the problem of j usti fication of i n d uction i s concerned, i t can no more be j ustified t h an we can j usti fy the fact t h at we h ave two eyes. The fact t h at we are t h e way we are, a n d t h at it h as worked wel l for us so far i n terms of our survival , does not guarantee t hat our percept u al and cogn i t i ve mechan isms w i l l cont i nue to work wel l for us i n t he fut ur e also. It i s not h ard to i magi n e envi ronments, i n w h i ch i n duction becomes a. l i abi l i ty rat her t h an an asset . D i nosau rs , bowheads, M ayans and t here are n u merous other examples-have all become ext i nct or nearly ext i n ct for not bei ng able to counteract properly the d i s t u rbances i n their environments, whether the d i s t urbances were natural or caused by other, or even t h e i r own , species. We m ay p rove to be no except ion .
Chapter 1 0 O n Computational Approaches to Metaphor and A nalogy
10.1
Intro duct ion
T h e field o f Artificial Intel l i gence ( A I ) , which concerns i tself with design ing and b u i l d i ng machi nes-usual ly in the form of com p u ter p rograms capable of exh i b i t i ng ' intel l i gent ' be h av i o r , has not been ob l i v i o u s to the role of metaphor an d analogy i n creat i v i ty and problem so l v i n g , two of the maj or p rocesses req u i r i ng i n t e l l i ge n ce . But i t s focus h as n o t e x a c t l y been on s i m i l ar ity-creat i ng metaphors and creati ve analogies . The term ' metaphor ' i n the A I l i t er at u r e i s almost always u sed res t r i c t i v e l y to refer to the i nstan ces of m e t ap h o r i n l an g u a ge . I n t h i s n ar rower s e n s e , metaphor h as recei ved r a t h e r scanty a t t e n t i o n i n A I . M o re o ve r , the few attem pts t h at h ave been made to model m e t a p h or s have all been com parison - t heoret i c in s p i r i t . T h at i s , they a l l a ss u m e t h at t h e bas i s o f any me t a p h o r i s some u n d er l y i ng s i m i l ari ty be t w e e n the source and the t arget , a n d t h e n t h ey either set out t o com pute the s i m i larity, or t a ke the sim i l ar i ty a s exp l i ci t ly g i ve n and set out to u s e t h i s i n fo r m a t i o n to determine t h e me a n i n g of a m e t a p h o r i c al p h r a s e . C lear l y, w h i le such ap pr oac h e s address t he mode of s i m i l ar i t y - based me t a p hor , and to some extent s u gg e st i v e m e t a p h o r , t he y leave s i m i lari ty- c reat i n g met aphors completely out i n the cold . Perhap s , this should not be s u r p r i s i n g g i v e n the st ate-of- t he-art of Natural Language P roces s i n g ( NL P ) , w h i ch s t i l l r e m ai n s i n i t s i n fa n cy i n s p i t e of all t h e advan ces of t h e past t h i r ty years . There are m any key issues s urr o u n d i n g l i t eral and conven t i o n al mean i n gs t h at h ave not yet b een ful l y and satisfactorily i n corporated in any N L P s ys t e m . S i m i l ar i t y c r e a t i ng metap h ors, h av i n g to do w i t h n o ve l and creat i v e u s e s of wor d s an d 357
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phrases , h ave remai ned an u n reach able and unreal i s t i c goal . I present a brief overview of the N L P approaches to metaphor in Section 2. I t i s in the area of analogy that we fi n d much more acti v ity. In the short h i story of A I , analogy h as recurred with great stubbornness as a theme un derlying A I models , and even as the subj ect of i nvestigation t h rough t hese models . T n the last few years t h i s recurrence h as i ntensified a great deal . However, the hub of almost all t h i s acti v i ty h as been pred i c t i ve analogy-the process of predicting further s i m il arit i es between the source and the target based on some existing s i m i l arities . Now we h ave already noted in the l ast chapter t h at p red i c t i ve analogy is related to only one mode of metaphor, namely suggesti ve metaphor, and even that only somewhat obliquely, s i n ce suggest i ve metaphor does not carry the force of j ustification t h at predic t i ve analogy does . Consequently, all these models of analogy h ave little relevance to metaphor. To be more speci fi c , w h i le all these models address some is sues concern ing s i m i l ari ty- based and suggesti ve metaphors , t hey fai l to t h row any l ight on the p rocess u nderl y i n g creati ve analogies and s i m i l ar ity-creat i ng metaphors . I discuss t h i s issue i n more detail i n Section 3 . Though , for t h e most part , p red i c t i ve analogy h as kept t h e l imelight focused on i t sel f, and away from the other modes of analogy, a few ( th ree, to be precise) comp u t ational approaches to analogy h ave sought to focus on proportional analogy relations-that i s , relations of the form "A i s to B as C i s to D . " F i rst , t here i s the l i ttle k nown work of M ary Hesse [ 1 959a, l 959b] , where she developed an algori t h m for computing the fou rt h term, given t h e other three terms, of a p roportional analogy relation i nvolving context-free verbal analogies, as i n "what i s to fish as nose i s to man ? . " Then , there i s the wi dely known work o f Evans [ 1 963] , w here he designed and i m plemented a n a lgor i t h m for choosing the fourth term from a given set of fi ve alternat i ves, given the other t h ree terms of a proportional analogy relation i n vo l v i n g configu rat ions of geomet r i c figures. Finally, t here i s the recent work of Douglas Hofstadter and Melan i e M i t chell [ 1 99 1 ] , wh ere t hey des i g n e d and i m plemented an al g ori t h m for generat i n g the fourth term , given the other t h ree, of a proportional analogy relat ion i nvolving strings of characters . W h i l e on l y t h ree m o d e l s of proport i o n al analo g y h ave b ee n s t u d i e d , g i ven t he
i ntensity of research effort t h at h as been spent in modeling predictive analogy and gi ven t h at proportional an alogy relat ions seem quite arti fi c i al com pared to t h e ' real - worl d ' dom ains t h at h ave been u sed for p r e d i c t i v e analo g y, i t is quite i ron ic t h at the m ost i n novat i ve app roach to m ode l i n g t h e process of red esc r i p t io n t h at u n d er l ies all truly creati ve metaphors and analogies should be m ade in the context of proportional analogies. Evans was
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quite aware of the need for a redescription component in his arch i tectu re, and did i nclude a p ri m i t i ve version of one i n his program . However, it was over twenty years before the gen i us of Douglas Hofstadter tackled the p roblem h ead o n . From the outset of h i s research on analogy, Hofstadter has exclusively foc used on the p rocess of redescr i ption and change of representation t hat accompanies all creat i ve analogies and metaphors . To study the cogn i t i ve processes u n derly ing t h i s creat i v i ty, he designed an elegantly s i m ple, and yet astoni s h ingly r ich , m icroworl d of character stri ngs in w h i ch proport ional anal ogy relations can be formulated that requ i re a process of redescri ption that i s quite s i m ilar to the one th at underlies creat i ve analogies and s i m i l ari ty creat i n g metap hors . Then he and his col leagues developed a probab i l i st i c computer p rogram to generate the fourth t e r m of a proportional analogy relation , gi ven t he other t h ree. U n l i ke Evans ' system , i n w h i ch the descrip tions of the terms A, B, an d C were generated i n t h e fi rst stage and were kept fi xed thereafter, com i n g u p w i t h the appropriate descri ptions of the terms A , B, and C was the mai n t ask of Hofstadter 's system . The descri ption of each of the terms A, B, and C was affected by the descript ions of the other two term s , and it in turn affected t he descri ption of each of them . I briefl y d i scuss h o w Evans i n corporated the con text- depen dency of descri ptions 1 n h i s archi tecture, and t hen p resent Hofstadter's system i n greater detai l i n Section 4 . O nce w e realize t hat t here i s a n element o f redescri ption u n derneath ev ery creati ve metaphor or anal ogy, and if we stop relyi n g on the keywords ' metaphor' and ' analogy ' to l e ad u s to the com putat ional systems t h at can model the cogn i t i ve p rocesses u n d e r l y i n g c reat i ve an al ogi es and proj ec t i ve metap hors , an i nte r e s t i n g a n d some w h at s u r p r i s i n g , perspect i ve emerges . Vl/e fi n d th at t here are , i n fact, man y c omputati o n a l system s that are ca pable of generat i ng creati ve analogies and metaphors-w i thout cal l i n g them exp licitly by t hese n ames-and b r i ng a b o u t t h e c reat ion of i m i l ar i t y i n the p rocess . I argue this point in Section 5 . Fol lowing that, I outline an ar chitect u re for modeling s i m i l arity-creat ing metaphors i n Sect ion 6. F i nally, Section 7 s u mmarizes the m a i n points of t h i s c h apt e r . ,
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C omputat i onal Approaches t o L i nguist ic Metaphors
10.2
A s I ment ioned above, t here have been few computat ional models of l inguis tic metaphors . These models can be d i v i ded i nto two b road classes based on thei r approaches . The models in one class expl i c i t l y represent the meani ngs of all metaphori cal usages a word can have, and t hen address the problem of deci d i n g w h i ch i s the correct mean i ng i n a gi ven contex t . Thus, t he prob lem t hey add ress i s essen t i ally t h at of word sense disambiguat i o n . I should perhaps emphas ize here t h at the problem i s not as t r i v i al as it may sou n d , given the e x i s t i n g state of the a r t of N L P systems. T wo notable models i n t h i s class are t hose of Carbonell [ 1 9 8 2] and M art i n ( 1 988] . Both th ese models address the t ask o f prov i d i n g a n N L P system w i t h an abi l i ty to handle ' conventional ' metaphors , t h at is, metap hors t h at are so much a part of the accepted everyday speech as to a lmost become a part of t h e l i teral l anguage, as i n ' p r i ces are soaring' or ' I want to k i l l t h i s process . ' A lso, b o t h t hese models are l argely mot i vated b y the work of Lakoff & Johnson ( 1 980] , in w h i ch the authors have shown t hat a l arge n umber of t he convent ional metaphors of language are deri ved from a few general metaphor schem as such as ' more i s up, less i s down , ' ' personi ficat i o n ' etc. G i ven t h i s , Carbone l l a n d M art i n each fel t t h at i f an N L P system c a n be gi ven exp l i c i t knowl edge of these general metaphor schemas , a n d an abil i ty to use t h i s knowledge, t h e n the user wou l d be a b l e to i nteract w i t h the system using a l arge n u mber of conventional met a p hors . S i nce the speakers of any languag e usually have an explicit knowl edge of t he convent ional metaphor schemas of thei r language, t here seems to be n o re as on to not provide this information to an N L P syste m . Though such an approach is clearly j ustified from an engi neeri n g stan d point , it is not very i n terest i n g from a cogni t i ve point of view, i f what we are i nterested in is how metap hors get their mean i ngs i n the fi rst p l ace. I t i s l i ke bei ng gi ven the m u l t i p l i cat ion table when one i s i nterested i n fi g u ri n g o u t t h e m u l t i p l i cation algor i t h m . The m o d e l s i n t h e second class act ually u ndertake to compute, i n some fas h i on , the mean i n g of a gi ven metaphor. Notable among t hese are t he system s p roposed or i m plemented by Sylvia Russell , Jerry Ho bbs, Eileen Way, J ud i t h Weiner, Yor i ck W i l k s and Dan Fass. A s one woul d probably expect , t here are w i de var i ations i n what i s consi dered to be t he ' meani ng' of a meta p hor what back g roun d knowled g e' is provided to t he model from which t h e mean i n g is com puted , and how exac t l y t h is com p u t ation i s done. The brief d i scussion below shou ld g i ve you some i d e a o f t h e various approaches . ,
'
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Russe l l [ 1 9 76] , who was perhaps t he fi rst com p u tational l i nguist to venture i nto t he t reacherous terrai n of metaphors , i m plemented a system to figure out the mean ings of metaphorically used verbs, as i n "the country leapt to prosperi ty," or "the ship plowed the sea." The background k nowledge of her system was provi ded in two forms. F i rs t , t here was a m u l t i - d i mensional m at r i x t h at represented the structu ral s i m i lar i t i es ( an d d i fferen ces ) between di fferent verbal concepts. For i nstance, the concept s ' l an d ' and ' sea' both had t he features ' fixed ' and ' t wo-di mensional , ' t hough ' l an d ' lacked the feat u re ' fl u i d ' t hat ' sea' had . Second , t here was add i t ional i n format i on p rovi ded for the verbs t h at gave expl i c i t ' n arrow ' an d ' b road ' con straints on what featu res t h e verb expects from i t s obj ects . For exam ple, the verb ' plow ' expected i t s object to be ' lan d ' o n a ' n arrow ' read i n g a n d ' two- d i mensional ' on a ' b road ' readi n g . Her algor i t hm then speci fied a n u m ber of heu ristics to resolve any clashes among the features of the verbal concepts const i t u t i n g the metaphorical sentence. ( If t here are no clashes, t hen the sentence i s not met aphori cal . ) For i nstance, one rule was that if t he object of a verb l acks the ' n arrow ' featu re expected by the verb , see if it has the ' b road ' feat ure. The ' mean i ng' of the metaphor was then con s t i t uted as a c l uster of feat u res taken from the feat ures of the concepts involved . Her p rogram finally sea rched for a verbal concept that best corresponded to t h i s cluster of feat u res, and used t h i s concept i n paraphrasing the metaphori cal sentence. Wei ner [ 1 984; 1 985] p roposed a system that rel ied on sal ience, p rototyp icality, and epitomization to arri ve at the meani ngs of the metaphors of t he form " X i s Y ," as i n "John's hands are i ce . " The main i dea was to use the mos t salient attributes of Y ( t he at tribute ' te m p erat ure' of ' i ce' i n the exam ple) to see i f they are a ppl i c a b le to X ( ' John's hands ' ) , and when t hey were, t hose at t r i b ut e s a p p l i ed t o X const i t u ted t h e me a n i n g of the metaphor. The backgroun d know ledge was a h ierarchy of concepts, w i t h the att r i b u tes and value restrictions for each attribute speci fied for each con cept u si ng a K L O N E network . Furt h e r , t h e at t r i b u tes of each c o n ce p t , a.s wel l as t h e ranges of their values , were g r aded in the order of t heir salience. ( See lwayama, To k u n ag a , and Tan aka [ 1 990] f o r an a l go r i t h m for com p u t i n g t h e sal i e n ce . ) P rototypicality was used here s o t h at t h e at tribu tes attached t o a concept were t he at t r i butes t h at a prototy p i cal i n s t a n ce of t h a t concept m i ght have. Thus, att r i b u t e s of the concept ' p erson ' wou l d i nc l ude ' h as two h and s , ' even though there are persons who h a.ve , t h ro u gh some u n fort u n ate acc i d en t , l os t one or both of their hands. Epi t omi z ati on was u sed i n the sense that if t h e t y p i c a.l val ue of the t r an s ferred a t t r i b u t e rep rese n t e d a n e x t r e m e val u e fo r the target concept ( X ) , t he n it wou l d be con sidered a better metaphor . For i n s t a nce , the range of temperat ure for ' i ce' i s m u c h l ower t h an t h e ran g e of
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temperat ure for 'John's hand s , ' and hence t here is all the more reason for t ransferring the temperature att r i bute to John's hands. Lastly, she uses the d i stance between X and Y i n the abstraction h ierarchy to decide whether the statement "X i s Y " i s l i teral , l i teral s i m i lari ty, or metaphor: If X and Y were d i stan t , t hen the statement was deemed to be a metaphor. W i l k s [ 1 975] started out by propos i ng a ' preference semant ics' framework in which, w h i l e agreement between the seman t i c feat ures of the concepts used together in a sentence was preferred , it was not absolutely necessary. Thus, in "my car drinks gasoline," though the concept ' d ri n k ' preferred to h ave its subject be 'ani mate , ' when this featu re was absent from the concept ' car , ' the ut terance was s t i l l accepted b u t flagged as metaphorical . Later on, W i l k s suggested t hat the system be prov i ded the backgroun d k n owledge about the worki ngs of the car, and t hen an i nterpret at ion for ' d r i n k ' be found by matching i t s meaning against the background k nowledge about the car. I n t h i s example, the system wou ld fi n d t h at ' d r i n k ' best matches ' use, ' and the u tterance wou l d correspond to "my car uses gasoline." ( See also the d i scussion in Fass and W i l ks [ 1 983] . ) Fass [ 1 989] extended t h i s approac h . I n h i s system Met * , when a n ut ter ance cou l d not be u nderstood l i t erally or metonym ically, t hen an attempt was made to find an u n derlyi ng analogy between the relevant concepts and, i f one was fou n d , i t became the basis of the metaphorical mean i ng of the utterance. The backgrou nd k nowledge for h i s system was prov i ded in the form of sen se- frames, which contai ned an abstract ion h ierarchy of concepts, as wel l as other expectat ions associ ated w i t h the concept s . For i nstance, the sense- frame for ' d r i n k 1 ' contai ned the i nformation t hat i t i s a subtype of con cepts ' i ngest 1 ' and 'expen d " ' and t hat it prefers its agent to be 'animal 1 ' and the object to be ' d r i n k 2 ' ( w h i ch i s the noun sense of d rink ) . On encounter i ng "my car drinks gasoli ne," Met * , after fail i ng to u nderstand it l iterally or metonymically, woul d find an an alogy between the parts of the sense-frames ' an i m al 1 ' a n d ' car1 , ' n amely t h at the an i m al d r i n k s 1 d ri nk 2 , and the car uses2 gasol i n e . The key to finding this an a logy was t he fact t hat both ' dri n k 1 ' and ' use2 ' are subtypes of 'expend1 ' and both ' d r i n k 2 ' and g aso l i n e 1 ' a r e sub types of ' l i q u i d 1 . ' ( See also Helmrei ch , I verson an d Laroche [ 1 990] for further extensions an d a paral lel i m plement ation of Met * . ) '
Hobbs [ 1 979, 1 990] p roposed a n axiomat i c approach t o b e able t o d raw p roper i n ferences from a metaphor . He suggested t hat for s imple metaphors , such as "John is a pig," the context would rule out certai n i nferences t h at coul d be draw n from the ut terance-for e x am p le t hat John has a t ai l . For certai n conventional metaphor schemas, such as the spatial schema to talk
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about var i ables in math ( as in "the var i able N i s a t zero" ) , one needs to prov i de an appropri ate axiom to the i n ference generat ing system . In the above example, the axiom could be "if X i s a variable and W is the cond i tion of Y being i t s value, then W i s a l s o t h e con d i t i on of X be i ng at Y . " For m o r e complex novel metaphors i n volving struct u ral analogies between d i fferent schemas , as in "we i nsist on serving up t hese veto p i tches that come over the p l ate the size of a pumpkin" ( said by a Democrati c congressman during the Ford admi n i s t ration in 1 9 7 5 ) , Hobbs, while ack nowledgi ng that no natural l anguage processi ng system existing today can i nterpret i t [ 1 99 0 , p . 68] , s uggested t h at i f the schernas were represen ted as com plex sets of axioms t h at were i nterrelated , w i t h i n each schema, by t h e co-occu rrences of the same predi cates , then the schemas cou l d be l i n ked by assum i n g i dent i ty between correspond i ng con d i t ions, as in t h e con d i t ion of being t h e Congress being identical to t he con d i t ion of being the pitcher, w i t h the text and the schemas prov i d i ng valuable c lues for making this iden t i ficat i o n . N ot i ce t h at all the models of metaph ors di scussed so fa r are 'syntact i c' i n t h e sense t h at they try to der i ve t h e mean i ng o f t h e metaphor f rom syntact i c objects : from the gi ven representations of the words or con cepts. Even when one talks about keeping ' semanti c ' i n format ion , i t ends u p being manipu lated in a purely syntact i c way. R ussel l' s system does not real ly know what two- d i mensional i s , nor does Met* k now what gasol i n e i s . For i n sta.nce, Met* woul d probably fi n d the ut terance " my car eats coca- cola" as acceptable as "my car drinks gasoli ne . " The syntactic approach of these models is the main reason for their bei ng l i m i ted to convent ional metaphors, or s i m i l a ri t y - b ase d metap hors at t he very best , for t h e creat i v i ty of met a p h o r comes from i n cor porat i ng new i nformation from the envi ronment, and the s y n t ac t i c a p p roa ch prov ides no mech anism to handle t h i s . The key to model i n g creat i ve meta phors, as we see l ater i n t h i s ch apter, comes from bri nging i nto the p i ct u re the objects to which the concepts refe r . There i s one i n teresting approach t hough , which, w h i le i t i s a l s o syntac t i c in a sense, t r i es to model c reat i ve m e t aphors . It i s t h e dyn a m i c t y p e h i era r chy system of Way [ 1 99 1 ] . T h i s syst e m i s al m ost ent i r e ly based o n the not ion of an abstract i o n hierarchy. However, the abstraction h i e r a r c h y h ere con t a i n s a l l possible ways of a 7Ta nging t h e co n cep ts h i e m 1·ch ically , a n d not m e rely some canonical way o f doi ng it t h at r e fl e c t s the c u l t u ral n o r m . In fact. , t h i s i s h o w Way 's system i n co r p o r a t es the i n format ion from the env i ronment , for one m ay view t h i s global a b st rac t i o n h ierarchy as represent i ng t h e s t at e of the world as i t actually i s , and not as it ap pears t h ro u g h the s t r u ct u re of o u r language. C o nce p ts ' N i xon ' a n d ' s u b m ar i n e ' have a superconcept ' t h i ngs that behave in a se cr e t or h i d d e n m a.n ner , ' even t hough t h i s su perroncept i s
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not expl icitly represented in our language and culture. C learly, this global h ierarchy i s almost useless due to i t s enormous size and the com putational complexity of hav i ng to traverse it. So, Way i n t roduced t he notion of ' m asks' w h i ch p resent only a smal l part of the global hierarchy. M asks organ ize the global h ierarchy by showing certain l i n ks and h i d i n g other l i n k s . For i nstance , the hierarchy i mposed b y our language c a n be t hought of as a . ' l i teral ' m ask placed over the global hierarchy. A metaphor, t he n , works by replacing the l i teral mask with another mask t h at shows a di fferent organi zat ion of the concept . If the new organi zat ion reveals new concept nodes and new l i n ks , t hen t h e metaphor i s novel . For i nstance, the l i t eral mask for our language and c u l tu re organi zes the concepts so th at concepts ' N i xon ' and ' s ubmari ne' are very far apart i n the h ierarchy-thei r lowest common superconcept may be ' t hings . ' H owever, when the metaphor " N i xon i s the s ubm arine of world leaders" i s presented , a d i fferent mask is put on the global h ierarchy. The concept ' t h i ngs that behave in a secret or h i d den manner' becomes visi ble, an d so do the l i n ks connecti n g it w i t h t he concepts ' N i xon ' and 'submarine' as i t s i m media.tes subconcepts. Way 's approach is i nteresting and origi n al , t hough i t amounts to deter m i n i ng in advance al l possi ble s i m i l arit ies between all the concepts. W i t h t h e i dea o f masks , h e r model shows h o w l iteral a n d conventional language can b i de crucial cogn i t i ve i n formation t hat is revealed by metaphors . P re sented i n t h i s way, her account is not very d i fferent from t he one I presented in C hapter 7 . However , her act ual i mp lementation of the model sli des back i nto the rut of syntact i c approaches . To i mp lement her i deas computat ion ally, Way developed an algor i t h m for i nterpreti n g metaphors t h at uses the formalism of conceptual graph theory developed by Sowa [ 1 984] . Her algo r i t h m d i d not act ual ly use the global h ierarchi cal networ k , but worked by crea ting a new concept node that i s closer to the source and the t arget con cepts. For i nstance, in t rying to i nterpret "the car is t h irsty," the system created a new concept n o d e t h at i s the i m me d i ate s u p erconcept o f ' car ' and 'animal' but a s ubconcept of ' mobi le-entity, ' w h i ch is the least common su perconcept of ' car ' and ' an i m al ' before the metaphor. A d e fi n i t i o n of t h i s concept was t hen created b y specializ in g t he defi n i tion o f i t s superconcept ( ' mobi le-enti ty ' ) w i t h respect to the vehi cle concept ( ' t hi rs t ' ) . The res u l t , for t h i s example, was t he concept ' mobi le-entity t hat requires .liquid . ' I m plemented i n t h i s way, Way 's approach has two m aj or drawbacks . First of al l , an y thing can be cons idered metaphori cal , for the new concept can al ways be created-t here i s not h i ng to constrain i t . S e co n d , and more i m por tant ly, the defi n i t ion of the new concep t , as wel l as which attributes t ransfer
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from the source concept to the target con cept , are deter m i ned entirely by the i nformation i n the defi n i t i on and schema fields of t h e relevant concepts, w h i ch are all syntacti c items. To sum u p , we see t h at the natu ral l anguage processi n g approaches to metaphor h ave al l relied on the gi ven representations of word mean ings, with some add i tional so called semant i c i n formation , to com p u te t h e meani ngs of metaphori cal utterances . The result i s t h at their abi l i ty to correctly i n terpret metaphors depends a great deal on the tech n i cal det ai l s of t heir representa tion formali s m . Also, i n most cases , t h e represen tat ions are tai lored to suit the few examples t h at their systems can process, t h ereby rai sing questions about the extens i b i l ity of the general pri nciples t h at they c l ai m to embody. Agai n , t h i s is not to belittle the i n tensi ty of the effort t h at these schol ars have spent i n trying to i n corporate met aphors i nto t h e i r com p u t ational systems, but only to h i g h light the i m mensity of the tas k , and to suggest t h at the best avenue for approachi n g s i m i l arity-creat i n g metaphor com pu tation ally may not be language after al l .
10.3
Computat ional Approaches t o Predict i ve Analogy
P red i c t i ve analogy h as received considerable attention in the s ho r t h i story of A I . In fac t , in A I , w hen people use the term ' an alogy, ' they al most al ways mean pred i c t i ve an alogy . I t is perhaps u n derstandable. It i s pred i c t i ve analogy t hat l u res u s i nto t h i n k i ng that the ex i s t i ng s i m i l arit ies between two o bj e c t s or s i t u a t i on s consti tute a reason to po s i t that t h ere m i gh t be other s i m i larit ies as wel l . And once we bite the bai t , pred i c t i ve analogy at once app ears as a p o we rfu l h e u r i s t i c for p r ob l e m sol ving. L u red by t h i s g l i tt e r of p rom i s e , several AT systems have been designed a n d i m p km e n te d over the years t h at i n corporate pr ed i c t i v e a n a l o gy in s o m e form or anot h e r . S i nce Kedar- C abelli [ 1 988] and Hall [ 1 989] pr ov i d e a d e t ai l ed overview of vario u s A I m o d e l s of p r edi c t i ve an a l og y , T m e n t i o n only a fe w models here to g i ve you a flavor of their ap p r o ac h e s , and to po i n t out t h ei r i n ad e q u acy in mode l i n g creat i ve a n al ogie s . Robert K l i ng [ 1 9 7 l a , 1 9 7 1 b] i m p l e m e n t e d a system Z O R B A - T for p rov i n g t h eorems by anal ogy. G i ven the proof o f a t h eo re m in one do m ai n ( say , abeli an g r o u p s ) , Z O R B A - 1 wou l d use t he p r oof to prove an analogous t heo rem i n another domai n ( say, com m u t at i ve r i n gs ) . A s s u m i n g t h at t h e proof of the new t heorem T' is analogous to t h e p roof of the known t h eo rem T ,
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Z O R B A - 1 wou l d fi rst produce a mapping between t he statements of T and T'. Then, start i ng w i t h t h i s i n i t i al mappi ng, Z ORB A - I woul d extend the mapping, applying i t to the axioms used in the proof of T, and i denti fy anal ogous axioms in the domai n of T ' . These analogous axioms are used by a logi c t heorem p rover to attempt a proof of T'. Thus, Z O R B A - 1 dras t ically cuts down the search space of the theorem prover b y focusing attention on a set of ax ioms t h at i s much smaller t h an the set of all axioms i n the domain of T'. Not i ce here t h at the success of any such approach very much depends on w hether t he proof of the unknown theorem is, in fact , analogous to the given proof. That i s , one needs to make the assumption-or determ i nati o n , to u s e Wei tzenfel d ' s term-t h at s i m i l arity i n the statements o f the theorems i m p l ies s i m i l ar i t ies in the proofs of the theorem . I f t h i s assumption does not hold for some pai r of theorems, t hen an alogy can actually be a h i n drance. G i ven t h at the proofs of two theorems t hat look s i m ilar are in fact not sim i l ar , a s_vs tem based on analogy i s sure to waste much effort in com p u t i n g the an ak0y, and t hen focusi ng on al l the wrong axioms p icked out b y the analogy. A system t h at p i cks out axioms randoml y woul d easily ou t perform t he analogical system in t h i s case. My point i s simply t hat the i m p l i ci t meta- level assumption t h at migh t make the analogical system usefu l i n some cases , severely l i m i t s i t s usefu lness as a general heurist i c . For i n stance, g i ven t he proof t hat t here are as many perfect squares ( 1 , 4, 9 , et c . ) as i n tegers, an analogi cal system woul d h ave a very tough t i me trying to prove (or di sprove ) if t here are as m any real n u mbers as i ntegers. To arri ve at Cantor's di agon a l ization argument that proves t he r e are more real num bers t han i ntegers req ui res a completely new way of look ing at the numbers, poss i b l y even comi ng up with a d i fferent set of ax ioms. Thus, any general purpose t heorem prover t h at a l w ays t ries t o prove n e w th eorems by analogy from past t heorems i s bound to discover only m u n d ane theor e m s , and wou ld never come u p w i t h any t h i ng creat i ve . T h i s i s evident i n t he fac t t h at no new and i nteres t i ng t heorem has ever been proven by any t heorem prover based on analogy. ( By ' new' I mean t h a t t h e t r u t h or fal s i t y of t h e t h eorem i s not yet k nown to mathematicians at l arge , and by ' i n teres t i n g ' I mean t h at the s tatement of the theorem i s consi dered a research problem worth studying at least by some m athemat ician s . ) T h i s argu ment can b e extended t o other com putational systems that use analogy as a heuri s t i c for generat i n g su pposedl y better hypot heses [ Carbone ll 1 98 6 ; Falken hainer, Forbus and Gent ner 1 9 8 9 ; Hol yoak and Thagard 1 989] , t h ough d i fferent examples n eed to be cons i dered for each system . I con-
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si der t wo recently developed systems here t h at t ry to pu t p red i c t i v e analogy to wor k . Falkenhainer, Forbus and Gentner i m p l emented a p rogram called Struct u re M apping Engi ne ( S M E ) t h at com p utes s i m i l ar i ti es between the gi ven representations of a source an d a targe t . Now , s i n ce t here can be many s i m i l arities between two given rep resentations, S M E foc u ses only on t hose s i m i l arities t hat are supported by Gentner's structure- mapping theory [ 1 983] . A ccordi ng to t h i s theory, w h i ch represents t h e sou rce and t h e target as sets of predicate calcu l u s form u las, it is ' good ' to m ap two- or more- place relat ions ( as opposed to one- place predi cates cal led ' at t r i b u tes ' ) , and even ' better' t o m ap t hose relat ions t h at are i nterrel ated by h igher-order rela tions ( t h at i s , relations t h at occur as argu men ts to other rel at ion s ) . Thus, i n m apping t h e source s i tuation ' water-flow ' t o t h e target s i t u at ion ' heat-flow' i n F i gure 1 0 . 1 , ' p ressur e , ' rather than ' d i ameter , ' i s m ap p ed onto ' tem per at ure . ' The ' goodness' of a mapping refers to its pred i ct abi l i ty, of course. That is, a mapping i s better if i t i s more l i kely to m ake correct p red ict ions about the target . The problem here i s t h at pred i ct abi l i ty de p ends on the autonomous st ruc t u re of the e x ternal environ ment , and can not be determ i n ed from the i n ternal structure of a theory or a represen tation alone. l h ave al ready bel abored t h i s point i n t he l as t chapter. Systemat i c i ty, however, i s a syntact i c ch aracteristic of a m app i n g between two represent ations. I n equ at i n g t h e two, one com m i t s the grave epistemologi cal error of n o t o n l y affi r m i n g t h at one's representa tions are always the ' right' ones and are ' complete , ' but also t h at the external worl d i s bound to con form to certai n art i ficial feat ures of t hese representa tions. O r , to look at i t from another perspect i ve, the reason s y st e mati c i ty works for t h i s small and art i fic i al e x a.m p l e as i t d o e s is because the repre sentations of the sou rce and the t arget are s p e c i fi c a l l y t ai l or e d to i t . The background a s sumption n eeded for t h e anal ogy t o be usefu l , n a m e l y t h at systemat i c i ty determi nes p r ed i c t ab i l i ty, i s b l atantly m a d e t r u e i n t h e gi ven repre s e n tatio n s of t h e sou rce and the target . A s l o n g as r e p resen t a t i o n s are t a i l o r e d t h i s way, sys t e m a t i c i t y wou l d con t i n u e to g i v e an i l l u s i o n of s u cces s . H o we v e r , i f t h e represen t a t i o n s a r e altered even s l i g h t l y, s y s te m a t i c i t y fa i l s m i sc r ab l y . Th i s p o i n t can be best a p p r ec i a te d by t h e exam p l e s provided by Hof stadter and M i t chell [ 1 99 1 , p p . 30-36. ] S u ppose the rep resen tation o f t he t arget i nc luded the i n formation about the fact th at t h e vol u m e of the c o f fee i n t h e beaker is g re a te r t h a.n the v o l u m e of the ice c u be [ F i gure 1 0 . 2] . T h e n systemat i c i ty alone would h a v e n o reason t o prefer mapping ' p res s u r e ' to ' temperat u r e ' t h a.n to ' vol u m e . ' O r s u p pose t h a t r a t e of flow w a s i n c l u d e d i n t h e r e p r e s e n t a t i o n of ' fl ow , ' so t h at i t became a fi ve- p l ace rel at i o n :
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S OURCE SITUATION (Water Flow)
w.VUA CO J J I I
TARGET S ITUATION
(Heat Flow) FIGURE
10. 1
et. a l . [ 1 9 89] . )
(a) : Two physical situations i nvolving flow. (From Falkenhainer
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CAUSE
FLOW (beaker, vial, water, p ipe)
GREATER
PRE S SURE (beaker)
PRE S S URE (vial) GREATER
LIQUID (water) FLAT-TOP (water) DIAMETER (beaker)
CLEAR (water)
DIAMETER (vial)
Water Flow ( S o u rc e )
GREATER
TEMPERATURE
(coffee)
TEMPERATU RE
(ice cube)
FLOW (coffee, ice cube, heat, bar) LIQUID (coffee) FLAT-TOP
(coffee)
Heat flow (T a r get) FIGURE 1 0. 1 (b) : Representations of the situations shown in Figure 1 0. 1 (a). (From Falkenhainer et. a!. [ 1 989] .)
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GREATER
VOLUME (ice cube)
VOLUME (coffee)
GREATER
TEMPERATURE (coffee)
TEMPERATURE (ice cube)
FLOW (coffee, ice cube, heat, bar) LIQUID (coffee) FLAT-TOP (coffee)
Heat flow (Ta r get) FIGURE 1 0. 2 : A different representation of the target situation. (From Hofstadter and Mitchell [ 1 990] .)
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' flow ( beaker, v i a l , water, p i p e , 1 0 ccfsecon d ) . ' O n e can g o o n a n d on here; it i s quite easy to generate hordes of examples fo r w hi c h system at i c i ty eit her does not p i ck the ' right' mappi ng, or pi ck s the wrong one. ( See also Car roll & M ack [ 1 985, p p . 4 1 �45) , for fu rther cri t i c i s m of the structure mapping theory. ) The p rogram A n alogical C o n s t rai n t Mapping Engi ne ( AC M E ) designed by Holyoak and Thagard [ 1 989] uses a slightly d i fferent approach and its authors argue that i t does not have the same problems as S M E . Like SME, A C M E works w i t h the gi ven representations o f the sou rce and the target and tries to fi n d a set of pairi ngs between the terms of the two represen tations. U n l i ke SM E , however, A C M E uses a c o n n e c tion is t data struct u re and a spread i n g- acti vat ion relaxat ion algori t h m to com pute the a n a logi cal m apping. But s ince my cri t i c i s m i s not d i rected at how the m appi ngs are computed, the detai ls of t h e algori t h m are i r rel evant here. A C M E uses t hree criteria to eval u ate w h i ch mappi ngs are the 'right ' ones: i somorp h i s m , seman t i c s i m i l ari ty, and pragm at i c centrali ty. While i somor p h i s m and seman t i c s i m i larity taken toget her amount somewhat loosely to Gentner's systemat i city principle, i t is t h e pragmat i c central i ty t h at is the mai n point of d i vergen ce between A C M E a n d S M E. The i dea beh i n d the p ragm at i s m of A C M E is to keep the search focu sed on t hose m appi ngs t h at are of most i nterest to the user of the system . For i n stance, in the example of ' heat-flow' and ' water-flow , ' su ppose the rep resentation of ' water-Row' i n cl uded the facts t h at the volume of the water i n the beaker i s greater t han the volume of the water in the v i al , and t h i s d i fferen ce in vol ume is caused by t h e fact t h at t he d i ameter of the beaker is greater t h an t h e d iameter of the vial [Figure 1 0. 3] . Now w i t h the representation of ' h eat-flow' contai n i ng the fact that the vol ume of the coffee i s g reate r t h an t h e vol ume of the i ce cube [Fi g u re 1 0 .2] , A C M E st ill does not t ry to ma p ' d i a m e t er ' t o ' t em perat ure' anJ i n fer t h at t he h i g h e r tem p erat ure of t he coffee i s caused by its greate r volume because this i s i rrelevan t to t h e go a l o f u n d e r s t an d i ng t h e heat flow . Th i s relevancy i n fo r m at io n , however, i s s upp l i e d by t h e u s e r , w h o a s s i g n s n. hi gh e r w e igh t to certai n mappings.
Thus, we see that A C M E is not a l l t h at much d i fferent from S M E. I t also constructs c e rtai n m a p p i ngs- t ak i n g i n t o acco u n t u s e r p r e fe re n ce b e s i d e s sy s te m at icity - be t ween t h e s ou r c e and the t a. r get . T h e ma p p i n gs are, however, s t i l l syntactic prope r t i e s of the g i ven rep r<"se n t at i o n s of sou rce an d t h e ta r g e t , and as such are no more t h an m i rag es as far as t h e i r ab i l ity to m a k e pred i c t ions about the t arget i s con cerned . The app ar e n t success of S M E and A C M E
h as
been demonst rated only i n
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CAUSE
�
FLOW (beaker, vial, water, pipe)
GREATER
PRE S S URE (beaker)
PRES SURE (vial)
CAUS E LIQUID (water) FLAT-TOP (water)
GREATER
A
CLEAR (water)
VOLUME (beaker) VOLUME (vial) GREATER
~
DIAMETER (beaker)
DIAMETER (vial)
Water Flow ( S o u rc e) FIGURE 1 0 . 3 : Extended representation o f the source situation u sed by A C M E . (B ased on Tab l e 1 0 in Holyoak and Thagard [ 1989] . )
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smal l toy domai ns where the representations are al l hand tai lored , and where a sol u t ion to the target problem or a t h eory for the target phenomenon is already known to t he person or persons who are c o m i n g up with the represen t ations. I n a real-world s i t u at i o n , when t h e r e i s a real p ro b l e m , the solution of w h i ch i s not k nown b u t w hi ch i t wou l d be i nteres t i n g to sol ve. ( For exam ple, a p roblem l i ke the ones di scu s s e d in Gordon [ 1 96 1 ] and Schon [ 1 963] . See also § 2 . 5 . 2 ) . A n approach based on SME an d A C M E wou ld p rod uce eit her only m u ndane theories and hypo t h e s e s , or none at al l , for it wou l d all depen d on how t h e t arget i s represented . A n d when one does not have a theory to exp l ai n the target phenomenon, or know how to solve the problem , i t is hard to come u p w i t h t he r i g h t repre s entati o n in the fi rst p l a c e : in fac t , t h e key to p roblem solv i n g l i es i n co m i n g u p with j ust s u ch a r e p r e se n tatio n . To s u m u p , we see t h at pre d i c t a b i l i ty can not be c a p t u r ed i n t h e sy n ta c t i c p roperties of the r e p rese n tat i ons . T herefore, t h e use of pred i c t i ve a n alogy w h i ch essen t i al l y m akes a hypot h e s i s about the extern al e n v i ron m ent ba.sed on some syntact ic p r o p ert i es of the rep resen tat ion s-as a general pu rpose heuristic in any domai n depen ds crucially on w hether the ass u m ption that s i m i l arities between the given representations deter m i ne predictab i l i ty i s sat i sfied or not . To t h i s end, perhaps the best a p p roach to p red i c t i ve analogy might be the one t aken by Russel l [ 1 987] . Fol low i n g Wei tzenfeld's theory of analogy, w h i ch we discussed in the last chapter, Rus s e l l p rovid e d an e x p l i c i t mech anism i n h i s system for t h e u ser to a d d determ i n at i o n s. For e x am p l e , i f one wanted t o say t h at an a lo g i es w i t h respect to n a t i o n al i t ies are re l e v a n t i n deter m i n i ng t h e languages peopl e s p ea k , t h e n one cou l d p u t i n a. ' d et e r m i nation r u le ' say i n g that i f two persons h ave t h e same n a t i on a l i t y then t h ey speak the same l anguage. These determ i n ation r ul es were then used as logi cal a x i oms in g e n e r at i n g analogical i n ferences . T h u s , We i t z e n feld ' s second-order ge n e r al i zat i o ns-t h e backgro u n d assu m p t i o n s of an a n a l o g i c a l i n ference were made expl i c i t here . The res u l t i ng arch i t ect u re i s m u ch .- l f' a n e r , mor� effici ent , l e s s prone t o err o n eo u s i n fe r e n ce s , an d easier to a d a p t as backgrou n d ass u m p t i o n s ar e changed in va r y i n g co n t e x t s .
Besi des problem-so l v i n g , t h e r e i s one o t h e r area i n A l w h i c h h as often u s e d pred i c t i ve anilJ ogy, n a m e l y l earn i ng [ W i n ston 1 9 7 8 ; 1 98 1 ; C a r b o n el l
1 985] . T h e r e are two ways i n w h ich p red i ct i ve a n a l ogy is asso w i t h learn i ng. One is as ' s i n gle- i n s t an ce general i z at i o n , ' and t h e other i s as ' s c h e m a i n d u ct i on . ' In si n gle- i n s t a n c e ge n e r ali za t i o n , one i m p u te s a c a u sa l s t r u c t ure on a. gi ven re p resen t at i on of the so u r ce , thereby h y p o t h e s i z i n g t h at certain prop ert i es i m ply certai n o t h e r prorert ies. T h u s , a l aw seems t o have been l e arn ed from an exam p l e . C l ear l y , t h i s correspon d s t o the view o f p r e d i c t i ve anal o g y t h at j u s t i fies i t as a fi rst-order general i zation , w h i ch w e 1 983;
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crit ically exam i ned i n the last chapter. The schema i n d uction approach is somewhat more conservat i ve. Here, after an analogy b as been successfu l ly used to pred i ct somet h i ng about the t arget , the analogy i s abstracted to a general ' l aw- l i ke' schema. It also sees pred i c t i ve analogy as a fi rst-order gen eral ization , except t h at two con firm i ng i nstan ces are required, one of w h i ch must be an experi mental veri ficat ion . Before we add ress t hese uses of pred i c t i ve analogy, we must d i s t i nguish between two forms of learn i ng. One type of learni n g occurs when new i n for mation i s gai ned from the envi ron ment . Examples of t h i s type of learni ng a r e : learn i ng t h at flu ids t e n d t o flow from a h igher to a lower level , ( a chi l d ] acqui r i ng the notion of object permanence, learning one's way to the grocery store upon moving to a new tow n , not i c i n g for the fi rst t i me that the fami l i ar figure of the Star of Dav i d h as t h ree parallelograms i n i t , etc . The other type of learn i ng occurs when one noti ces some new connection between the p ieces of knowledge t h at one already has, as in d iscoveri n g a new theorem . Here all t he relevant i n formation i s provi ded by t h e knowledge struct ures-or concept networks in our ter m i nology-t h at the cognitive agent already h ad . T here is no i nteraction w i t h the envi ron men t , and no new i n formati on is gleaned from i t . ( Thoug h , of course, if we t ake i nto accoun t the cogni t i ve relations of the concept networks , t hen the new i nformat i on might be app l i cable to the environ ment i n such a way t h at seems l i ke the cogni t i ve agent i s get t i ng new i n formation from the envi ronment . For i n st ance, once I discover Pythagoras ' th eore m , t hen hav i n g the knowledge that Joh n ' s farm is 4 m i les due east from my p l ace, and B i l l 's restaurant i s 3 m i les due north from John's far m , I ca n conc l ude t hat B i l l 's restaurant is 5 m i les from my place. H owever, d i scoveri n g the Pythagorean theorem i tse l f-and b y ' d i scoveri n g ' 1 mean com i n g u p w i t h th e p roof o f i t-does n o t req u i re any n e w i n formation from the envi ronment . ) Now as far as l e a rn i n g of t h e fi rst type i s concerned , where new i n for mation is gai ned from the environ ment , learni ng by p red i c t i ve analogy is n o more t h an a myt h . T h i s poi n t i s m ade quite c l e ar ly a n d ast utely by Rus sell ( 1 987, pp. 96-97] . Whether the s u pposedly learned l aw is deri ved from s i ngle i n s t ance general i zation , or from schema i n d u c t i o n , its s t at u s remain s essen t i al l y t h at o f a c o nj ec t u r e , a n d s i n ce i t does n o t say any t h i ng about the env i ronment , t here i s not h i ng learned .
One might wel l argue here-an argu ment t h at i s often advanced to j us t i fy t he role of pre d i c t i ve analogy in learning-t hat the learn i n g lies not in com i n g u p w i t h the generalization or the i n duced schema, but in u s i ng it to m ake a hypot hesis about some u nk nown dom ai n , and in trying to ver i fy the hypot hesis, for whether the h y p ot h e s i s i s confirmed or refuted, we end u p
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learn i n g somet h i n g new about the u n known target . T h i s ver i fi cation step is i n corporated in the schema i nduction approach even in generat i n g the schema in the first p l ace, for t here must be at least one successfu l ap p l i cation of t he analogy from the source to an u n k nown t arget before t h e schema i s formed . Noti ce, however, t h at by t h i s argument any process that m akes any k i n d o f prediction about the t arget envi ronment wou l d q u al i fy a s a n a i d t o learn i ng . For example, consi der generat i ng random h y p o t h eses . Even a random hypothes i s , on bei ng experi mental l y veri fied , wou l d tel l us somet h i ng about the t arget envi ron ment. O r consider ' pred i c t i ve di san alogy, ' which works by not i c i ng some exi s t i ng s i m i l ar i t i es between the source and th e target , and t hen, based on these si m i l ar i t i e s , i t pred icts t hat a certai n ch aracteri stic of the source domai n , about w h i ch it is not k nown if it exists in the target en v i ronment or not , does not exist in the target environ men t . The poi nt here is s i mp l y t h at predi ct i ve analogy is no better tool in t h i s sense of lear n i n g t han any o t h e r process t h at also makes p red i c t ions abo u t the target object, unless, of course, i t ca n be shown t h at t he real world i s structured i n s u ch a way that the predictions m ade by p red i c t i ve analogy are a better source of hypotheses t h an any other pred i c t i ve process ( such as pred i c t i ve di sanalogy ) . H owever, t h e search for any such b l an ket reason t h at shows w hy a hypothe s i s from pred i c t i ve analogy i s j usti fied h as been n ot h i n g bu t fut i l e as I h ave discussed at l e ng t h i n th e l ast chapter. T here remai ns one m ore sense of l earn i n g t o con sider, namely when learn i n g i n volves notic i ng novel con n ect i o n s between exist i n g k n o w l e dge st ruc t u res . This i s w here we find t h at the AI a p p r o ac h e s t o analogy are most germane. One of t he goals of cogn i t ion is c learly to strive for a certain economy of representation [ Rosch 1 9 78) . I n this r e s p e c t , t h e signifi cance of not i c i n g t h at two k n o w l ed g e s t r u ct u re s , acq u i red i n q u i te d i fferent contex t s , have s i m i l ar i t ies c a.. n n ot br overr m p h a.s i zcd , s i n ce o n e c a n r e p l ace t h e two structures w i t h a s i n g l e more a b s t ract s t r u ct u re . G e n t n e r ' s sys t e m a t i c i ty principle m i ght serve wel l h ere to focus at tent i o n on h i g h l y structured simi l ari t i e s . Schema i n d u c t i o n comes i n h a n d y t o ge n e rate a.n abst ract ed model t h at u n i fie s t he source a n d t arget c o n c e p t net w o r k s-al l I n a t h e m at i cal o b j ects start o u t t h i s way. To sum up, we see t h at the m ai n co n t r i b u t i o n of A I a p p r o a ch e s t o p red i c t i ve a na l ogy h as b ee n to develop t e c h n i q u e s for c o m p u t i n g e x i s t i ng s i m i lari ties between the source and the target from t hei r gi ven rep rese n t at i o n s-t h at i s , syntac t i c analogy. T h u s , w h i l e these a p p ro ac he s model some of the cog n i t i ve p rocesses related to a n alogy an d met a p h o r-s u ch as h i g h l i g h t i n g and down p l ayi n g , general i z a t i o n , abst ract ion (§7 . 4 . 1 ) -t h ey leave c reat i ve analo-
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gies and s i m i l arity-creat i n g projective metaphors completely out in the col d . T hese approaches to syntact i c analogy can also model t h e cogni t i ve p rocess u n derl y i n g suggest i ve metaphor, as long as the exis t i n g s i m i l ar i ties are not seen as j ust i fy ing the hypotheses generated by suggestive metaphor, and the met ric of s i m i l ari ty is not used as a. reflection of the potenti al of the source ( as in p i c k i n g the most s i m i l ar source, because it i s more l i kely to s ucceed ) .
A Computat ional Model of C reat ive Analogies : Douglas Hofstadter
1 0 .4
I n sharp contrast to all t hese approaches to analogy that h ave sought to focus on com p u t i ng s i m i l arit ies between the exist i n g description s of the source and the t arget , i t was Douglas Hofsta.d ter who real i zed t hat the crux of c reati v i ty l i es i n com ing u p w i t h the right descri ptions i n th e first place [ Hofstadter 1 98 1 -85] . To study the cogni t i ve process t h at generates d i fferent descriptions of t he same obj ect i n d i fferent contexts, H ofst a.dter designed an elegantly s i m ple, and yet s u rprisi ngly rich , m i croworld [Hofsta.dter 1 984] .
The objects of Hofsta.d ter's m i croworld were stri ngs of characters ' a. ' t h rough ' z , ' s u c h a.s 'xyz , ' 'abc,' and ' w . ' O n ly a few concepts, such as ' copy ' ( ' a. ' is a copy of ' a.' ) , ' s uccessor' ( ' d ' i s t he successor of ' c ' ) , and ' p rede cessor' ( ' w ' is the predecessor of ' x ' ) were al lowed for describing the objects i n t h i s m i c roworld . Yet , t here were sur prisi ngly many ways of describing any gi ven object i n t h i s m i croworl d . For i nstance, a seemi ngly simple obj ect ' abc' cou l d be descri bed as "a t h ree-character right-moving successor group s t a r t i n g wit h 'a' ," "a t h ree- character l e ft - m o vi n g p redecessor group s tarti n g w i t h ' c ' , "a ( two- c h aracter ) s uccessor group fol lowed by the s uccessor of t he l ast ch aract er of the grou p , " and so o n . "
To model the effect o f d i fferent contexts i n se l e c t i n g d i fferent descrip t ions of objects in the c h aract e r s t r i ng m icroworld, Hofstadter consi dered proport ional analogy relations of the fo r m 'A i s to B a.s C i s to D' [§ 1 . 6 . 2] . Take t h e p roport ional analogy relat ions shown i n F i gure 1 0 . 4 . Though the terms A, B and C are the same in al l t h ree analogies shown t here, t hey need to be descri bed d i fferently for each analogy ( o r else the a n a lo gy cannot be com p rehended ) . For instance, i n l 0 . 4 ( a) , t he term C i s t aken to be "a t hree element right-mov i n g s u ccessor grou p start i n g with ' i ' , t h e l ast element of w h i c h is a two-element copy group ' k k ' '' In 1 0 . 4 ( b ) , it is considered to be "a t h ree-element left- moving predecessor group t h e first element of which i s a t w o- e l e m e nt copy grou p ' k k ' a n d t he ot her two element s are s i ngle letters . " -
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A
B
c
D
(a)
aabc
aabd
ijkk
ij l l
(b)
a abc
aabd
ijkk
hjkk
(c)
aabc
aabd
ijkk
ijkl
FIGURE 1 0.4: Proportional analogies in Hofstadter' s micoworld of character strings. Even though the terms A, B and C are the same in each of the three analogies, they require different descriptions .
And i n 1 0 . 4 ( c ) , t he same term is descri bed as "a fo u r- c h aracte r g ro u p w i t h i t s l as t character as ' k ' . " I n each case, i t i s the o t h e r ter m s o f a n a l ogy rela t ions ( A , B and D ) t hat affect w h i ch descri ption of C i s ' p roper , ' w h i c h , i n t u r n , affects w h i ch descript ions of A , B an d D are seen as ' p roper . ' Thus, the p rocess of generat i n g descri p t i o n s req u i res complex i n teract i o n s b e t w ee n t he descriptions of the fou r terms , for the descri ption of each term affects t he de s cr i p t i o n of the other t h ree t e r ms , w h i l e , at the same t i m e , being affected by t hem . I-Iofstadter and h i s c o lle ag u e M e l a n i e M i t ch e l l d e s i g n e d a n d i m p l e m en t e d a c o m p u t a t i o n al s y s t e m c al le d C o py cat that solves p ropor t i o n a l ana l o gy re lations ( p rod uces the fourth term , given t h e o t h e r t h ree ) in t h i s m i c rowo r l d of character stri ngs . Copycat p r ov i d e s an excel l e n t m o d e l of an alogies t h at a re not b ased on e x i s t i n g s i m i l ar i t ies but t h at c reate t h e s i m i l a r i t i e s . Before exam i n i ng t h i s system , however, i t wou l d be u sefu l to take a q u i c k look at Evans ' system for sol v i n g p roport i o n al ana l o g i es t h at was i m p lemented i n t h e early s i x t i es [ Evan s 1 96 3 , 1 968] . T h ere i s a special reason for tak i ng t h i s deto u r . Evan s ' system i s v er y w i dely k n o w n , a n d i s heral ded fo r i t s success in s o l vi n g t he geom e t r i c analogy p roblems of i n tel l i ge n c e test s . In fact , t h e p e rc e p t i o n of i t s success h a s been so c o m p l e t e that , u n t i l H o fs t a d t e r c a m e u p w i t h h i s m i c rowo r l d , p ro p o r t i o n a l analog i es had ceased t o b e a d o m a i n for A I and cogn i t i ve modeling. G i ven t h i s ge ne r a l fe e l i n g , it is nece s s a r y to h i g h l ight the l i m i t at ions of Evans' system with respect to p ropor t i o n al a na logy relat ions r e q u i r i ng r e d e s c r i pti on , in order to fu lly a p p rec i ate t h e s i g n i fi c a nce
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of Hofstadter and M i t chel l ' s wor k . T h i s is, of course, not meant to devalue Evan s ' i m mense contri but ion in any way, w h i ch was quite remarkable, gi ven t he exi s t i n g state of the art at the t i me, but only to point out t h at the i n teres t i n g aspects o f the proport ional analogy relation were n o t even close t o exhausted b y Evans . I n fac t , Evan s h i m self was q u i t e aware o f the need for context sen s i t i v i ty i n generat i n g t he descriptions of the terms of the analogy relat i on . He even t ried to i n corporate context-sens i t i vi ty in h i s descri p t ion-generat i ng module i n a somewh at pri m i t i ve way. Seei n g the need for redescrip t ion in the context of exam ples l i ke t hose used by Evans , and understan d i n g Evans ' app roach might help you to better appreci ate the com plexi ty of the t ask u n dert aken by 1-Tofstadter and M i tchel l . 10.4. 1
An Aside : C o nt ext - S ensit ivity of D es cript ions i n Evans ' Approach
Evans was i nterested in b u i l d i ng a com p uter p rogram to solve proportional analogy rel at ions i nvolving configu rat ions of geometr i c figures , such as the ones shown earlier in Cha pter 1 ( Fi gure 1 . 1 ) . S pecifically, the problem he had his program add ress was : gi ven t he t h ree terms A, B, and C of a proport ional analogy relat ion 'A i s to B as C i s to 0,' choose the fourth term from a given set of fi ve a l te rn a t i ve s ( Fi g u re 1 0 . 5 ) . Eva n s ' approach was t o break t h i s tas k i nto two stages . I n t h e fi rst stage, the obj ects A, B, C, and each of t he fi ve alternat i ves were broken into their respect i ve componen t s , and the rel ationships between t hese components were com p u ted . For i nstance, in F i gure 1 0 . 5 , t he obj ect. A would be decomposed as a t r i a ngl e Tl a n d a t r i a n g l e T 2 . T h e re l at i on s h i p s b e t ween these two com p o n e n t s wo u l d express t h e fact t h a t Tl is i n s i de T 2 . I n o u r termi nology of C h a p t e r 5, t h i s process can b e seen as t h at of generat i n g a description of e a c h o b j e c t A , B , C , e t c . T h ere i s one o t h e r t h i n g t hat Evans h ad h i s p rogram d o in t h e fi rst s t age , w h i c h w a s to figure out w h i c h of t h e com p onent figures i n each p a i r of o b j e c t s are ' s i m i l ar ' For i n s t an ce , con s i deri n g t h e p a ir ( A , B) in Figure 1 0 . 5 , it wou l d com p u t e t hat T2 and T3 are s i m i lar, and T l and T3 a re s i m i l ar albei t of d i fferent sizes . In d e t erm i n i n g ' s i m i l ari ty, ' the t ransformat ions t h at w e re factored ou t , bes i des a ch ange o f scale, i n c l u ded reflection a.n d r o t a t i o n .
I n t he second stage, Evans' p rogram generated rules-t here cou l d be more t h an one-t h at convert o bj e c t A i nto object B, t a ki n g i nto account the de scri p t i ons of A a n d B, and the si m i l a r i t y b e t ween thei r com ponents, t h at were
Chapter
1 0:
379
Compu tational Approaches
A
1
2
@
D
D
c
B
3
4
5
@ 0
FIGURE 1 0 . 5 : An example of the kind of geometric analogy problems solved by Evan s ' ANALOGY program. Given figure s A, B and C, the program picks out the fourth figure D (from the five give n alternatives, numbered 1 through 5) that best completes the analogy ' A is to B as C is to D ' . The program picks out figure (4) in this exmple.
0 0 (i)
(ii)
D (iii)
(iv)
(v)
(v i )
FIGURE 1 0 . 6 : Figures for the quotation from Evans [ 1 968] .
(vii)
Part
380
TJI: Th e
Implications
D (iii)
(ii)
(i)
Ll
(iv)
(v)
FIGURE 10.7: Figures for the q uotation from Ev ans [1968].
produced i n the first st age. T h u s , for F i g ure 10 . .5, a rule wou l d be to remove the i n ner tri angle, wh i l e h•e p i n g the o u ter triangle the same. A not her rule, for t he same exam ple, wou l d be to remove the outer t r i angle, while m aki n g the i nner t riangle l arger. Evan s ' n e x t step was to general i ze these r u les, i f n ecessary, so that they a p p l y to the object C a n d convert i t to o n e of t h e five given altern at i ves . For i n stan ce, a genera l i zation of t h e fi rst of t he t wo r u l es men t ioned above wou l d be to remove the inner figure while keep i ng the outer figu re the same. F i n al l y, h i s program selected the most appropriat e rule general i zat ion based on a h e u r i s t i c , a n d chose the al terna.ti ve ( from the g i ven set of five ) t h at res u l ted from app l y i ng t h is generali zed rule to the obj ect C. Because h i s algor i t h m d oes not change t h e d e scri ptions of the objects once they are deri ved in the first stage, it m ight appear at fi rst that Evans overlooked t h e c o n te x t - s en s i t i v i ty of descri ption s t h a t is responsi bl e for the creat i on of s i m i l arity i n proporti on al an alogi es, such as t h e ones we d iscussed in C h ap ter 2 [§2 .4 . 2, see also Figures 2.2 an d 2.3] . However, on taking a closer look at h i s d ec o m po si tion algor i t h m , 1 we fi nd that Evans was ac u t e ly aware of this p rob l em : to u n d er s tand certain proport ional ana l ogy relations, the f1gures i n wh ich the objects A, B, C, and Dare decomposed d ep en d on one another. For instance, be wrote: "Th er e appear to tion process: one
be
two d i st i nct approaches to the decomposi
attempt to b reak up a figure on Gestalt cri teri a , s u ch as some form alization of ' goo d continuation,' to separate , say, [ F igure 10.6 (i )] into [ Figure 10.6 (ii)] and [Fig ure 10.6 ( i i i ) ] . Al ternat i vely one can perform the decompos i tion on the basis of i n form ation external to the figure i tself, as in our case, from the other p rob l e m figu res . . . . [I]f Figure A consists of [ Fig u re 10.6 (iv)] a n d Figure B of ( F i gure 10.6 (v)], i t wo u l d be
1See Evans
[1968],
can
Sec. 5.3.3, pp. 302-:306.
Chapter 10: Com p u tational Approaches
38 1
D
0
(iii)
( ii)
(i)
(iv)
(v)
(vi)
FIGURE 10.8: Figure s for the q uotat ion from Eva ns [1968].
having fou n d, tri v i al ly, t h at F igure B con s i sts of two d i s t i nct pieces, [Figure 1 0 .6 ( vi ) ] an d [ Fig ure 1 0 .6 (vii ) ] , to attempt to fi n d one or bot h of these s u bfig u res, u p to si mil ari ty transfor mation, in F i gu r e A. S o me com b i n ation of t h ese ' int ri n s i c ' and ' contex t ' h e u ristics should be suitable as t he basis for a qu ite usefu l decompos i t ion p rogram . . . " [Evans 1 968, p . 303]. natural,
And l a te r. .
.
"A figure may
of course
be
s usceptible to various decompos i t i ons .
Which, if any, of t hese is appropriate depen d s on the other figu res of the problem. In the terms we h ave u sed , 'int rinsic' decomposi tion i s i nad e q u at e and 'context' decomposition methods, on which we have based our decomposition program, must be used. For ex am p le , Fi gur e A [ F igure 1 0 . 7 (i)] and P i gu re B =[Figure 10.7 (i i)] re q uire a decomposition of A i nt o [Figure 1 0.7 (ii)] and [Fig ure 1 0 .7 ( i i i )] (thus the rule gene rat e d will involve t h e removal of th e [Figure 10.7 (iii)]), whereas w i t h the same Figure A, Fig ur e B [Figure 1 0 . 7 ( i v)J will require decomposition of A i n to [Figure 10.7 (iv)] and [Figure 10.7 (v)]" [Evans 1968, p. 305]. =
=
Sin ce the description of any object very much depends on the figures i nt o is decomposed, Evans' program did h ave some capability to handle redescription i n proportional analogy r e l atio n s , where the description of an object is not kept fixed, but al lo we d to ch ange based on the context p rovi d e d by the ot h e r figures. which it
Yet, E van s' program had this capability in a very l i m i ted way. Fir st of all, even though ' c onte x tu a l ' decomposition is hi g hly desir ab le , Evans o bserv ed that context a l o ne is insufficient in certain situations t o p rov i d e the right
decomposition.
382
Part ITT: Th e Implications
A
B
D
c
FIGURE 10.9: A proportional a nalogy relation for which ' context' decomposit ion fails. To understa nd this a nalogy requ ire s that each of t he Fig ure s A and B be decomposed in terms of a triangle, a square, and a circle.
"If F ig u r e A is [ Figure
1 0 . 8 (i) J and Figure B is [Figure 10.8 (ii)J, viewi n g these figures as each consisting of t he parts [Fig ure 10.8 (iii)] an d [Figure 10.8 (iv)] will fai l i f the desired rule i n vo l ve s , say, removing the [ Fi gure 10.8 (iv )] from in side the [ F ig ure 10.8 (v)] but lea v in g it inside t h e [F i gur e 10.8 (vi)] '' [Evans 1968, P- 306] .
t h en
The proportion al an alogy r e l a t i on shown in Figure 10.9 i nvolves such a rule. Evans' p ropose d solution to this limitation was to incorporate in to the decom posit io n program some 'intrinsic' criteria, such as 'look at all decompositions i n to simple-closed-curve subfigures.' However, the 'intrinsic' criteria neces sary to 'correctly' decompose the figures would vary q u i t e a bit from case
to case. For instance, the intrinsic criterion would
n ot
work for the propor
ti o n al ana l ogy relation shown in Figure 10.10 (or those shown in
and
2.3
F i g ures
2.2
of Chapter 2), wh er e there are jus t too many ways to break each of
Chapter 10: Com pu tationa} Approaches
D
c
B
A
383
FIGURE 10.10: A proportional analogy relation for which bot h 'intr in sic' and
'context' decompositions fail. Context decomposition fail s beca use none of the fi gures break s easily i nt o ' simple' fi gures that ca n be used as contextual cl ues for decomposing other figures. I ntrin sic decomposition fail s because there are too many way s to break each figure into simply-closed-curve subfigures.
the figures
si mply-closed-cu rve su bfigures . Moreover, for t h i s e x ampl e , e i t h er , because he requ i red th at at lea st one of the objects A an d B c an be d eco m p ose d simply in a 'natural' w ay. (His program wou l d decompose t he simpler of the objects A and B into s u b fig u res , and then look for occurrences of thes e subfigures in the more complex of the two objects.) into
Evans' 'context' decomposi t i on would not work
A second major limitation o f Evans' approach comes from the fact that the pri m i t i ve relations and propert i e s i n terms of which a figure can be de scribed are all d ecide d beforehand. Thu s , Evans' program cannot solve the proportional anal o g y relation of F igure 10.1 1 ( or that of Figure 2.2 of Ch ap ter 2) because it lacks the primitives to describe eccen tr i c ity and its orienta tion. Of course, one can correct this by adding the required p r i m i ti ves , but then the re are always more ex amp les t h at involve sti l l new primitives. One might quite
t he
reasonably
argue here that, in
p r i m itive s of the d es c ri p tio n must be
a.
computational set t i ng
provided to
the system o t he r w i se , w h ere wo u l d the y come from?) But my point is simply th a. t if one w ant s to admit richness of descripti ons, and the ability to describe a figure us i ng different sets of primitives, the s et of all possible primitives may become so l a rge that even simple figures would end up having
at least,
explicitly. (Since,
a g reat
many
descri pti ons. Then it wou ld b e quite inefficient to precompute
them all, i n Evans' sty l e, especia.lly since most of them would not be
nee d e d
384
Part III: Th e Implications
A
D
c
B
LJQ FIGURE 10.11: A proportional analogy relat ion which show s the l imitation placed by choosing a priori t he relations and attributes in t erms of which the fi gures ca n b e described. Evans' program cannot handle this analogy b eca use it is not prov ided with relations t o represent eccentricity and it s orientation. in any given context. The problem these examples bring out is the need to use the relations and properties of the other figures, besides their subfigures, as contextual clues to the decomposition process, and even to choose the relations and properties in terms of which the figures would be described after looking at all the figures. The architecture of Evans' program is ill suited to have this flexibility because the process of decomposing a figure, and that of computing the properties and relations between its subfigures are done in separate stages; and each figure is processed separately. What is needed is some way of
making the figures
A, B,
and C interact, and making the sub fi g ures into which they are decomposed as well as the properties and relations between these subfigures-depend on
the result of this interaction.
This is exactly how
D ougl as Hofstadter
approa.ched the p ro bl e m about twenty years later.
10.4.2
Resumption: Hofstadter and Mitchell's Copycat
Let us now return to Hofstadter's
m i c r owo rl d
of character strings. We have
already seen some examples of proportional analogy relations in this domain
( Figure
10.4] that showed that the descriptions of the objects of an analogy
need to be d y n a m ical l y gen e r a ted . Some other in te r est i n g examples given by Hofstadter domain.
mi gh t
provide
a
glimpse of the subtlety of this innocent looking
Consider the three
exam p les
shown
in F i gure
10.12.
In 10.12(a ) ,
Chapter 10: Computational Approaches
385
A
B
c
D
(a)
abc
abd
xyz
wyz
(b)
abc
abd
ffifrJJJ
mrrjjjj
(c)
abc
abd
mrrJJJ
mrrkkk
FIGURE 10.12: More examples of proportional anal ogie s in Hofstadte r's microworl d of character strings that require rede script ions.
are connected with the conce pts 'last' p h eno menon that Hofstadter refers to 'successor' slips into ' p redecessor . ' ) In
the concepts 'first' and 'successor' in A and 'predecessor,' respectively, inC; a as slipping.
10.12(b),
(In going from A to C,
the succession order of a character in A (described as a successor
group starting with 'a') is slipped into the length
of
the
corresponding
copy
grou p inC (desc r i b ed as three copy groups of in c reas i ng l eng ths ) . In 10.12(c), where the
terms A,
Band C are the same as in
( b), A
and Care described as
three-element sequences each , and the individual elements are equated with the elements ( copy
in C.
These exam p les
be attained
groups) in the
(characters) in A
co rre s p o n d ing po siti ons
reveal a surprising degree of conceptual
depth that can
in this m i c r o wo rl d .
a n d Mitchell's Copycat p r ogr am is designed to generate t,he of the proportional analogy relation g i ven the ot h er three. Unlike Evans' ap p roach , C o pyca t does not compute descriptions of the objects of the proportional analogy in a separate i ni ti al module. Instead, the task of generating the descriptions is seen as an inseparable part of comprehending the analogy. A detailed account of Copycat's design, implementation, and several examples of analogies so l ve d by i t can be foun d in Hofstadter [1984], Mitchell and Hofstadter [1989; 1990a.; l990b], and Hofstaclter an d Mitchell [1991]. Here, I only summ ari ze some of its key feat ures and then discuss its signi ficance i n m o deling c r eat i ve an al ogies .
Hofstadter
fourt h term
The arch itec t u r e of Copycat is
i n s pired by the
biolog i cal p rocesses that
take pl ace inside a cell, where the seemingly random activities sim p l e enzymes end
of various
up building quite complex products such as
proteins.
386
Part III: Th e Implications
Inside the cell there is no central process or main enzyme that oversees or controls the final product.
N or is there any kind of built-in hierarchy that
makes certain enzymes more inAuentiai than others. Thus, the contribution of each individual enzyme taken by itself is insignificant. Yet, a large num ber of cooperating individual enzymes can collectively assemble
a.
complex
biomolecu !e. There are two key features of Copycat that reAect this underlying biolog ical metaphor. One i s its distributed architecture, where the whole process of generating descriptions and creating mappings between the descriptions is carried out by small simple agents called codele ts. For example, might notice that there is characters
'a'
a
a.
codelet
'successor' relation between the neighboring
an d 'b,' an observation that might or might not turn out to
be of significance eventually. Thus, codelets can be seen as counterparts of enzymes, where the action of each coclelet by itself is insignificant, but a bunch of codelets together can lead to a complex and insightful description of the object.
In this respect, Copycat is similar to the Hearsay
understanding system [ Erman el a!.
II speech
1980].
The other key feature that Copycat borrows from its biological source is the probabilistic interaction of the processes. The enzymes inside a cell all seem to act randomly, if we look at them microscopically. Yet, a macroscopic order emerges from this apparent random interaction. A similar approach is taken in Copycat by incorporating probabilistic parameters at various places. This probabilistic approach ofCopycat makes it quite unique and unlike other distributed
AI systems like Hearsay I I; and, as we see later, it is a crucial
factor in Copycat's ability to model human creativity. There are three major components of Copycat.
There is the slip n et,
a.
network of Platonic concepts, which is somewhat analogous to our notion of a.
concept network. The sli pnet contains nodes representing various Platonic
concepts such
as
'opposite,' 'successor,' etc.
and links between the nodes
that cap t ure the relationships between the concepts.
The length of
a.
link
between two nod es reAects their conceptual proximity.
The sli pn e t is dynam i c i n the sen se that the nod es acquire different lev els of activation, which decay over time, and they spread their activation to neighboring nodes, where neighborhood is defined in terms of conceptual proximity (length of the link). Moreover, the lengths of the links themselves can also change, since every link has some label associated with i t that corre sponds to a node of the sli pnet, and when that node is activated, all the links that have that label get shortened . 'predecessor' are connected by
a.
For instance, the nodes 'successor' and
link that has the label 'opposite . ' When the
Chapter 10: Computational Approach es
387
node representing the con cept 'opposi te' is act i vated , lhe nodes ' successor' and 'predecessor' are brought in closer pro x i m i ty ( as wel l as other nodes, such as 'leftmost' and ' ri ght most , ' t h at, are l i n ked by 'opposite' too ) . T here i s also a degree o f depth associated with each concept i n the s l i p net . For i n stan ce, the concept 'opposi te' is deemed deeper lhan the concept ' s uccessor , ' w h i ch in turn i s considered 'deeper' t h an the concept 'a. ' Depth i s a stat i c notion and reflects the abstract ness of a concept. I n a somewhat crude comparison , i t can be l i kened to t h e order of a rel ation i n l ogi c-the second-order relation i s deep er t h a n the fi rst-order relat ion , which i n t u rn is deeper t h an the obj ects . Depth is used to con st rai n the con cept u al s l i p page ( a term Hofstadter u ses to refer to t h e temporary and context-dependent i dentificat ion of two d i s t i n ct concepts as one, such as iden t i fying 'successor' w i t h ' p r ed e c essor ' i n com prehendi ng the an alogy " ' abc' i s to ' abel' as ' xyz' is to ' w yz"'), so t h at a dee per concept is more l i kely to m ai nt ai n i t s i dent i ty and less l i kely t o slip i nto anot her con cept . The second m ajor component of Copycat is the wo-rkspace, w h i ch i n i t ially contai n s the act ual raw data ( t he terms of t h e analogy ) but l ater ends u p contai n i ng i nstan ces of the slipnet concepts t h at form the descriptions of the terms. Loosely speaking, the initial state o f the workspace can be iden t i fied w i t h our sensory motor data set that i s bei n g organ i zed by a concept net work ( the s l i p n et ) via a cogni t i ve relation (instances). T t is the codelets that organi ze the data i n the workspace i nto var i ous descri ption s. For i n stan ce, i n solv i n g the analogy " 'aabc' i s to ' aab d ' as 'ijkk' i s to what?" a codelet m i gh t n ot i ce that the neigh bori n g obj ects 'a' and 'a' in 'aab d ' are the same, and chu n k them toge t h er in a ' sameness' group. E ach ob ject in the workspace is assigned a measu re of sal ien ce t h at deter it is that t he objec t wou ld attract the attent ion of codel ets. The salience i s a. d yn am i c property that d e pend s o n the extent Lo which the current des c r i pt i on s of the object are b u i l t out of the high ly activated no des
mines how likely
of the s l i p n e t , and on how isolated t hat object, i s wit h respect to the other object s in t h e Workspace . Both these factors l en d to increase the salience. Th e i d ea here is that if an object, is currently being d escri bed i n terms of h i g h l y a c t i ve node s, i t should h ave a high salience. Also, an isolated ob ject is gi ven a hi g h sali e n ce because, given the goal of i ntegrating all obje c ts into i nstan ces of sl i p net con cept s , if an object is i s ol a t e d , then i t needs more atte n t ion . F i n al l y, t h ere is t h e codemck, which is a pool of codelets that are wai t i ng to be run . Each codelet i n th e coderack is as s i g n e d a measure of u rgency that determines how l i kel y t h at codel et is to be chosen to be e x e c u t ed in the
388
Part III: The Implications
n ear fut u re. At each time step, a codelet is pi cked up from the coderack and executed . The decision w h ich codelet to run depends on t he u rgencies of t he codelets. However, t h i s deci sion is made on a p robabilistic basis , and not in t h e strict order of decreas i n g u rgen cies. That i s , whi l e a l ow u rgency codelet is less likely to be picked up in favor of a higher u rgency codelet, it is possible nonetheless . Codelets are t h e agents act ually responsible for organi zing t h e workspace, bringing concepts from the s lipnet to bear on the items and structures in the workspace, and for changing the activation levels of concepts in the slipnet depending on how things stand in the workspace. There are top-down c ode l e t s which are activated in response to the acti vation l evels in the s l ipnet, t h at look for parti c u l ar feat u res in the obj ects in the workspace; and there are bottom-up c odel ets that look aroun d for anything interesting in t he character strings . ,
As codelets are being removed from the coderack and executed, new codelets are con stantly being added to the coderack in three ways. First , bottom- u p codelets are al ways being added to the coderack . Second , as t he slipnet activation pat tern changes, new top-down codelets are added to t he pool of waiting codelets in response. Finall y, some codelets, when t hey are exec uted, create fol low- u p codelets , w h i ch are added to t he coderack . .A II Copycat runs start out w i t h a preassigned set of bot to m u p codelets in t he coderack and the t h ree given terms of t he p roportional analogy i n t he workspace. This sit uation quickly changes , though, as the objects i n th e workspace i n Auence t he activation l evels o f t h e slipnet, which in turn i n fluence the description s bei n g generated i n the workspace. The system as a whole strives for a u n i fied structure in wh i ch gi ven t he terms A, B, and C of the analogy relation "A is to B as Cis to w h at ? t h e descriptions of A, B and C are such that there is a r u le for changing A into B, and a mapping (set of 'bridges') is built between A and C. The fourth term is then arrived at by a pp l y i n g the translated (or 'slipped') rule, given the A-to-C bridges, to the description of C, while extending the mapping between A an d C to B and t h e fourt h ter m -
-
"-
.
The probabilist i c approach of Copycat is evident in two of its th ree com ponents. In the workspace, it i s i n corporated in the salience of the objects , which makes some obj ect s more likely to recei ve attenti on than others. I n the code rack, it is evidenced in the u rgency levels of the codelets , which make some codelets more likely to be executed than others. There is an overall con t rolli n g parameter called lempemture that controls how these likelihoods are a c t ua l ly deter m i ned from the l e n gt h of the l i nks, salience of the objects, or
Chapter 10: Computational Approa.ches
389
t h e u rgency l evels , w i t h low tem peratu res resu l t i ng i n large variations i n t h e probabili ties, and vi ce-versa. For i n stance, i f a c odelet X i n t he coderack has t w i ce as high an u rgency level as anot her codelet Y, t hen if the t e mp erat u re i s high t he rat i o of the probabi l i ty that X w i l l be chosen to the probab i l i ty t h at Y w i l l be chosen wou l d be m u ch l ess t h an two. O n t h e other hand, i f the temperat u re i s low , the rat io wou l d b e m u c h larger t h an two. I nt u i t i vely, at higher temperatu res the system is more random ( t h at i s , un bi ased ) and at l ower temperature i t i s more b i ased ( t hat i s , non-random ) . The tem perat u re i s computed from the degree of overal l structure seen i n the works pace. ( I n the origin al design, t he s l i p net was also supposed t o b e probab i l i s t i c i n the sense t hat i f any concept node were act i vated , i t s act i vat ion level wou l d be likely to p ropagate to the n eighbori ng nodes, w i t h the l ikelihood depen ding on t he length of the link connect i ng the act i vated node to the neighboring node. In the Copycat i m plementation , however, spreading of act i vat i on was kept determi n is t i c . A c t i vat ion levels themselves, th ough , make the s l i pnet probab i l i s t i c in two ways. One i s t h at t hey are us e d probab i l i stically by codelets-a s l i p net node w i t h a high act i vat ion level i s more l i kely to be used by a codelet in an act ual descri p t i on. The other i s that the act i vat ion of a node i n the s l i pnet affects the l ength s of al l those links that are l abeled by t h at node, t hereby affecting s l i pp age ) .
At t he m acro level , t h e nondeter m i n i s m o f Copycat is fe l t in t h a t , giveu tbe t hree terms of the analogy, t h e program does not al ways come up w i t h t he same fourt h ter m . For e x am ple, in a thousand run s o f the p rogram w i t h t h e an alogy " ' abc' i s to ' ab el ' a s 'mrrjjj' i s to w h at?", t h e answer ' m rrkkk' was given 705 t i mes, 'mrrjjk ' 203 t i m es, 'mrr jkk' 4 5 times, 'mrrjjjj' 3 9 ti m e s , 'mrr dd d ' s i x t i mes, and ' m r rj jd ' two t i mes. Not i ce t h at each answer i n vol ves a different set of description s for the three given terms, and different ways of slipping t h e descriptions and making b ri d ge s . Thus, though the program
clear statistica.l preference for certaiu descriptions a.nd structural or g anization, it is nonetheless c a p a ble of co m ing up with radically new ways of looking at t he terms, which m igh t or might n o t t u rn out to be i ns ig h t ful an d cre ative .
shows a
It
is t h is nondeterminism of C op yc a t
model of human
that makes it such an attractive
creativity, and specifically of creative anal ogi es . The re search on human creat i v i ty has show n-and the history of our civilization clearly and u n ambig u o usl y attests to i t-t ha t all insightful i dea s are init i al l y fel t t o be radical, offbea t , and shocking. We have a l ready discussed i n earl i er chapters Schon's st u dy of how the in novatio n i n the synthetic-fiber p aint brush came a b out [Schon 1963]. One is also reminded of Gordon's making the familiar stmnge [ 196 1] wher e it is s u gges t ed lhal in or d e r to solve some
390
Part III: Th e Implication s
part i c u l arly i nt riguing problem about a fam i l i ar s i t u a t i on or produ c t , one must view it in a st range way-a suggestion t h at was based o n observing several b rai n-storm i n g sessions where a group of people was trying to solve some real problem about some real produ c t . In the h i s tory of science and m at hematics also we find t hat all creat i ve i nsights were cons idered rad i cal at the t i me they were fi rst proposed . O ne is remi n ded here of Kepler's i dea t hat the S u n m i ght be the object around w h i ch the Earth revolves rather t han v ice-versa, H uygen 's i dea t hat light m ight be a wave, the quantu m mechani c a l n o t i o n t hat parti cles behave l i ke waves , Einstei n ' s concept t h at m ass and energy are i nterconvertible, etc. One i nterest i n g t h i ng about this aspect of creat i v i ty i s t h at i t defies a determ i n i s t i c ch aracteri zation . W h i le seeki n g t h e most s i m i lar source, w h i ch i the b asis of pred i c t i ve analogy, offers a clear cri terion for orderi ng the prospec t i ve sou rce domai ns, seeking a 'strange ' source domai n p resent s no such clear choice. G i ven a certain representation of the t arget domai n , t here m ight be m any poss i b l e source domai ns t hat are rad i cally d i fferent from i t , and each one mi g h t b e d i fferent i n a d i fferent way. Moreover, most o f t hese source domai n s are l i kely to res u l t in l i t t l e or no creati ve i nsight i nto the target environmen t . T h i s is precisely why creat i v i ty i s so h ard to teach even to h u mans, let alone to model com putat i on al l y. So wh i le i t i s the radi cal i deas that might lead to creati ve i nsights, one cannot encou rage t hem i nd i scri m i n ately, s i n ce otherw i se m u ch wa. s ted effort wou l d be i n cu rred . However, if a rad i cal i dea seems to be p romi s i n g , i t shou l d b e al lowed t o persist a t least long enough s o t h at i t s ful l i m p ac t can be assessed before a dec i sion i s m ade to accept or rej ect i t . I n terest i n gly, the h i st o ry of h u m an i ty i tsel f shows a m a n i festation of t h i s principle. W h i l e people and i n sti t u tions are gene r al l y conservat i ve, revolutionary i deas d o emer ge a n d become accepted from l i me to t i me . Thus, a determ i n i st i c approach faces a no- w i n s i tuation . I f i t t ries al l
' - t range' ways of look i n g at t h e t arge t , then t here may be a great deal of
wasted effort , for most of these wou l d l ead to not h i n g i n teresti n g . If it s t i cks to ' fam i l i ar' ways, t hen no creat i ve i n s i g ht s wou l d be p o ssi b l e If one t r i e s t o · m i x , ' or 'dovetai l , ' the fam i l i ar ways w i t h t he strange ways, the problem is t h at there are so many strange ways , and one cannot know a priori which of them are goi ng to be prom i s i n g . .
T h i s problem i s beau t i fu l l y sol ved b y Hofstadter a n d M i t chell b y incorpo rat i ng nondeter m i n i s m in t he i r a rc h i t ec t u r e , w h i ch res u l t s in an e ffe c t they refer
to as
a pa ·ra llel l c 1-ra ccd s ca n .
e x p l ored s i m u l t aneou sly. W h e n
a
M any ways of look i ng at t h e t arget are
pat h looks prom i s i n g , t he p robab i l i t ies are
Ch ap t er 10: Comp u t at ion a l Approa.ches
39 1
changed to reflect that , an d i t is more l i kely t h at t h e path w i l l be explored further. On the other h a n d , when a pattern seems to be emergi ng, even less l i kely pat h s t hat fit t hat pattern are explored . T h i s is ak i n to the s i t uation w hen , once the i dea t h at the pai n t brush m i gh t work l i ke a pump begi n s to t ake hol d , even those hypot heses t h at wou ld be consi dered totally offbeat by t hemselves-su ch as t h at the spaces between the fi bers m ight hold t he pai nt-become can d i d ates for experi mentation and verification . A t the m acro level , t h i s effect i s visible i n the fact that , w h i le most of the t i me the p rogram prod uces somew h at conservati ve-reason able but not always very i m agi n a t i ve or i nsightful-answers , it does come u p w i t h deepl y i nsightfu l answers somet i mes . ( A n d , of course, i t also comes u p w i t h some very m u ndane and l i teral answers . Perhaps t h i s only goes to show t h at creat i v i ty and ext reme l i teral m i n ded ness might be t wo si des of the same coi n _ ) 2
To s u m u p t h i s d i scussion , Hofstadter and M i tchel l ' s Copycat remai ns the only com p u t at ional system to date t hat models creat i ve an alogies i n a real sen se. What now rem ains to be seen i s how these ideas can be applied to some real-world domai n . H ofstadter and his colleague Robert French have already embar ked on a new proj ect , called Tabletop, w h ere the Copycat archi tecture is bei n g app l i ed to sol v i n g i n terpret i ve an alogies in a d i fferent microworld [ Fren ch and Hofstadter 1 99 1] . The Tabletop m i croworld consists of the t o p o f a t a b l e on wh i ch several objects ( l i ke c u p s , s au ce rs , glasses , salt shakers , and so on ) are placed . Two subject s , H en ry and Eliza, s i t on oppos i te ends of t he table. Henry reaches out and touches an object on the table. Eliza i s now asked to do the same t h i ng as Hen ry. T h u s , the pr o blem for Eliza i s to i nterpret Henry's act ion from her ow n point of view and carry it o u t . This microworld has m o r e of a real- world fl avor, a n d does n ot have t he art ificial aura t h at alway s s u rroun d s proport ional analogies n o matter 21
a m rem i n d ed h ere of an anecdote recou nted
by H ofsta.dtcr:
"[W]hen
I gave a lec t u re
on analogies in the P h y s i cs Department at t h e C a l i forn i a l n s l i l u le of Tec h n o l ogy seve r a l
way 4 is to A ? '
years ago , o n e R i c h a r d F'ey n m an sal i n i. h e fro n t row a n d b a n tered w i t h me a l l the
t h r o u g h t h e l e c t u r e . . . [ H ) e wou l d r e l i a b l y answer each q u estion ' W hat is [as i n ' W h at i s to
151
as
4
is to
1 4 1 ' ] wi t h t h e same answer ' 4 1 , '
to X
a n d insist
as
t h at i t was good
answer , p r o b a b l y t h e best . I t see med to me t h at Fey n m an not only w as a c t i n g t he part of
was rel i s h i n g i t . It was h a r d to tell how m u c h h e was p l ay i n g . . . [After t h ree years,] I r a n i n t o Richard Fey n m an at a co n feren ce . I r e m i n ded him of my lec t u re at CaiTech t h ree y ea r s ear l i e r ; h i s some w h a t va.gue reco l l ection of i t was t h ai i t w as 'silly. ' I t o o k t h a t as a c h a r i t a b l e way of s ay i n g t h at he h ad n ' t seen any poinL i n i L . W h i c h m a d e m e t h i n k t h a l m ay b e h i s ' v i l l age- i diot ' stance w as d u e LO g e n u i n e p u z z l eme n t , a n d n o l j u st an acl '' [ H ofstadler 1 9 8 5 , p. 574 a n d p. 603) t h e ' v i l l age- i d i o t ' b u t. even
d e v i l 's ad vocate and how m u c h he was s i ncere
392
Part III: Th e Implications
what t heir domai n . O ne s t i l l wonders i f t h e process o f redescription and creation o f s i m i larity can not be stud ied d i rectly in a real-world domai n . I believe t h at it can be, and with the existing state of tech nology i n A I . T h i s , precisely, i s the subject of our discussion in the next sect ion .
10.5
P roj ect ive ( S imilarity- Creat ing ) Met aphor in Art ificial Int elligence
\Ne h ave seen t hat al l com p u t at i onal approaches to metaphor and analogy h ave remained focused on syntact i c metap hors and analogies. Hofstadter and M i t chel l 's Copycat provi des a notable exception, but i t i s confined to an art i fi c i al m i c roworld . D oes this mean t hat the advent of a comp utational system t h at can model s i m i l ari ty- creat i n g metap h ors and analogies in a real worl d dom a i n m u s t awai t m any more years of theoreti cal research?
On t h e cont rary, I wou l d l i ke to argue i n t h i s sect ion t hat the A I technol ogy for model i ng proj ecti ve metaphors and creati ve analogies already exists. I n fact , once we stop u s i ng the terms ' metaphor' and 'analogy ' to seek out AI systems t h at are capable o f d i splaying the creation o f s i m i l ari ty, a n d look for t he act u al p rocess of redescr i p t i on t h at underlies creati ve metaphors and ana logi es, we fi n d perhaps somewhat surprisi ngly, t h at t here are al ready m any computat ional systems t h at are capable of producing creat ive i nstan ces of metaphor or analogy, t hough the creat i vity of these com p u t at i on al systems has not been stud ied as such. ,
To m ake this arg u m e n t , I s t a r t by arguing t h at t h e process of proj ection , about the redescri pt i on t h at i s re q u i r ed by cre at i v e m e t ap hors and a.nalogies, can best be seen as t op d o w n grouping, somet h i n g t hat i s q u i t e c o m m on p l a c e i n com p u t at i o n al system s . Then , I d i scuss t he issue of novel p roj e c t i o n vs . conven t io n a l p r o je c t i on si nce only the former can g i ve r i se to c reat i ve m etaphors and analogies. F i n al l y, I s h ow how t h e creat ion of simi larity c a n be ex p l ai n e d from t h i s p e rs p ec t i ve w h i c h b r i ngs
'
-
'
,
.
10.5.1
P roj ection as ' Top- Down' G roup ing
Rec al l from o u r d i s c u s s i o n i n Chapter 5 t h at p roj ect i o n is t h e process of i ntegrat i n g t h e sensori m otor data set , w h i c h is t h e percept ual e n c o d i n g of the en v i ron me n t i n to a gi v e n concept network, such t h at the structure of ,
Chapter 10: Compu tational Approaches
393
the concept network is kept i n vari ant , but the corres p o n den ce between the concepts and t he chunks of the sensori motor data set-or , in other words , the grouping or o n t ology o f t h e sensori m otor d a t a set-i s altered . N o w i n order to fi n d a n equi valent mech an i s m , i f o n e exi s t s , i n t h e d o m ai n o f exist i ng computational systems we must fi rst deter m i n e what a concept network and a sensorimotor data set mean i n the context of such s yste m s . A s emphasi zed i n Chapter 5, a sensori m otor d a t a set i s the i n p u t that form s the raw m aterial for conceptuali zation , an d concept networks p r ov i de abs tract symbols t h at are used for structuring t h e sensori m otor d ata set . For i n stance, when we see a b i rch t ree , the sen sory s t i m u l i t h at o u r eyes receive for m the sensorimotor data set , w h i ch i s categori zed as a ' b i rch t re e ' i n t h e conceptual i zation p rocess. Now t here are m any comp u tat i onal systems in w h i ch t h e i n p u t data forms the raw material that i s organ i zed i n terms of abst rac t. s y m b o l s i n t h e cou rse of processing. For i nstance, con si der a parser for a for m al l angu age-a very commonp lace com p u t a t i onal system . The i n p u t to the parser is a s t r i n g of characters . Assuming t h at the string is wel l - formed in the formal l anguage, the p arser w i l l e n d up representing i t as a parse tree. H ere, t h e i n p u t string can be thought of as a sensori motor data set . A l so, the words ( term i n a l s ) and syntacti c categories ( non-ter m i n al s ) appearing in a parse t ree c a n be li kened to the symbols of a concept network-t he gram m ar of the for m a l l a n g u age relates the te r m i n al s and n o n - t e r m i n a l s i n spec i fi c w ay s l i ke the op P r a t i o n a l structure of a concept netwo r k . Thus , the p roc e ss of p a. rsi n g becomes essen t ially t hat of i ntegrat i ng the sen sorimotor data set ( t he i n p u t stri n g ) i n to t h e abstract struct ure of t h e concept network ( t he g ram m ar of t h e l a n g u a ge ) . B ut t h i s i s p reci s e l y what we h ave ca l l ed the pro c e ss of con ce p t u a l i z a t i o n -a process t h at works by form i ng a c og n i t i v e r e l at i o n b e t wee n a con cept n et. work and a sensorimotor data set . I n deed ,
as s i m p l e
to i l l ustrate m any,
an d
co m m o n p l ace
as t h e exam p l e
if not al l , aspects of
of
a
p ar
·er i s , i t hel p s
t h e c o n ce p t u a.l i z11.t i o n p rocess i n
com p u t at i o n al se t t i n g . For i n st a n ce , n o t i c e
that t h e
i n put
st r i n g , t h e
a.
s e n so
r imotor data set , i s i n d e p e n den t l y s t r u c t u red . The o r d e r of the symbols i n the st r i ng i s somet h i n g t h at the p 11. rs e r c a n n o t a l t e r . At t he s a rn e t i rn e , t he s t r u c t u re of the l a n g u age , the concept networ k , i s abo a u t o n o mo u s . I t d o e s not depen d on t h e i n p u t s t r i n g . T he i n t e r a c t i ve n a t u re of t h e con cr p t u al i z a. tion process is a l so c learl y brought out i n t h i s example, si nce t h e parse - t ree correspond i ng to any given i n p u t st r i n g is t r u l y determ i ned in part by the st ru c t u r e of t h e l anguage an d in part by t h e structure of t h e s l r i u g . T h i s exam p l e a l so
h e l p s to h i g h l ight the
d i ff'ereuce bet ween
t h r mech a -
Pari TIJ: Th e Implications
394
an d ac c o m m o d a t i o n . C o n s i d e r p roj e c t i on fi rs t . It co n·e ' top-dow n ' grouping i n w h i c h t he ru les of the gramm ar ( t he struct u re of t he concept n e t work ) are kept i n vari ant but t h e grouping of the i n p u t st ring-w h ich groups of symbols are a ssi g n e d to w h i c h non- termi nals is a l t e red to m a i n t ai n c o h e r e n c y . Note here that c oh e r e n c y refers to mat c h i n g t h e s t r u c t u r e of t he gram mar to t h e s t r u c t u r e of the st r i n g ; o r , i n ot her w o r d s , t o t h e con d i t ion t h at the string can be p ar s e d i n the g r a m m a r . n i s m s of p r oj e c t i on
s po n d s to t h e
must be e m p h as i zed t h at my use of the term ' t o p - d o wn ' here is q u i te t he q u o t at i o n m a r k s , from i t s t r a d i t i o n a l u s age i n t h e context of pars i n g a s wel l as m any other com putational systems . I n pa r s i n g , for i n s t a n c e , t h e t e r m s top - d o w n a n d bottom - u p refer to two d i fferent s t r at egies t h at c a n be used to de t e rm i n e whether t he i n p u t string can be m ade to correspond to t h e gram m ar of t he for m a l l a n g u age . I n t he t op - d o w n st rategy, one a p p l ies t h e r u l es of t h e gram m ar i n a. ce rt a i n order to e n u m e r at e parse t rees , c h e ck i n g at each s t e p to s ee if t h e c u r re n t p a rse- t ree c o r r es p o n d s t o t h e i n p u t s t r i ng . I n t h e b o t t o m - u p s t r a t egy , on t h e o t her h a n d , o n e s t ar t s w i t h t h e i n p u t s t r i n g , a n d p ro d u ces al l p o ss i b le p ar t i a l pa rses of i t u n t i l a c om p l e te p a rse- t ree is pro d u c ed . H owever, in our sense, b o t h t he s e s t r a teg ie s woul d b e c a l l e d ' t o p - d ow n ' p r o c ess e s , t h e reason b e i n g t h at even i n t h e bottom u p p a rs i n g , t h e i n p u t s t r i n g i s b e i ng i n t e g r a t ed i n to t he s t r u c t u re of the grammar, or in o t he r word s t h e sen s o r i m o t o r d a t a. set i s b e i n g orga. n i zed i n t e r m s o f t h e c o n c e pt network . It
d i ffe r e n t , hen ce
A
i n my sense c orre s p o n d s to t h e mech an i s m of i n acc o m m o d a t i o n , t h e o n t o l ogy a n d t h e g r o u p i n g of t he s e n so r i m o t or d at a. set is fi xed . a n d it is the s t r u c t u re of t h e co n ce p t n e t work t h a t m u s t confor m . I n t h e c o n t e x t of t h e parser, i t m ea n s t h at t h e i n p u t s t r i ng i s a l re a d y g rou p e d i n cer t a.i n w a y s , a n d the goal i s to modify I he s t r u c t u re of t he gram m a r so t h at t h e i n p u t - s t r i n g c an be p arsed . T his is ' bottom - u p '
a p p roach
accom m o d at i on . R e c a l l t h a t
p rec i s e l y
w h at
g r a m m ar learn i n g al go r i t h m s at tempt to
of accom m o d a t i o n ,
t h u s . i s manifested
achieve.
M y foc u s of i n t erest h e re b e i n g the m e c h a.n i s m of
be
noted
that
proj ection,
systems. it
must
t h e corres p on d i n g · to p - dow n ' g r ou p i n g i s p e r fo r m e d by many
co m p u t a t i o n a l sy s t e m s . A s c e n e- a n a l y s i s s y s t e m t h at p ro d u ces s c r i p t ion o r
T h e p rocess
i n va r i ous m ac h i n e learn i n g
a.
verbal de
seman t i c- net- l i ke rep rese n t a t i o n o f an i m age on t h e b a s i s of its rep rese n t a.t i on i n t h e for m of a.n a r r a y of p i x e l s . i s esse n t i al l y ca r ry i n g o u t a p r oj e c t i o n by grou p i n g the p i x e l s a n d m a k i n g t h e ' gro u p s ' co r r esp on d to a bs t r a ct c o n c e p t s s u ch a s ' h ou s e ' a n d ' r o o f . ' A med i cal d i agnos i s e x p e r t sys t e m , i n p r o d u c i n g a d i a.g n o s i s from· t h e sym ptoms, i s proj ec t i ng t he concept net w o r k of d i seases o n t o t h e set of gi ven symptoms . W h e n a st o r ya
Ch ap t er 10: Computation al A pproaches
395
u n derstan d i ng system organi zes the narrat i ve i nformation i n the story as a frame or a scri p t , i t i s essen t i ally projecti ng the concept network t h at is the frame or the scr i p t onto the i n p u t sensor i motor data set t h a.t i s the text of the story. 10.5.2
Novel vs . Convent ional P roj ect ion
G i ven t h at many computational systems are capab le of project ion , cou pled w i t h the thesis that projection is the p rocess u nderly i n g metaphors, we nat u rally ask : Can a computational system capable of proj ection also produce creat i ve metaphors? To answer t h i s questi on , we h ave to rem i n d ou rselves t h at not all projections produce metaphors , but only n ovel proj ect i on s . That i s , to recogn ize a. body of clouds i n the sky as 'clouds' also i n vol ves project ion , s i nce one h as to group the perceptual field appropriately a n d l i n k i t w i t h the concept ' clouds' i n order to m ake the recogn i t ion . T h i s act of recog n i t ion , however , i s not metaphorical si nce the grou p i n g, as wel l as t h e association of the group i n g with the concept , i s conventional . But to recogn ize i n the body of clouds a ' kangaroo' i s a n ovel project ion , an d m i g h t b e con si dered metaphor i cal . So to answer the question above, we fi rst m u s t d i s t i n g u i s h between con ventional and novel proj ections in t h e c o n t e x t o f com p u t at i o n al s y s t em s . Noti ce t h at t h i s d i s t inction can not be m ad e on t h e b as i s of fam i l i ar i ty w i t h the stimulus. That i s , we can not say t h at t h e fi rst L i me a parser en cou nters a sentence, i t s re cog n i t ion amou n t s to a n ovel p roj ec t i o n . T h i s wou l d be l i ke argui n g t h at the first t i m e I see a cow I h ave n e v e r seen before, and recognize i t a.s a ' cow , ' I produce a. creati ve metap hor. Before a d d r e ss i n g t h i s i ssue
in
a.
com putat ional
t h e corres p on d i n g p roblem of separat i n g t h e
t io n al is
ad d ressed
in the context
assign ' conve n t i o n al ' referen t s
In d eed ,
we
set t i n g , let u s s e e h o w
metaphori cal from the
of h u man cogn i t i o n .
conven
O n e a.p p roa.ch is to
( w h i ch are parts of the external worl d ) to
a u t o m at i ca l l y ass i g n m o s t objects n.n d f'vcnts
all
in the worl d ( w hich w e access t h ro u gh the sen sori motor d a t a set ) t o certa i n concepts for biological or cultural reasons, a s i n r e c og n i z i n g a.n o b j ec t a s a ' cow ' almost effortlessly. It merely reflects t h e i n t e r s u b j ect i ve every d ay usage of t he concepts i n any g i ven s o c i ety. G i ve n t h e c o n ve n t i o n a l refe re n t s of t h e concepts, any proj ection t h at associ ates a. concept w i t h an obj ect in the world t hat i s not the conventional referent of the concept can be d ubbed 'novel . ' I n d e e d , t h i s d u al o r s p l i t referen ce-one conventional a n d o n e sustai ned by the n ovel proj ection-i s s o m et i m es touted as t h e m o s t ch aract e r i s t i c feat u re the concep t s .
396
Part III: Th e Implications
of metaphors [Ricoeur 1 976] . N ot i ce, h owever, t h at t h i s method of d i s t i nguishing between conventi onal and novel projections requi res t h e God's-eye view of t h e external world and t he cogni t i ve agent . This i s because when I see someth i ng and recognize i t as a ' horse , ' t o deter m i ne w hether t h i s proj ection i s convent ional o r novel I need to k now t hat the object I see i s reall y a horse; i n other words , whether the obj ect i s i ncl uded i n t h e convent ional referent of ' horse' or not . B u t how c a n I k now t h at , u nless I have some way of accessing the conventional referent of ' horse ' ? Though for computat ional systems t h e designer or the user of t he system has t h e necessary God 's-eye view, for cogni t i ve model ing of s i m i lar i ty-creat ing metaphors one must be able to characterize novel proj ect ions w i t hout resorting to the God 's-eye view. W h i l e I h ave d iscussed t h i s problem elsewhere at length [Indurkhya, in preparat ion] , for my pu rpose h ere I only need to note that s i n ce concept s are i nternal a n d fu l l y accessible to t h e cogni t i ve agent , i f t he notion of ' con vent i on al ' is i ntrod uced from the poi nt of view of concept u al izat i on , then no God's-eye view is requ i red . Thus, g i ven some obj ect ( p art of t he sensori m otor data set ) , a certai n conceptualization of i t i s v iewed as ' conventional ' by the cogni t i ve agent , and any other concept ualizat ion of it woul d t hen be called 'novel . ' For i nstance, when I look at clouds and see a kangaroo t here, what m akes it a novel p rojection i s the fact that I am aware, at the same t i me, t h at i t i s a group of clouds , which i s t he conventional concept u al ization of w h at 1 am seeing. In t h i s way, t he s p l i t - r e fe r e nc e characteristic of metap hors is turned i nto split-concept ual izat ion. This however, only covers t hose novel p roj ections t h at h ave b een termed by Gordon [ 1 96 1 , pp. 35-36] as ' making the fam i l i ar strange . ' There is the fam i l i ar ( con ve n t i o nal ) conceptu a l i zati o n of t h e o b j e c t o r event . Then in making a novel proj ection w i t h another concept network, the familiar obj ect or event is made to appear st range. There i s another class of novel p rojec t i ons, corres p onding to G ordon 's ' m ak i n g the strange familiar , ' in w h i ch there d oe s not exi s t any convent i onal concept ualization of the obj ect or event , and t herefore any projection is novel . For i nstance, on looki ng at aurora b orealis or r i d i ng a rol ler coaster for the first t i me, one may feel completely at a loss for words to describe t he sensations that one is experiencing. In such s i t uation , any concept ualizat ion ( descri ption ) t h at one can come u p w i t h i s goin g to be metaphori cal . To i denti fy such projections as ' novel , ' the cogni t i ve agent needs to be able to deem certai n sensori motor data sets as non-conceptual . A n y concept u al ization o f a n o n -concep t ual sensorimotor data set wou l d be a novel proj ection, and hence metaphorical .
Ch ap t er 1 0: Com pu t at i onal A pproaches
397
Let us now apply these insights to com putational systems, so t h at we can see w h i ch systems are capabl e of making n ovel projections, or metaphors , and w h i ch are not . S i n ce we have already tal ked a bit abou t parsers , let me begi n by cons i dering the example of a parser for Natural Language, say a fragment of Engli s h . I h ave already noted that when t h e parser p rod uces a p arse-tree ( o r a set of parse- t rees ) when p resen ted with a wel l-formed ex pression or sentence of the fragmen t , i t i s essentially proj ect i n g the concept network t h at i s the gramm ar of the fragment onto t h e sensorimotor d a t a set t h at is the i n p u t expression. Now each of these proj ections must be dubbed conventional , whether we consider it from the God 's eye- view or the parser's eye -view, because the corresponden ce between the parts of t h e i n p u t expres sion and the syntact i c categories of the gram mar is both somet h i n g i ntended by the designer of the parser and something that the parser n at u ral ly comes up with. We then ask : Can such a parser ever p roduce a n ovel proj ec t ion? Let us see. Consider first the possi b i l i ty of 'making the fam i l i a.r strange. ' That i s , for an i nput expression that can be parsed by the p a r s e r , we ask whether it can be p arsed in a non - convention al way. The answer i s n egat i ve because the group i ngs of the i nput expression an d their correspondence w i t h the non termi n als of t he gramm ar are fi xed by t h e gram mar and b u i l t i n to t h e parse r . It is a s if t h e proj e c t i o n m e ch a n i s m i s h ard- w i red in the p a r s e r , s i n ce gi ven any expression t here is only one u n i q u e way to i nt e gr a t e it i n to the concept network of the gramm ar . I
m u s t emphasize th at I a m not t al k i n g a b o u t ambigu i t i es here. A ny p arser for a n at u ral l an g u age i s bou n d to h ave ambigu iti es-i n fac t , t h i s i s why I c h o se t h e example o f a parser fo r a n a t u r a l l an g u age rather t h an a formal l ang u ag e . B u t a l l the am b i g u i t i es a r e a l r e a d y a part of t h e grammar, at least i n t h e way I am e n vi s i o n i n g t h i s parse r . T h e word ' deep ' m i ght enter i n t o d iffere n t comb i n at i o n s w i t h t h e o t h e r wo r d s of the sentence, but it w o ul d n o t corres p o n d t o the word ' p eep . ' This poi n t c a n be ap p r e c i a t ed i n anot her w ay by c on s i d e r i ng the fact t h at i n everyd ay l an g u age, we often use a m b i g u o u s expressi o n s b u t thei r d u al or m u l t i - fo l d con c e p t u a l i z a t i o n s a r e not termed metaphori cal . }or i n st ance, ' Can you d r i ve ? ' c an be a genu ine query or an i n d i rect request, b u t bot h t h ese con ce p t u al i za t i o n s of i t w o u l d reason able
be called conven t ional .
G i ven t h at t here is no poss i bi l i ty of h a.v i n g a d u al c o n c e p t u al i z at i o n h e r e , let us e x p l o r e the o t h e r alternat i ve for c reat i n g novel proje c t i on s , w h i c h is to have t he parser project i t s concept network o n t o t hose sensor i m otor data s e t s for w h i ch n o convent ional concept ualization e x i s t s . T h i s a m o u n t s to
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Part III: The Implications
parsing a sentence outside the fragment for w h i ch the gramm ar was written , by u s i ng the same gram mar rules . B u t any such attempt wou l d result i n an abrupt ' i l legal syntax ' or ' word not in the lexi con ' response. Thus, we find our parser q u i te i ncapable of p roducing novel p roject ions. T h e reas on for this fai l u re i s that a p arser works i n a noise-free and defi n i t i ve domai n . A word i s either a member of the lexi con , or i s not-there is no i n - betwee n . A n d when it is a member, t here is no dou bt as to what it i s ( notw i t hstanding ambigu i ties, o f course ) . Does t h i s mean t h at i f w e modify o u r example to work i n a noisy an d u ncertai n domai n , i t woul d be able to generate novel projections? Let u s see. T here are several examp les of Af systems t hat typi cal l y work o n a noisy domai n : speech u n derstan d i n g systems , mach i ne v ision systems , h an d w r i t i n g recogn i t ion system s , j ust to mention a few . S i nce I started w i t h t h e parser, let me choose a s peech u n derstan d i ng system , say H earsay- 1 1 [ Erman et al. 1 980] ,3 as the example of a com putat ional system that has a 'top-dow n ' mechan ism a n d t h at works i n a noisy domai n . Hearsay- I I i s an A I system t h at recognizes a small su bset of spoken Engl i s h . A person speaks in front of a m i crophone and H earsay- I I produces a wri t ten version of the speech . The env i ronment i s typically noisy: t here are i nd i vi dual variations, accents, presence of other sources of sou n d , reflected soun d from the surroun d i ng objects etc. to cont am i n ate the speech . To recognize s p ee c h am i d st all t h i s noise, the system makes several assumptions about w h at the speech is l i kely to be. This b i as i s reflected i n the organization and t h e rules of t h e system . The i m portant t h i n g to note with this example is t hat there is no pre-establ i shed correspondence between the acoustic pattern recei ved from t he m i crophone and t he lexicon of t he system . Now to g i ve t he system a capabi l i ty of pro duc ing n ove l proj ec t i on s , s u p p os e that the speech recogn i t ion system h as t wo m o d u les: one c on t a i n i n g t h e r u les for re cog n i z i n g a s u b s e t of Engl is h and t he other cont ai n i n g the rules for re co g n i z i n g a s u bset of Fr e n ch . Each of t h e s e sets of rules forms a concept network . Now suppose t h at the system is p resented with an acous t i c pattern from the m i c rophone, w h i ch it recog n i zes as some sentence in French . T h at , t h e n , becomes the co n ve n t ional conceptual i zation of the i n p u t patter n . But what i f we were to force the system to recognize the i n p u t pattern using the rules of English. W h i l e i n most i n s t an ces the system would probably. fai l , i t is 3
! n w h at fo l l o w s ,
I a m ideal i z i n g H earsay- l l
for t h e sake of my argu m e n t . T h e idealiza
t i o n , howeve r , is not u n r eal i s t i c . In fa c t speech u n derstan d i n g systems h ave matured q u i t e
a b i t s i n ce H earsay- I I , a n d t h ere i s n o t h i n g i n my
c a p a b i l i ty to speech u n derstan d i n g sys t e m s .
a rg u me n t s t h at
at t r i b u tes a n on-exist i n g
Ch apt er 10: Computational A pproach es
399
possible t h at at least in some i n st ances , esp e c i a l l y when t h e r e i s much noise cont am i n at i ng the u tteran ces , s om e t h i ng me an i n gfu l m i g h t res u l t . When i t does , i t amounts to a novel p ro j e c t i o n s i nce the Engl i s h c o n ce p t u al i z at i on o f the French u tterance i s non- conventional . t h i s scenario seems a bit far- fetched to yo u , c o n s i d e r t h e h u merous book L u i s d ' A n t i n Van R oot e n . 4 It contai n s t e x t i n French ( which i s somewhat nonsensical , b u t m ea n i n gfu l ) t h a t , w hen read alou d , sounds l i ke Mother Goose 's N u r se r y R h y m e s . If
Mots D 'He u res: Ga uss es R a m es by
You might also con si der two other modu les, one fo r recog n i z i ng conversa t ion pertain i n g to real-estate busi ness and the other about the stock market , i n stead . It i s not an u n com mon experien ce t h at i n a noisy e n v i ro n m en t , such as a p arty, on catchi n g fragments of a co n v e rs at i o n w h at we m a ke o f i t ver y m u ch depends o n w h at we t h i n k i s b e i ng t a l ked abou t . O n b e i n g i n fo r m e d otherwise, t here is i n va r i abl y a ' regrou p i n g ' of t h e s a m e p e r c ep t u al d a t a . To my m i n d ; t h i s i s no d i ffe r e n t from t he ' reg ro u pi n g ' of t h e p a t t e rn re ce i ved from t he m i crophone t h at takes p l ace w he n a s y s t e m s u ch as Hearsay- I I de c ides to use Engli s h rules i nstead of French ; or the ' regro u p i n g ' t h a. t t akes p l ace i n our percep t u a l apparatus when we t ry to ' see' t h e p ro cess of p ai n t ing as pumping i nstead of smeari n g . to be r e a c h e d h e re i s t h at t h ere e x i s t com puta of producing n o ve l p ro j ect i o n s a n d i n s ta n ce s A h an d w r i t i ng r ec og n i t i on system t h at i n te r p r ets a
T h e obvious c o n c l u si o n
t ional
s y s te m s t h at are c ap a b l e
of creat i ve m e t a p h or s .
chi l d 's dood l i n g as c h a.racters i s p r o d u c i n g a c re a t i ve m e t a p h o r. A m ac h i ne v i sion syste m , d esig n ed to reco g n i z e h o u s e s , i f on b e i n g p r e se n t e d w i t h a. picture of ca mel i n terprets i t as some sort of h o u se i s e s s en t i a l l y c a r r y i n g o u t a. novel or m et a p h orica l projec t i o n . N o t e t h at al l t h ese n ovel project ions are not arbitrary ; U1 al i s , t h e sensor i m o t o r data set i s not a pass i ve receptor of project i on s , but con s t ra i n s t h e poss i b le concept u al i z at i o n s . l n recog n i z i ng a. c h i l d ' s d oo d l i n g , the system wou l d i n vari ably zoom i n o n vari ous 'ob j ect i ve ' fe a t u r e s of the doodl i ng and ' see' t h e m n o t o n l y as re l evan t , but a.s a key to the i de n t i fi c at i on p roces s . I n t h i s way, a we l l - d es i g n e d sy�tern of s u ffi c i e n t complexity c a n quite i m press i t s h u m an d esigners by prod u c i ng i n teres t i n g conceptuali zat ions when o p e rated i n d o m ai n s o t h e r t h an t h e ones for w h i ch i t was inte n de d . W h at i s n e e d e d i s a systemat i c s t u d y of t h i s creat i v i ty. 4! am grateful to Dr. M e l a n i e M i tchell for b r i n g i n g t h i s i n teres t i 1 1 g and u n u s u al book to my attention .
Part III:
400
The
Implications
.... .... >
.. .. .. . . ·. . ·.. · '·: .. . :· . . :· .... .. .
.
Scene analysis system picture of a camel
repre sentation of the camel as a house FIGURE 10.13 : An example of novel proj ection in a computational setting. The scene analysis system would have normally represented the camel as an animal concept. But forced to u se the house concepts, it could meaningfully represent it as a house, thereby creating similarities between a camel and a house.
10.5.3
The C reat ion of S imilarity
In the l i g h t o f our p r e v i o u s d i sc u s s i o n , let u s now see how t h e creat ion of s i m i
l a r i t y m i ght t ake p l ace i n a . com p u t a t i on al set t i n g . C o n s i de r a m ach i ne v i sion syst e m t h at acce p t s
a
d i g i t i zed i m a ge of a scene an d pro d u c e s
l i ke represent at ion of it [ F i g u re 1 0 . 1 3] . This carrying o u t a p rocess of con cept u a l i zat i o n .
co m p u t a t i o n al
a.
seman t i c-net
system i s c l e arly
T h e sensori motor d at a set for
t h i s system is t h e d i g i t i zed i m age, w h i c h h as i t s own autonomou s -structure, a n d t h e concept
network i s
t h e l a n g u age of the semant i c net .
A cc ommo
d at ion , in t h i s cont ext , corresponds to the s i t uati on i n w h i c h the d i g i t i zed i m age i s a l ready grou ped i nt o regi o n s , and t h e s t r u c t u re of t h e s e m an t i c net i s ad apt e d to represen t the gro u p e d i m age .
P ro j e c t i o n correspon d s to the
s i t u a t i o n i n w h i ch the system i s gi ven a seman t i c net rep re s ent at i on ,
an d
Chapter 1 0: Com p u tationa1 Approa.ches
401
tries to deter m i ne i f any part o f t h e sem an t i c n e t digi t i zed i m age .
IS,
i n deed , present i n the
I n order to give t h e m achine vision system a capab i l i ty for novel projec tion, suppose t h at it h as two concept networks : one fo r rep resenting house scenes w i t h concepts l i ke ' roof, ' ' c h i mney,' ' wal l , ' ' door , ' ' yard , ' etc . , and t he other for represent i n g ani m al s w i t h concepts such as ' h o rse , ' ' camel , ' 'trun k , ' ' hump , ' ' legs , ' ' t ai l , ' etc. O n bei ng presented with t h e d igi t i zed i m age of, say, a came l , the system woul d recogn ize it as such , and represent it as a sem an tic net from the ' an i m a l ' concept network . T h i s wou l d be the convent ional representation of the i n p u t i m age. Now if one comp ares t h i s representation w i t h some prev iously stored rep resent at i on of a house, t h ere wou l d be n o s i m i l arities between the two. One reason i s t h at the an i mal concepts are largely d i sj o i n t w i t h t h e house con cepts . A n d also struct u rall y, one uses very d i fferent r egi o n i ng and l a bel i ng techn i q ues for i dent i fy i ng an an i m al t h an for ident i fy i n g a h o use. H owever, if the system i s forced to ' see' the i m age of t h e c a m el t h r o ug h the ' house' concept network , then the same digit ized i m age i s com pletely reorgan i zed . D i fferent regioni n g ( regroupin g) and l abel i n g ( remappi n g ) rout i n es wou l d t ake over a n d t ry to i dentify t h e i m age a s a house. T h e h u m p o f the an i mal might b e labeled a s ' r o o f , ' t h e neck a s ' ch i m n ey, ' e t c . T h i s regrou p i n g would c re a t e the s i m i l arit ies between t he i m age of t he c a m e l and a house, s i m ilarities t h at were not t here between their 'con ventional ' representations. Thus , we see that i t i s quite possi ble to m odel t h e c reat ion of s i m i larity w i t h exist i ng A l systems . With t h i s backgrou n d l now o u t l i n e a n arch i tect u re for mode l i ng s i m i l ari ty- creat i ng metap hors and d i sc u s s t h e r e s e a r c h i ssues posed by i t . 10.6
Mo deling Met ap hor
as
C hange of
Representation T h e cent ral i dea i s to model the p rocess u n d e r l y i n g i rn i l ar i ty- c rea t i n g m e t a phors as change of 1·ep res e n t a t io n . The model wou l d h ave concept networ ks t hat rep res e n t sensori motor data set s . T h e concept n et w o rks wou l d cont a i 1 1 high-level concepts-i n a s e m an t i c n e t or some s i m i l ar for m al i s m -t h at p ro vide t he p r i m i t i ves for represe n t at i on . Sensorimotor d a t a s e t s wou l d con t a i n r a w s e n s e data (output from a m i crophone or a d i g i t al camera) t h at needs to b e organ i zed by u s i n g the conc e pt s [rom concept networks _
402
Part liT: Th e Implication s
When the model wou l d encounter any sensorimotor data set , i t woul d i mmediately seek t o represent i t i n some way i n terms o f i t s concept s ; j ust as we are automat i cally organ izing and fi l tering our sense- i mp ressions to see i nstan t i at ions of the concepts in our envi ronment . The representation of a sensori motor data set t h at the model wou l d settle on , w i thout any outside factor affect i ng it, we wou l d cal l the ' conventional ' representation of the sen sori motor data set . Now s i m i l arity-creat i ng metaphors can be produced by forcing the model to change the representation of the sensorimotor data set from the ' convent ional ' to a ' nove l ' one. The model can be forced to do this by l i m i t i ng the set of concepts and concept networks i t h as avail able for representing t h e sensori motor data set . T h i s cou l d be done by prov i d i ng the representation of t h e source object ( for i n stance, a semant i c net representa t ion of the house that i s being proj ected onto the p i c t u re of a camel ) , and con st rai n i n g the model to u se only t hose concepts t h at are used in the given representat i o n , or c losely rel ated ones . Thus, t he set of concepts that the system wou l d be forced to use woul d become the sou rce, and the sensori motor data set t hat woul d be concep tualized wou l d become the target . The model wou l d work by prod u c i ng a conceptual i zat ion of the target sensori motor data set i n terms of the source concepts . The r e s u l t i n g representat i on wo u l d be metaphori cal , i f i t woul d b e s o me t h i n g t h at t h e system w o u l d not h ave pro d u ce d b y i t s e l f when the source were not expl i c i t l y gi ven . The arch i tect u re of a com p u tational system based on t h i s approach i s shown i n Figure 1 0 . 1 4 . A key d i fference between t h e concept networks and sensori m otor data sets , namely the degree of abstraction, must be emphasized here, s i n ce it wou l d not do to have the t arget be p resented a s a . concept n e t work or the sou rce as a sensori motor data se t . You m ight recall t he d i s c u s s i on of the l ast sect ion about the creat i on of s i m i l ar i t y. If the t arget sen sori mo tor data set is a l re ady c o n ce pt u a l i z ed in some way, and t h i s representation i s p r o v i d e d to t h e model, i n stead of t h e raw data, then o n l y e x i s t i n g si m i l ari t ies between i t and the given rep resentation of t he sou rce can be gleaned . To cre ate s i mi l a r it i e s , one must have access to the u n r epr es e n te d , raw sensory data from the target so that i t can be c o n c e ptu a l i z e d anew�t h a.t is, rep r ese n t e d d i fferently. S i m i larly, i f the representation of the source i s not provided ; and only an u n rep r e sen t e d sou rce object i s gi ven , t hen one m ight not be able to find any s i m i l ar i ties at al l . }or i n st ance , if one is given only the bit - m ap i m ages of a. h ouse a n d a. camel , not much can be g ai n e d by a bi t by b i t comparison o f t h e two i m a g e s . T n fa c t , i f the i m ages were of two very simi l ar houses, even then
Chapt er 1 0: Com put a t i onal Approaches
403
PROJECTION:
' top-dow n ' grouping
FIGURE 10.14: An architecture for modeling similarity-creating metaphors.
404
Part III:
The
Im pli cations
l i t t le can be learned from a bit by bit compari son of the i m ages . The reason for t h i s is t h at it is the concepts t h at m ake us see t h i ngs as s i m i lar. It i s t he concept ' t r i angle' that m akes us see two otherwise very dissimi l ar figures as ali ke. I t is the concept ' house' t h at m akes us see an i gloo and a mansion as s i m i lar. Th u s , i t does not hel p to do away with the concept networks altogether and always t ry to find s i m i larit ies between the sensori motor d at a sets correspond i n g to t h e source a n d the t arget . H aving clarified this poi nt, let us t u rn b ack to t h e architecture of Fig u re 1 0 . 1 4 . O ne t h i ng to not i ce i s t h at i t i s not necessary, or even suggested , that the conventional concept ual izat ion be determi ned for each sensorimotor data set . G i ve n the source concept network and the t arget sensori motor data set , the system woul d d i rectly proj ect the source onto the t arget . Comput i n g the conventional represen tation of the target sensorimotor data set i s not n eeded at all in this process. Only i f the system i s expl icitly asked whether the proj ection i s an instance of creati ve metaphor, t hen it woul d h ave to figure out the conventional representation of t he t arget sensorimotor data set and compare i t with the conceptual i zat ion in terms of the source concept network . In t h i s sense, as long as the source is prov i ded, the system does not i nvoke d i ffer en t processes to compute conventional p roj ection and novel p roject ion . In fac t , one m i g h t s ay t h at in a sense t h e system is not even aware whet her the p roject ion i s conventional or novel . The second t h ing to notice i s that by taking ' conventional ' to mean the representation of the sensori motor data set to which the system naturally sett les, I am l i m i ting t he sense of 'novel ' to i nc lude only ' making the fam i l i ar st range' ; and leav i n g out t hose novel proj ections that result from conceptu a.l izing the se n s ori mo t or d a t a sets t h a t h ave n o nat u ral c on c e p t u ali z ation s , correspond i ng to ' m a k i ng the st range fam i l i ar . ' T h u s , when a m ach i ne v i sion system t h at i s designed to ge n er a t e concept u al represent a t i on of house scenes, o n being p r es e nt e d w i t h a p i c t u r e of a camel comes u p w i t h a representa t i on of it i n terms of h ouse-related con cepts l i ke ' roof, ' 'chimn ey,' et c . , t h i s re p rese n t a t i o n wou l d be termed ' conventional , ' and h e n c e n on - m e t a p ho r i c al , according to our characterizat ion . W h i l e t h i s m ay seem o d d at first , you m u s t remember t h at as far as t he mach i ne v i sion system i s concerned , it i s i ndeed a house that it sees in t he camel - p i ct ure. I t k n ows of no other conceptual iza tion of that i m age . I t is only we, havi n g the God 's-eye view and being ful l y aware of another more conventional concep t u al i zation of the camel p ictur e , who see the m ac h i ne vi sion system 's re p r e se n t at ion of t he camel p i c t ure as novel , and hence m e t ap h or i c a l . Indeed , t h i s p recise p o i n t , made in t he context
of h u m a n c ogni t i on , i s the
Chap t er 10: Computational A pproaches
405
t heme of Coli n Turbayne's excel lent Myth of Me t a p h o 1·. Tur bayn e argued t hat w h at we regard as the ontology of real i ty i s only a p roject ion, albeit a convent ional one, of our concept networks . H owever , when we overlook t h i s fac t , and t ake our convent ional projections to be the u n i que i m m u t able ontology of real i ty, t hen our view of real i ty becomes nothing b u t a myth . The i nabi l i ty o f t h e m achine vision system t o see beyon d i t s concept network only demonst rates t h i s poi n t more clearly. For a com p u t a t ional system to be able to regard certai n sen sorimotor data sets as 'st range' or non-conceptuali zable, and yet be able to come up w i t h some reasonable concep t u al i zat ion w hen the sou rce i s explicitly gi ven , woul d req u i re a certai n degree of self- awareness. Perhaps one way to i ncor porate t h i s feat u re woul d be to h ave the system generate a confiden ce factor, along w i t h the convention al conceptualizat i o n , when presen ted with a sen sor i motor data set . A low confidence factor, then , wou l d be taken as the sign to mean t h at t h e sensori motor data set i s ' s t range , ' and t herefore any concept u a l i zat ion of it is metaphori caL W i t h t h i s much backgrou n d , we can now identify t h ree major research i ssues in designing and b u i l d i n g com putat ional models of creat i ve metaphors . I discuss b e l ow how each i ssue m i g h t be add ressed w i t h i n the exist i ng A I technology. •
Fin ding a s u i t a ble la nguage jo1· the concept n e t wo rks : T h i s m ight seem to be the easiest problem s i nce A I representat ional l anguages have evolved quite a b i t s i n ce sem an t i c nets [B rach m an 1 9 7 8 ; Brachman e t a l . 1 983] . There are a l s o some A I representation schemes especial l y de signed for r e p r e s e n t i n g concept networks corres p o n d i n g to p h y s i c a l sys tems and processes (Hayes 1979; Forbus 1984 ; Bobrow 1 985] , something
t h a t would be requi red to model creat i ve metap h ors l i ke ' pai n t i ng-as '
pumping.
For now , I wo u l d suggest a si mple scheme t h at h as 'obj ect , ' ' att ribute , ' a n d ' ac t i on ' nod e s . O b j e c t nodes re p resen t ob j ect s a n d act i o n nodes r ep r ese n t operators t h at change objects t o o t h e r ob j e c t s , or c h a n ge attributes of an obj ect. Each node woul d contai n a proced u re t h a t en c a p s u l a t e s the ' mean i ng' of the obj ect , act i o n , or at tribute rep resented. For i n s t a n c e , in model i ng Schon 's pai nt i n g - a s - p u m p i n g m e t a p hor that we h ave al read y e n cou n tered i n t h e earl ier cha pters, the ' p u m p ' node wou l d contai n a procedure to decide w h e n so m e t h i n g m i g h t be c o n s i d ered a pump. I t might i n c l u d e t h e fac t , a r n o n g ot h e r s , t hat a pump needs to be a hol low con t ai ner with some sort of open i ng. Exaclly how to represent t h i s ' p r o c e d u r a l ' part of a concept net work wo u l d depend
Pa.rt III: Th e !m plica. i ions
406
crucially on how the sensorimotor data sets are descri bed , s i n ce it is t hese ' p rocedu res' t h at woul d h ave to i n teract w i t h the sensori motor data sets to determine how the sensorimotor dat a set might be repre sented . For i n stance, in viewing pai n t i n g as p u m p i ng, it is the p roce d u re correspon d i n g to ' p u m p ' t h at wou l d h ave to fi n d a s u i t able chu n k i n t h e sensori motor data set o f p a i n t i n g to b e i dentified a s ' p u m p . ' •
Finding a s u i t a ble descrip t i o n la nguage fo r t h e s e n s o ·r i m o t o r d a t a s e t s :
Recall t h at the sensori motor data sets are struct u red objects t hemselves that resist arbi t rary conceptual i zat ion . Therefore, one woul d h ave to fi n d some way of describing sensorimotor data sets as wel l . In a model of visual metaphors, for i n stance, the sensori motor data set coul d be descri bed as a set of p i xels w i t h at tributes, or as a structured set of l i n e segments and regions. I n any case, the descri p ti on of the senso ri motor data set wou l d h ave to be q u i te detai led , i n terms of m inute com ponents and m i c ro-st ruct u res; s i n ce otherwi se, the conceptu a l i z a tion process wou l d not prod u ce anyth i n g i nterest i ng. Thus, we might not h ave an object ' brush' i n the sensori motor data set of pai n t i ng, but, i nstead , t here must be ' fibers , ' ' droplets , ' etc . ; w e may not have ' t ri angle , ' ' hexagon ' e t c . in t h e sensori motor data s e t of the figure of the Star of D a v i d , b u t there must be l i ne segments. A l so, the description of the sensori motor data set shoul d be as t heory neut ral as possi ble, si nce otherwise it woul d not adm i t d i fferent concep t ua l i zat ions. For i nstance, if the sensori motor data set corresponding to the Star of D a v i d i s descri bed as two i n verted t riangles, i t can n ever be reorgan i zed to produce a hexagon in the m i d d l e . If the sensori m otor d a t a set o f pai n t i n g i s d e s c r i b e d as a smear i n g p roces s , t he n it can no longer be r eo rg ani z e d as p u m p i n g . This i s because t he s e n s o r i motor data sets are at t h e lowest level of ab s t rac t i o n-t hey g rou ped t oge t h e r i n
i n to s m a l l e r •
d i fferent ways but
can n o t
be fu r t h e r
can
be
b roken d o w n
units.
t h e p rocess of p mjection between t h e s o u rce con cept n e t wo rk the t a r·get s e nsorimotor data s e t : T h i s i s the heart of the problem . The projection process wou l d res u l t i n a conceptual re p re s en t a t i on of t h e t arget sensorimotor data set t h at i s part i a l l y i somor p h i c to the Modeling and
source c o n c e p t n e t wo r k , and yet does not violate the s t r u c t u re o f t h e t a.r ge t sen sori motor data set . This process c a n b e l i kened t o a some w hat s i m p lifi ed case of s pee c h recogn i t i o n . In speech recogn i t i o n , the problem is t h at of com i n g u p w i t h a grammatical , m e a n i n gfu l s e n t e n c e , gi ven a n acou s t i c s i g nal . Now the acousti c s i g n al c a n be considered t o
Ch apt er 10: Com p u tat ional Approa.ches
407
be the t arget sensori motor d ata set , and the gram mati cal , mean i ngful sen ten ce-the ou t p u t of the speech recogn i zer-can be con s i d ered to be a concept- level rep resen tation of t he target . The t ask i s 'somewhat s i m p l i fied ' because, w i t h the sou rce concept network gi ven to us, we are told w h at the resulting sentence m ight be, (or t h at it i s ' Engl i s h ' i n stead o f ' French ' ) . Th at i s , i nstead of t r y i n g to fi nd a n y mean i ngfu l pattern i n the acoustic s i gn a l , we are gi ven a pat tern , and are told t o fi n d what p a r t s of i t , i f any, o c c u r i n the acoustic signal . This a n a l ogy i m m ed i a tely suggests that the p rocess m ight be modeled as a ' b l ackboard system ' [N i i 1 986] . The blackboard con t rol structure has been s uccessfu l ly used as an underl y i n g arc h i tec t u re for a variety of A I app l icat ions i n c l u d i n g speech recogn iti on [Erman e t al. 1 980] , scene analysi s [N agao & M atsuyama 1 980] , a n d i n terpretation of elect ron density m aps of protei n crystals [Terry 1 983] . ln fac t , if we consider the example of the Star of D av i d , the p rocess of i n teraction t hat gener ates different concept ual representations of i t , such as t wo overl apping triangles , i s essen t i al l y a scene an alysis problem i n d i sg u i se. In modeli ng t h e process of i n teraction u n derly i n g generat i ve metaphor a blackboard system , the proced u re at t ached to each node i n the con cept network of the source i s consi dered a ' k n ow ledge s o u rce . ' 'When t he source i nterac t s w i t h the t a rg e t , all the knowledge sou rces are act i vated i n parallel , w h i ch then com pete a n d cooperate with one another to arri ve at a s u i table organ ization , or grou ping, of the target sensori motor data set . These wou l d be the top-dow n k nowledge sou rces t h a t woul d be looki n g for cert ain specific feat ures i n t h e target sensori mo tor d at a. set . One m i g h t a l s o i n c l u d e bo t t o m - u p k n ow ledge sou rces t h a t r e c o g n i z e cer t a i n fea t u res of th e t a r ge t sensor i m otor data set an d prop agate u pwards the constra i n t s that the struc t u re of t h e sensori motor as
d a t a set puts on
how it m i g h t be concep t u al i zed . A s u i table i n ter p re
tation woul d b e fo u n d when t h e t o p - d o w n
expectations of t he sou rce ag r e e w it h the bottom - u p const rai nts of t h e t arget . ( N o t i c e the absence of q u o t a t i o n marks aro u n d the term t o p- d o w n and b o t t om - u p here, si nce I am u s i n g both t he s e terms in t h e i r t rad i t ional sen se. As 1 em p h as i zed earlier u s i n g t h e exam p l e o f a parse r , both the t o p - d ow n and b o t t o m- u p control st r ategies corr espond to t h e ' top-clow n ' g r o u p i ng in t he sense used i n t h i s chapte r . )
O n e m i gh t
also
u se a
n o n - de t e r m i n i s t i c
app roach
Hofs t adter an d M i t c h el l ' s Copycat . l n fa c t ,
s i m i la r
i n the l ight
remarks abou t t h e relat ions h i p of n on- d e t e r m i n i sm
to t h at of
of my p r e v i o u s
to c reat i v i ty, t h i s
Part III:
408
The
Tmplications
approach seems much more promi s i ng. A sign i fi cant d i fference, t hough by no means a major archi tect u ral one, between the way Copycat is set up and the way I am envisioning t h e p roposed model woul d be in the i n i t i al con d i tions. Reca l l t h at i n Copycat , a l l runs start w i t h a fi xed set o f bottom- u p codelets, w i t h preset u rgency levels, i n t h e coderack . I n the p roposed model , however, t he source concept network woul d cause certai n nodes in t he s l i p net to be act i vated at the start of a r u n , t hereby creat i n g an i n i tial pressure that wou l d be d i fferent for d i fferent sources . Thus, the same t arget sensori motor data set woul d be assigned different descriptions when d i fferent sources are used; and the same sou rce woul d be given d i fferent i nterpret at ions when d i fferent target sensor i m otor data sets are present . M oreover , the dichotomy of ' nove l ' vs . ' convent ional ' descri ptions can be capt u red i n t h i s i n i t ial bias of the s l i pnet . A descript ion assigned to a gi ven sensori motor data set wou l d be v iewed as ' convent ional ' i f i t were arrived at most of the t i m e w i t h no i n i t i al bias to the s l i pnet , and any other descript i on wou l d b e consi dered ' novel . '
10.7
Conclusions
The main points of t h i s chapter can be s u m m ariz e d as follows. F i rs t , t here
is the methodologi cal inadequacy of almost all t radi tional approaches to metaphor an d analogy that focus on fi n d i n g some exist i n g s i m i larit ies be tween t he given representations of the source and t he t arget . These ap proaches are bas i cally flawed-i n as far as their potential to model creati ve analogies or metaphors i s concerned-not because t hey characteri ze s i m i l a rity i n t h i s way or t hat way, or whether they use t h is algorithm or t h at al gori t h m in comp u t i n g the s i m i l arities, but because they are always work i n g w i t h some gi ven representations t h at h ave been fixed i n ad van c e , w h e r eas the creat i v i ty of met aphors an d analogi es, as I have argued i n t h e earlier chap ters , comes from changi n g t hese a p ri o r i representations i n novel way s , a p rocess t h at often generates new cogni t i ve i n for m at i on t hat was not p resent in the old represent ations. Changi ng representations, however, requ i r es one to i nteract w i t h the perceptual d a t a d i rectly, since it i s the autonomous struc t u re of the pe r ce p t ual data t h at constrai n s the possi ble ways i n w h i ch t hey can be repres e n te d .
From t h i s p o i n t of view, i t is the m o del of analogy i m p lemen t ed by H o f stadter and M i tche l l t hat seems much more prom i s i n g . By focus i n g on the process by w hich t h e represent at i on s are i n i t i ally ge n er ated t hey were able ,
Ch apt er 10: Com p u tational Approa.ch es
409
to model m any i nst ances of creat i ve a n a l ogies t h at requ i red new ways of looki ng at the objects . Though t h i s model was con fi n ed to an art i fi c i al mi croworl d , I argued t hat once we real ize t h at i t i s the p rocess of redescription or changi ng representation that u n derl ies creati ve metap hors and analogies, we see at once t h at t here are many exist i ng AI systems-i n the domai ns such as scene recogni t i o n , handwri t i n g recogn i t ion and speech recogn i t ion-that can generate i nstances of creati ve met aphor or analogy. A gai nst t h e backd rop of t h i s d i scussion , I ou t l i ned a system to model creat i ve metap hors and analogies as changes of rep resentat ion . T h e i dea is t hat when the source concept network i s expl i c i t l y give n , the system i s forced to concep t u al i ze the target sensori motor data set usi n g o n l y those concepts. T h i s can res u l t in a changed representat ion of t h e t arget sensorimotor data set-changed from what the representat ion m i gh t be when t h e sou rce i s not given-thereby creati n g s i m i larities between the sou rce and the t arget . I n t h i s connection, 1 must note that the p rocess of change of representa tion p l ays a key role i n m any other aspects of cogn i t ion . l n problem sol v i ng, for i n s t ance, new approaches and new i nsights often i n volve a changed repre sentation . Though t h i s h as been recogn i zed as far back as A m arel [ 1 968] , i t is only recently t h at change o f representation i s gett i n g a more serious atten tion from A I researchers [ I
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and Th o ugh t , Cam b r i d ge U n i v .
P ress, Cam b r i dge , U . K . ; Chap.
7 ( pp .
1 7 3- 1 9 2 ) .
R a tl i ff F . ,
1 976,
" O n t h e Psycbop h y s i o l ogi c a.l B as i s of l
n i ve r s al
Color Term s , "
Proceedings of t h e A m e rica n Ph ilosoph ical Society 1 20, n o .
5
( O ctober
1 976 ) , pp. 3 1 1 -330. R ed d y M .J . , 1 9 7 9 , " T h e
Con d u i t Metaphor-A C ase of Frame Conflict
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P ress
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O r ton y ( eel . )
Camb r i d ge , U K , p p .
1 97 6 , " P i erce and t h e Economy of Research ," Science 4 3, p p . 7 1 -98 . N.,
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Me taph o 1· a n d
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Name Index Brach man , R.J., 405, 412 B r oad W., 56, 63, 412
Abbott, Edwin, 135, 180 A b r a mov ,
I., 108, 414
,
Acconci, Vito, 6
Bunuel, Luis, 25, 414
Achinstein, P. , 325, 349, 411, 428
Bunch,
Agassi, J. , 325, 411
B u rks, Art h u r W., 349, 412
B.L.,
349, 412
Allwood, C.M., 335, 411
Burns, B.C., 17, 426
Amarel, S., 409, 411
Bush, George H.W., 337, 351
Anderegg, M.A., 23, 24, 411
Buy, Ugo, 121
Andersen, M., 50, 411
Cage, John, 6, 412
Antonioni, Michelangelo, 23-25, 246,
Camac, Mary I<., 3, 45-46, 412
252, 253, 256, 427
Campbell, D.T., 104, 428
Arb i b , M.A., 187, 217, 286, 290,
Cam p b ell, Joseph, 5, 22, 49, 412
411, 421
Canguilhern, G., 56, 412
A r maj ani Siah, 6 ,
Aycock, Alice, 6
C ar b onell , J.G., 3, 360, 366, 373,
B ar ham , J., 120, 411
Ca rn ap , R., 33, 324-326, 343, 413
413
B ar ke r , S., 349, 411, 428 Bateson,
G.,
Carnot, Sadi, 57, 333
Carroll, J.M., 371, 413 Carter, Michael, 33
132, 290, 411
Baum, Fran k , 1
Benjamin, Richard,
23
Cassirer, Emst, 7, 10, 94, 111, 113-
115,
Berger, P.L., 161,411
Berggren ,
Berlin,
D.,
290,
B., 107-110, 294, 299, 411
Binkley, T., 306, 307, 411 Black, Max, 3-5, 10, 54, 66, 68-73,
75, 78, 81, 83, 86, 248, 262,
,
,
286,289,290,303,314, 412
Bobrow, D., Bohr, Niels,
132, 144, 186,286, 287,
292, 29 8 413 Champa, T\.S., 43, 413 Chaplin, Charlie, 23, 25 Chase, S., 309, 413 Christie, J u li e 23 Clement, C.A., 40, 329-332,
286, 287, 411
413,
415
405, 412 50, 55, 60, 411
Clift, Eleanor, 337
Boland, Eavan, 41, 48, 246-251, 253-
Cohn, P.M., 211, 231, 233, 242, 413
254, 278-279, 292, 307, 310,
Collins, A., 163, 413
311
Con nor,
433
K., 17, 414
Metaphor an d Cognition
434
329-333,336, 339, 366, 367,
Corballis, M.C., 339, 415
371, 375, 413-416
Darwin, Charles, 55, 60, 416
Gephardt, Richard, 351
De Kooning, Willem, 6
Gerhart, Mary, 106, 416
De Valois, R . L , 108-109, 414
Gerrig, R.J., 87, 416
.
Deregowski, J.B., 10 4, 414
Gick, Mary L., 33, 40, 56, 263, 267-
Descartes, Rene, 106
274, 318, 329-332, 416
Desforges, Abbe Pierre, 105
Gillam, B., 339, 416
Dretske, Fred I., 250, 414
Gineste, Marie-Dominique, 75
Dukakis, Michael, 351
Gitter, D.L., 56, 416 Glucksburg, Sam, 3, 45-46, 412
Edwards, Gwynne, 25, 414
Goodman, Nelson, 7, 9, 10, 35, 94,
E hren fels, Christian von, 95
111-116, 118, 127, 128, 131,
Eliasson, M., 335, 411
134, 151, 158, 166, 169, 179,
Eliot, T.S., 48 Em m et Dorothy M., 286-287, 414 ,
Engel, !v!., 431 Erman, L.D., 187, 386, 398, 407,
414 Evans, Thomas G ., 358, 377-38.5,
414
354, 412, 416, 428 Gordon, William J.J., 56, 58, 6062, 64, 270, 276, 332, 333, 373, 389, 396, 416 Gray, William, 336 Green, M., 98, 421
Ewing Lauren, 6 ,
Greiner, R., 373, 416
Falken h ainer, B., 3, 39, 366-367,
414, 415
Gruber, H.E., 5, 55-56, 416 Halasz, F., 335, 417
Fass, Dan, 3, 360, 362, 414
Halford, G.S., 157, 233, 417
Fauconnier, G., 132, 415
Hall, R.P., 365,417
Favreau, O.E., 339, 415 Feynman, Richard, 352, 391, 41 5 Fikes, R.E., 412
Forbus, K.D., 366-367, 405
186, 253, 306, 317, 348, 349,
,
414,
4 15
Fox, H.N., 6, 415 Franklin, Benjamin, 62 French, Robert M., 391, 415
Harrod, R., 323-326, 343, 417 Hart, C, 104-105, 417
Hartline, H.K., 106, 417 Hausman, Carl R., 3-5 ' 66 ' 75-76 ,
86,417 Hayes, P.J., 405, 417
Hayes-Roth, F., 414
Hedren, Tippi, 24
Gacs, Peter, 350
Heider, El eanor, 109; 417
Galileo, Ga li l ei , 336, 350
H e lmreich ,
Gardner, Howard, 431
G ent n e r , D.R., 258, 307, 30 8, 415
Gentner, Dedre 3, 33, 40, 56-58, 163,258,307-308,312,313, ,
S., 36 2, 417 Hemingway, E rnes t 1 Henle, P., 2, 417 ,
Herskovits, M.J., 104, 428
Name In dex
435
Hesse, Mary B., 5, 33, 54, 56, 132, 270,277,286,290,303,322, 325, 358, 411, 417-418 Higginbotham, Virginia, 25, 418 Hintikka,Jaakko, 306, 418
Jones, Roger S., 106, 420
Jun g, Carl G., 158, 160, 418, 420 K ohl er, W., 96, 421
Kovecses, Z., 6, 422 Ka.mp, H., 307, 420
Hinton, G.E., 427 Hitchcock, Alfred, 6, 22-24, 44, 64,
115, 116, 252, 429, 431
K an iz s a, G., 339, 420
K an t, Immanuel, 7, 94, 111-115,
127,158,160, 276,288,420,
Hobbs, Jerry R., 360, 362-363, 418 Hoeller, S.A., 158, 418
Katz, A.N., 310, 420
Hoffman, R.R., 87, 418 Hofstadter,Douglas R., 31,166, 358359,367,370,376-378,384392,407, 408, 415, 418, 423424 Holland, Dorothy, 157, 170, 419 Holland, J.H., 132, 166, 187, 241, 267, 318, 320, 354, 419
K ay, P., 107-llO, 294, 299, 411,
420 Kedar-Cabelli, S., 365, 420
Kei l, F.C., 46-47, 420 Kekule, 62 Kelly, M.H., 46-47, 420 Kemper, S., 87, 418 Kempton, W., 6, 421
Holstein, B. I . , 5, 56, 419 Holyoak, I\eith J., 33, 40, 56, 263, 267-274, 318, 329-332, 339, 366, 371, 372, 416, 419 Rubel, D.H., 106,
421
170, 185, 355,
419
Keynes, J.M., 324, 326-327, 346,
349, 421 Kfoury, A .J ., 217, 421 KiLtay, Eva F., 4, 5, 48, 65, 67, 6-
89, 299, 421
Hume, David, 343, 419
Klee, Paul, 21, 25-26
Indurkhya, Bipin, 28, 67, 84-86,
Koesller, A., 56, 62-63, 421
Kling, R.E., 365, 421
236,256,258,274, J04,344,
396, 416,
419
I
F
Inbelder, Barbel, 116,419, 42.5-426
Kor[, R.E., 409, 421
Iverson, E., 362, 417
Krausser, P., 112, 1.58-1.19, 421
lwayarna, M., 361, 420
Kubrick, Stanley, 43, 44, 421 Kuhn, Thomas S., 275-276,
Jacobs,
G.H., 108, 414
Jeziorski, M., 56-58, 333, 336, 4 15
Johnson, Mark, 2, 66, 78,
79,
82,
84, 94, 1 2 4-12 8, 131' 251' 262, 289,
293-297, 306
,
307,
G.,
Lakatos, Imre, 169, 422 Lakoff,
George, 2, 5, 6,
19-20, 66-
67, 7 -85, 90, 94, 124-12 '
131, 132, 1.51, 156-157, 262,
360, 420, 422 Johnson, Michael
421-
422
3, 17, 40,249,
252, 309-3111 420, 423
26 3, 286
2 7, 290,292-301,
306 , 308-309, 360, 422
Meiaphor
436
Langer, S u s a n n e K., 113-114, 413, 422
Laroche, F., 362, 417 Lean , Dav i d , 23-25, 411 Leigh , Jan e t , 6 Lesser , Vi ctor R., 414 Let t v i n , J.Y., 106, 422 Levesque , H.J., 412 Lev i n , S.R., 296, 422 Lev i ne , M.W., 108 Lev i n so n , E., 339, 428 Levy, A., 192, 422 L i bby, Wal te r, 56, 62, 422 L i p p m an n , R.P., 1 87, 422 Lowry, M., 409, 422 L u c k m an n , T., 1 61, 411 L u r i a, Alexan der R., 1 00 1 02 109, -
,
423
M
Corm ac, E ar l R., 76
M ac k ,R.L., 371, 413
Mac L a u ry, R.E., 11 0, 423 Mac Cormac, Earl R., 7, 19, 66, 77-78,82,125,286-287,290,
and Cognition
Mi l le r , R.M., 263, 341, 423 Mi t ch e l l , Mela n i e , 358, 367, 370, 377-378,384-392,399,407, 408, 418, 423-424
Mol l , R.N.,217, 421 Mon d r i a n , Piet , 42-43,63,246,252254,278-279,307,311,413, 424
Moran , T.P., 335, 417 Morri s , Rob ert , 6 Mos s , A.E.St.G., 110, 424 Nagao , M., 407, 424 Neisser, U l r i c , 249, 424 Nel son , Bery l , 197, 347 Nel so n , Thomas A. , 44, 424 New m a n , Barnet t , 6 Newm an, J.R., 350, 424 Newto n , S i r Isaac , 55 N i i , H.P., 407, 4 24 Nisbet t , R.E., 419 N i x o n , R i ch ard 262,28.5,301,308,
309
Nowott ny, W., 28, 424
292-301,303,306,307,309,
O ' Toole, Peter, 24
423
Mac Lane, S., 192, 265, 423 Mal'cev, AI., 19 7 , 231, 423 Malgady,
Robert G., 3, 17, 40, 249,
252, 309-311, 420, 423 Marschark, M., 310, 420
Mart i n , James H., 3, 360, 423 Mat s u yama, T., 407, 424 M at u ran a I-I.R., 120, 422, 423 McCabe, A l l yssa, 45, 310, 423 McCu l l och W.S., 422 Mc D an i el , C.K., 109, 420 Melis, E ri c a, 335 Mel v i l l e , H e rman , 1, 16, 19 ,
,
Metzinger, Jean,
49, 55
Mi l le r , A.I., 5, 50, 55-56, 423
Oppenheim, Dennis, 6
Or tony, Andrew, 3, 26, 28, 40, 47, 251,309,311,312,424,426,
430 Osgood, D.W., 428 Paivio, A., 310, 420 Partee, Barbara H., 155, 424
Peterson, C., 428 Petrie, H.G., 5, 169, 424 Piaget,, Jean, 7, 9-10, 94, 116 -12 3
,
126, 128, 131-132,134,151, 157,165,168,292,303,354, 419, 425-426
P i nker, S., 185, 426
437
Name In dex P i t t s , W.H . , 422
Scheffler , I., 30 7 , 42
Plat o , 9 5 , 426 P oll i o , H.R., 17, 426 Pollock, Ja ck s o n , 6 Polya , G., 5 6 , 426 P o pp er , Karl R., 1 6 4 , 242, 426 Pri n c e , G.M., 4 1 6
S c o t t , W.A. , 1 32 , 428
Qu i n n , Nao m i , 6 , 157, 1 70 , 2 8 6, 309 , 4 1 9 , 426
Searle, John R., 2 9 6 , 428 Segall, M. H., 104, 428 Sekuler, R., 339, 428 Se well, E., 286-2 8 7 , 428 Sharif, Omar, 23 S hi rl ey, E.S., 349, 428 Shlain, Leon ard M., 5 0 , 428 Shurkin, J., 338, 428
Ratliff, Floyd, 1 0 7- 1 09 , 426
Siegel, R.l<., 3 39, 428
Reddy, D.R., 414
Sim o n , John , 25, 428
Reddy, M.J., 6, 426
Sizzi, Fra n cesco, 3 36 , 350
Rescher, N., 3 4 9 , 4 1 2 , 426 Reyno ld s , R.E., 28, 4 2 6 , 430 Rich a r d s , I. A., 3, 66, 2 8 6 , 289 , 290, 427 Ricoeur, Paul, 3, 10, 54, 66, 74-75, 8 1 ) 86, 25 1 ) 286, 290, 396 , 427 Rifk i n , N., 2 4 , 427 Rig ue t, J., 19 7 Rob b i n s , James , 3 3 6 , 427 R o ge r s , H., 2 1 7 , 4 27 Rosch, Eleanor, 159, 375, 427
Skor s t ad, J. , 3, 39, 415
Rothbart, D., 5, 55, 427
Rowell, L., 6, 427
Rumclhart,
D.E., 187, 427
S m i t h , M.K., 17, 426 So l o m o n , Stanley J., 23 , 429 Sowa, J.F., 364, 429 48, 74, 24624 7 , 249, 251-254 , 278, 292,
Spender, Stephen, 42, 307
Srb, A.M., 347, 430
Sternberg, R.J., 4, 31 0 - 312, 429 Stevens, Wal la c e , 73 Stewart, James , 22, 23, 4 4 , 64
Sticht, T.G., 5, 429 Stillman, J.M., 336, 429 Stove, David C., 344-348, 429 Stratton, G.M., 167-168, 429
Russell, Allan, 106, 416
Stuftrt, P., 3, 'I 16
Russell, S.J., 373-374, 427
Subr;umtnia.n, D., 409. 429
Russell, Sylvia W., 360, 361, 36 3 ,
Sweetser, E.E., 304, 429
427 Ryder, Winona, 23
Sacks, Oliver, 1 10 , 428 Salmon, W.C., 3 4 3 , 428 Sandburg, Carl , 2, 40, 50 Sandu, G., 306, 418 Schon, Do n al d A., 5, 6, 56, 59-61, 64, 85, 271, 274, 276, 332,
3 3 3, 373, 389, 405, 428
Szeminska.,
A., 116,426
Tanaka, H., 361,420 Taylor, Rod, 24
Terry, A., 407, 429
Thagard, P.R., 366, 37l, 419 Thomas, Dylan, l Tokunaga, T., 361, 420
Tourangeau,
R., 4, 310-312, 429
Metaphor and Cognition
438
Truffau t, Francois, 24, 44, 116, 252, 429
T u bey, Charl es, 336 Tu rbay n e , Colin M., 106, 168, 286-
Wil son, W.H., 157, 233, 417 Win n e r, Ellen, 28, 431 W i nston, P at r i ck, H., 373, 431 Wood , R., 6, 431
289, 405, 429
Tu r ner, Mark, 2, 5, 66, 67, 79, 81, 83, 85, 286, 294, 295, 297, 300, 422
T u r ner, Victor, 6, 429 l l m a n, S., 185, 429 Van Eyck, Jan, 22, 25, 26 Van Rooten, L. d ' An tin, 399, 429 Varel a, F. , 120, 423 Ver brugge, R.R., 4 , 5, 17, 28, 30, 249, 430 Vitti, Monica, 23
Von Wright , G.II., 33, 343, 430 Vosniadou, S., 28, 430 Waggoner, J.E., 4, 5, 430 Wal l ace, B., 347, 430 Way, Eileen C., 360, 363-364, 430 Wegener, P., 290, 430 Weiner, E.J., 3, 360 361, 430 ,
J.S., 327-329, 373, 430 Wermus, H., 121, 430 Wertheimer, Max, 96 Wheeler, C.J., 286, 430
34 1 , :366,
Wheelwright, P.E., 5, 66,
76-77,
Weitzenfeld,
430
Whitford, Frank, 22, 42, 430 Whittock,
Trevor, 6,
23-24, 43, 430
Whorf, Benjamin Lee, 80-81, 100, 430-431
Wiesel, T.N., 170, 419 Wi lks , Yori ck , 360 , 362, 414, 431 Williams, R.J., 427 Wilson, P.T.,
28,
430
Zadeh, L.H., 77, 431
Subject Index !1-word algebra, 211 4'33" (Cage), 5 2001: A Space Odyssey (Kubrick), 43 Achilles ( N ew m a n ) , 5 Birds, The ( Hitchcock), 24, 26, 252 Cathedral ( P ollo ck ) , 5 Challenge1·, space shuttle, 3.52
Psycho
(Hitchcock), 6, 23 (Hitch cock), 22, 44, 64
Rear Window
(IL D es e1·to Rosso) ( A n tonioni ) , 23 Seascape (S p e n d e r ) , 42, 48, 74, 247 Red D e se r t , The
Theaetetus (PIa to), 95
Wall Street JoU?'n(d, 336 While H a w lh o m in the West of he-
Composition with Blue and Vellow
land (Eavan Boland), 41
(Monclrian), 4 2, 246, 252
(Baum), 1,
Discreet Charm of the Bomyeoisie,
Wizard of Oz, The
(Bunuel), 25 Doctor Zhivago ( L ea n ) , 23 Excavations (Kooni ng), 5 F latland (Abbott), 13 5- 1 36, 180 Fog (Sandburg ), 2, 4 0
Boston Globe, 337, 350
The
Buffalo
lan
Th oma s ) ,
Lawrence of
News, 1
Abstract symbolism in Klee, 21, 25
in M o n d ri a n , 63
Force that through the g1·een fuse drives the flowe1·, The
26
Abst rac t i o n, in syntactic metaphor,
(Dy
263
1
Accommod ation , 164-169
Arabia (David L ean) ,
as 'bottom-up' process, 148, 1 5,
24
(Metzinger), 49 Love Song of J. A lfn:rl P1·ujmck (Eliot),
Le Gouter
394
as restructuring concept networks, J118
48
biological, ll8
Man-iage of Giovanni(?), Anwlfini and Ciovanna Cenami (II), The (Van Eyck), 22 Mermaids (Richard Benjamin), 2:3 Moby Dick (Melville), 1, 16, 19, 26 Modem Times (Chaplin), 23, 25 Old Man and the Sea, The (Hemingway), 1 Pa1·k near L(ucerne) (Kiee), 21
stn1ctureof concept work, 133
cha11ges
examples
of
determining number in
a
net
of uays
year, 166
imitation, 165 in
mathematical
mapping a
439
proofs, 169
terrain,
133, 166
Metaphor an d Cognition
440
g r o upi n g p e r sp e c t i ve on, 1 74 in a p arser, 394
between fluid- flow a nd h e at - flow,
57
in a t h r e e- l aye re d co g n i t i v e sys
bet ween software a n d myt h , 49
b etween Le Go'Uter(Met z i n ger)
tem , 18 2 in l aye r e d co g n i t i v e system, 185 Acco m m o d at i o n ( P i a g e t ) , J 18-12:3,
and q u a n t um m e ch anics ,49 creat i ve , see Creat i ve anal ogy d iffe r e n t sen ses of, 28
128 A CME , see An a l o g i c a l C o n s t r a i n t
ogy
M ap p i n g E n gi n e Ad ap t at i o n ( P ia g e t ) ,
pre d ic t i v e , see P red i c t ive ana l -
119
proportional, see P ro p o r t i o n a l
Ad m i s s ib i l i t y
a n a lo g y
of a c l a s s of o p erators, 221
sim p l e, see Simple analogy
of an operator, 220
s t a r ry-s ky- t h r o u gh - the-smo ked
ALG I ( a l g ebra ) , 209,
216, 224, 227
A L G 2 ( a l g e b r a ) , 209, 211 , 216,221,
g l ass ( Bl ac k ) , Anom aly,
69, 72, 73,81
17, 18
A p p arent motion
224, 227
effect of c ul t ur a l background ,
Algebra.
10 2
d efi n i tion of, 205
e x p e rim e n t s of Kolers,
96 ex p e ri m ent s of We r t h ei m e r , 96 ex peri m ents w i t h colored fig u r e s , 98
ex am p l es of, 205 fini te, 209 finitely generated,
216
i n fi n ite , 209 Algebra of c l asses, d efi n i t i o n of, 223
A p p earan ces,
A l g e b r as , p r od u c t of, 224
A pt n es s of meta p h ors, see Me t aph o r
A n a l og i c a l Con s t rai n t .ifap p i n g En-
of ( Kan t ) , 112
ical apt n ess A rg um ent by ana l o gy ,
gine, :371-:37:3 Ana l og i c al inference.
wo r ld
see
Predictive
Arti culat i n g the
analogy
A nal ogical reasoning,
see
Predic
t i ve analogy
c
o n t e n t domain (1\ i t
ta.y), 88, 89 Assimilation, 118-120
Analogical symbols, 114
b i o l o gic al , 118, 134
A n al ogi e s
cog n i t iv e , 1:34
as basis of metaphors, 4
in political rhetoric,
337
underlies i n d u c t i on , 354
A ss oc iat ed c o m m o n p l a c es ,
A nalog y as a g ener a l h e u ris t ic ,
formation of memory, 134 vs. p rojection, 134
similarit y-based, 50
366
between b i o l ogica l sys tems and cognitive systems (Piaget), 120
Predic
see
tive a11alogy
68
A s t ro l o g y , 342 Asy mme try in sim p l e
empirical
gy , 30 17, 19, 254
a n alo
Asymmetry of m e t a p ho r
st u d ie s of, 17
Subject Index
441
in Black's i n teraction t heory,
69-
mo deling si rni lari ty-crea t i ng metaphor as , 401
70
in interact i on t h eori es, 4, 5
Clas s , 191
A ugmen tation , 85
emp t y , 191
Bap tism , 23 Baseb a l l World Series ( 1 9 9 1 ) , 351 Ben zene, m o l ecular s t r u c t u re of, 62 Between-domains similarit y , cri t er i o n of (Tou rangeau & Stern b e rg ),
3 12
disjoint, 192
u nion of, 191
Biject ive f u n ctio n , 20 :3 cl i f u n ctio nal relation an d , 204 Biol ogical metaphor u n derlying Copy cat,
:386
Biological systems
ass i milation a , n d acco m m o d a t , io n i n , 118 cognitive sys tems a n d, 120 Blackboard system, 4 07 Botto m - u p k now ledge s o u r ces, 4 07 Bot tom-u p p r o cess
Clas ses vs. set s , 192 Closed systems ( Piaget ) , 1 5 7
C losure of a class of o b jects of an alge bra, 214
over o p e rato r s , 216 C l u s t e r i n g effect, in concept net;vo r k s , 156 Co delets (Copyca t), 387, 388, 408 Coderack ( Copycat ) , 387, 408 Codomai n , of a relat i o n , 1 9 4 Cof11nctional
in parsing, 394
in visual cognition. 186 vs. 'bottom-up' process, 394
BuddhiBm, 22, 23 Buddhist metaphysics, 4:3
Ca n t o r 's theorem, 3:33, 366
1 12
Chain of subalgebra.s, 229 of s u b c l asses , 198
Change of rep resentation
of
power of, 194 Classes
prod uct of, 1 94
Bijection, 20 1
Categories (I
finite, 1 9 1 infinite, 191
i n t ersection of, 191
B i b l e , 22
basis
C i rcular i t y in concep t network s , 1 5 7
creative analogies, 3.59
b as i s of metaphor, 7.5
in cognition, 409
correspondence, 229
relatio n , 19G C og n i t i o n actiou-oriemed
n.get),
approach to (Pi
llc'
biologiml basis of, 120
Cognitive domains (Scott e/ 132 C ogniti v e model, 133
ambiguous, 176 complete, 178, 235, 236 defi n ilion of, 233
extension of, 2:38
full, 178, 235, 236 fully resolved, 235, 236
rrl.),
442
Metaphor a.n d Cognition
gi ves descri p t i o n s to obj ects i n env i ron ment , 1 76 groups t h e env i ronment, 1 6 9 i n Spinner's w o r l d , 1 4 1 o p t i mal, 2 3 5 , 2 :3 6 refinement o f , 1 78 , 238 represent s envi ron ment by a concept net wor k , 1 76 rest r i c t i o n of, 238 synonyms i n , 1 78 u namb iguous, 2 3 5 , 236 Cogn i t i ve m o d e l s ' notat ional systems' and ( G o o d man ) , 1 79 accommodat i ng, 24 1 concept d r i ven . 2 4 0 concept u alized vers i o n s of reali ty, 1 69 c o rrespond to ' wo r l d s ' ( G o o d m an ) , 1 69 equ i valent , 236 experient ial versions of rea l i ty, 1 69
over the same envi ronmen t , 236 p roj ect i ve, 240 s t r o n g l y equ i va l ent , 23 6
C o g n i t i ve
relat i o n , 1 6 1 - 1 64
accom m o d at i n g ,
1 65
environment , 1 6 1
d r i ve n ,
1 65
e p i morph i c , 235
24 0 , 24 1 i n S pinne r ' s world , 1 4 1 i n c ohe renc y of, 1 64 , 1 6 9
h o m o m orph i c ,
i so m or p h i c , 236
makes concept net work mean i ngfu l , 1 6 1 pr oj ec t i ve , 1 6 5
303
local, 234 , 24 1 of cogni t i ve models (and relat i ons ) , 1 33 of cogni t i ve relations, 1 63 of proj ect i ve models, 242 v s . intern al consistency, 7 Color b li nd n ess, 95 Color percept i on , 1 0 1 Color uni versals, 1 09 , 1 1 0 neurphysiol ogi cal basi s for, 1 0 7 Com m u n i o n r i t ual, i nterpretati on of, 5 , 22 Com parison t heory, s e e Theories of metaphor, compari son the ory
Complex s y m bo l, 2 1 , C o m p o ne nt s
26
of a s y m b o l , 1 5 3
C o m p os i t i o n
d i fu n c t i o n a l , 2 3 5 envi ronment
24 1
full, 234 , 24 1 i s not internal consistency, 1 46 ,
of a descr i p t io n , 2 1 2
concept d r i ven , 1 6 5
c reates
Cogn i t i ve relati ons, 1 32 Cogn i t i ve system m u lt i - layered, 1 82 , 247 t hree layered, 1 82 Coherency correctness and, 30 1 fini te representability of, 1 63 ,
226 of funct ions , 203 of operators, 204 of r elat i ons , 1 94 of transformat ions, 1 70
o f correspon d en ces ,
C o m p o s i t i o n al se m an t i c s , 6 7 , 8 6
Computab i l i ty o f operators, 2 1 7
Com p u t able fu n c t i o n ,
Concept network
232
Su bject Index
443 Co n t ex t u a l d e co m positio n ( i n Evan s '
defin i t i o n of, 2 3 2
p rogram ) ,
fi n i t e , 1 5 5 g en e r a t i n g set of, 1 5 3
38 1
C o n ve n t i o n a l i n t e r p ret ation s
i n a parse r , 393 i n fi n i t e , 1 56 source, 253 subnetwork o f , 1 .5 :3
C on ve n t i o n a l m e t a p h o r , 1 9 , 293
t arget , 254
C o n ven t i o n a l m e t a p h o r sc he m as ,
of m o de l s , 54 o f S pi n n e r ' s cog n i t i ve m od els ,
1 46
Concept n e t wo r k s , 1 3 2 , 1 5 1 - 1 58 as poten t i a.! re p r e s e n t a t i o n s ,
141,
1 52 at p e r c e p t u a l l evel,
360
i n H o b b s ' model, 362
1 80
c i r c u l a r i t y of, 1 57 closed sys t e m s ( P i aget ) a n d , 1 5 7
Con v e n t i onal metap hors , 1, 2,
13, 20, 6 7 , 7 8 , 7 9 , 1 26 , 2962 9 8 , 3 1 0 , 360, 363 com p u tational m odels o f , 360
C o n ve n t i o n a l - m e t a p h o r i cal d i c h ot o my,
c l u s t e r i n g effect i n , 1 5 6
2 1 , 286
com po n e n t s o f, 1 5 1
i n s y m bo l s ,
21
const rai nts on , 1 55
Copern i c u s ' as t ro n omy, 2 7 .5
d erived , 1 5 7
Co py c at ( H o fs t a d ter & M i t c h e l l ) ,
ex am p l es of
384 -39 1 , 4 0 8
3 7 7,
nat u ral n u m be r system , 1 5 1
m aj o r co m p o n e n t s o f ,
s t ree t m a p , 1 5 1
nondet e r m i n i s m i n ,
fin i t e l y g e n era t e d , 1 .5 .5
Correct ness
i n he r i te d, 1 5 8
con ven tion a l v s . met ap h o ric a l ,
3 06
learned , 1 5 7
i d e n t i fied w i t h c o h e re n cy, 30 1
of S p i n ner , 1 4 1
rad i al s t r u c t u re
o b j ec t i vi ly of, 3 0 7
i n , 1 56
represen t a t i o n l a ngauge for, 4 0.5 role of operators Concep t ,
wholeness
386 388-3 90 , 4 0 7
in,
1. 5 2
v s . t r u t h , 303 vs.
u n d e r s t a n d i n g , 305
Concl at i on
of, 9 5
Conceptual g r a p h t h eory ( Sow a ) .
con d i t i o n ( LakofF ) , 82
Corres p o n d e n ce
bct weeu
364
a l gebras , 224
229
Concep t u al i z a t i o n , i n a p 1 1rse r , : J 9 : l
d i fu n c ti o n a l ,
Co ngruences , 23 1
gi ves r i se to c h a i n of s u b �t l ge b r a.s ,
C o n s t ant operator , 204 Construct i v i s m , P i a ge t ' s , J 2 J , 1 28 Cons t r u c t i v i s t approach to cogn i -
tion ,
Content domain ( K i l t ay ) , 88-89 get , 1.5
p reser ves c l o s u r e ,
229
bet ween co ncept network
1 11
Contex t , i dent i fies source
229
i n verse of, 226
a.ml
tar
and
en v i ron m e n t , J 48, 16 1
between c o n cept n e t work a n d
worl d of
S p i n ner, 1 4 1
444
Me t aphor and Cogn i t ion
between sen sory st ates and worl d of S p i n n er , 1 38 bet w een s y m b o l s an d object s , 1 44 Co r r esponden c es b et w een a l gebra.s compos i t i o n of, 226 exa m p les of, 224 i n d u ce grou p i ngs, 227 Created Wor l d ( J u n g ) , 1 6 0 C re
between software a n d my t ho l ogy, 4 9 B l ack ' s exp l a. n a n t i o n of, 6 8 brought about b y change i n concep t u a l i zat i o n , 8 1 by n on- v er b a l an alogies , 4 9 by pro j e c t i v e m e t a p h o r , 2 7 1 c a u s e d by redescri p t i o n , 54 c l u es offere d by B l ack , 72
in a m ach i n e v i s i o n syste m , 4 0 0 i n com p a r i son - t heoret i c framewor k , 53, 65
i n H a u s m an ' s a p p r o ac h , 75
in perspec t i val t h eo r y , 4 , 86 in pre - t h eoret i c m o de l s , 55
in S an d b u rg ' s Fog, 3 i n s i m i l e , 48
Love Song of J. A IJ1·ed P1·uJr·ock ( E l i o t ) , 48
C reat u r a ( J u ng ) ,
1 60
K i t t ay ' s e x p l a n at i o n of, 67
65
p r o b l e m s rai sed by,
D a n i language, color terms i n , 1 0 9
Dead metap h o r , 1 9 , 6 7 , 293 fou r sen ses of, 294, 297 Deri va . t i o n from ' women ' t o ' d angerous t h i n gs ' , 1 56 Deri vat i o n s , 84 , 85
c i r c u l ar , 84 Des c r i p t i o n as a l ab e l e d ordered t ree , 1 5 3 in
a.
cog n i t i v e model ,
236
of a s y m b o l , 1 5:3
of an object i n a cog n i t i ve m o de l , 1 76
De t e r m i n at i o n r u l e ( R u sse l l ) , 373 D e t e r m i n i n g s t r u c t u res ( We i tzenfe l d ) ,
:3 28 D i aphor ( W heel w r i ght ) , 6 6 , 76-78
Dichotomy
is not arb i t rary, 64 p a r a d o x of ,
77
Creat i ve analogies co m p u t a t io n a l model of, 3 7 6 i n Copycat , 385-39 1 Creat i ve a n al ogy, 50 C r eat i v e m e t a p ho r s i n B ol a n d ' s poem , 4 1 i n com p u t at i o n al system s , 3 9 5 , 399 i n Ricoe u r ' s account, 7 4 Crea t i ve p ro b le m s o l v i n g , 5 6 C u b i s m , 5 5 , 60
60
in
psycholog i c al s t u d i es of, 4 5 rooted i n a. cogn i t i ve p h e n o m enon , 84 W hee l w r i g h t ' s ex p l an a t i o n of,
54
conven t i o n al vs. m e t ap h o r i ca l ,
2 1 , 286 l i teral vs. m e t ap h o r i c a l , 293 novel vs. c o n ve n t i o n al ,
408
Su bject In dex
445
2 4 , 2 4 6 , 253 1 6 , 2 0 , 247 D i ct i onary meanin g s , 249
E p i m or p h is m ,
D i fferen ces , r o l e o f
E p i tomization , i n VVei n e r ' s model
sou rce v s . targe t ,
D i c t i o nary m ean i n g ,
i n cogn i tion , 2 9 0 D i fferent i at i on ( P iaget ) ,
1 20 , 1 22
s t r u c t u re of, 1 60
230,
235
E p i p h o r ( W h ee l w r i g h t ) ,
6 6 , 76-78
of metaphor, 3 6 1 201
E q uiva l e n ce rel at i o n ,
Evaluation fu n c t i o n , o n s t r u c t u ra l
D i fu n c t i onal
des c r i p t i o n s ,
cogn i t i ve relat i o n , 2:35
2 2 9 , 230 2 0 0 , 202
212 60
corres p o n d e n c e ,
Evol u t i o n , t h eory o f, 5.5 ,
relat i o n , 1 9 6 ,
E x per i e n tia l o n t ology o f S p i n n e r ' s
biject i ve fu n c t i o n an d , 2 0 4 eq u i vale n ce relation an d ,
20 1
250 D i rect analogy ( G ordon ) , 5 8 , 333 p redict ive analogy a.nd , 58 D i g i ta l i zat i o n ( D re t s ke ) ,
D i rected acyclic g rap h , 2 1 1 D i rectly emerge n t concep t s , 8 1
1 92
D omain of a relat i on , 1 94 Domai n s - i n t erac t i o n t heory,
1 63 , 24 1 1 55 , 232 F i n i tely gen erated algebra, 2 1 6 , 2 3 2 F i rs t - O rd e r Logic , 84 Fli g h t , p r e history o f, 1 04 , 1 2 7 For m ( B a t e s o n ) , 1 32 o f coheren cy,
1 14
D i sj o i nt ( pai r w i s e ) grou p i n g s , 1 92 D i sj o i n t classes,
v i e w of c ogn i t i o n ( L a k o ff" ) , 1 24 E x t e n sion of a cogn i t i ve m o d el , 238 Ex t r a- I i n g uis tic condition ( H a u s m an ) , 4 , 76 F i nite represen tability
D i s c o n n ected relat i o n , 1 9 8 D i s c ur s i ve s y m b ol s ,
world, 1 44
Experien t i a l
see
T he-
ories o f metaphor, domai n s i n tero,ct i o n t h eory D y nami c eq u i l i b rium ( M o n d r i a n ) ,
43 D y n am i c t y p e h i erarch y ( E i leen
Way ) ,
363
D y n amical objects ( P i erce ) , 76
of concept n e t wo r k s ,
Fo r w a r d grou pi n g , i n d u ced by
Fram e of refe re n c e , ll 5 , 1 28
French revo l u t ion , Full gro u p i ng, 1 92
338
Fu n c t i on , defi n i ti on of, 20 3 P u n c t i o n it l c o n c t" p t B , 14 ]
Effectory vector ( S p i n n e r ) , 1 3 6
Functional
E i n s t ei n ' s t h eory of relat i v i ty, 2 7 5
Fu n c L i o n a l rel at i on , 1 96 , 2 0 3
E l e c t r i c a l c i rc u i t s , a s t ar g et r eal m ,
Fu zzy se l - L h eor y
258 Empty
109
1 32 , 1 60 for S p i n ne r , 1 44
Env i ronment ,
a.
cogn i t i ve m o d e l ,
1 69 o n t ology of,
cones p o n d e n c e , 2 2 9
i n ex p l ai n i n g c o l o r ' u n i versa.l s ' ,
class, 1 9 1
g r ou ped in
a re-
l at i o n , 20 1
1 60
i n for m <:tl i z i n g
metaphors, 7 7
G eneral i z a t i o n ( P i aget ) ,
1 20
Generat i n g c l ass ( of an algebra) , 2 1 5
446
Me t ap h or a n d Cogn i t ion
G e n erat i n g set ( of a concept n e t
creat i o n o f s i m i l ar i ty a n d , 5 3 ,
wor k ) , 1 5 3
6 5 , 68 , 7 0
a s a set of p r i m i t i ve s , 1 55
H i nd u i s m , 23
m i n i m a l , 1 55
H o m eomo r p h s ( We i t ze n fe l d ) , :328
G e ne r a t i o n ( of
sy m b ol s ) ,
1 53
H o m o m or p h i s m , 2 4 0 , 24 1
G e n e rat i o n h i s t ory ( o f o b j e c t s
1n
an a l g e b r a ) , 2 0 9 G e ne r a t i ve met a p h o r ( S ch o n ) 2 7 6 , ,
G e s t a l t psychol ogy, 9 6 , 100 G es t a l t s t ru c t u r e of p recon c e p t s , 1 2 6 G ro u p i n g
p sy c h o l ogy,
96
i n S p i n n e r ' s cogn itive model s , 144 i n d u ced by
a
rel at i o n
o f o b j e c t s i n e n v i ro n m e n t , 1 6 9 of t r a n s fo r m at i o n s
e n v i ro n -
1 11
m en t , 17 0- 1 72
h o m o m o r p h i s m , 230
I m ag i n at i o n a p p roach t o u n d e r s t an d i n g , 2 5 0 i n u n de r s t an d i n g m e t ap h o r , 251 I m i tation
I n co h e re n cy ( of cogn i t i ve r e l at i o n
d e fi n i t i o n of, 192
or
exam ples o f , 1 9 3
cog n i t
i ve m o d el ) fi n i t e mean s ,
det ectable by
192 , 1 9 7
i ndu ced by rel at i o n , 1 94 , 1 9 6 , 198 , 2 0 0 pairw i s e d i s j o i n t , 1 92 , 1 98 par t ition , 1 9 2 , 1 9 6
( G ood m an ) general i zed , :34 9
G r ue paradox
241 Individuality condition
1 64 ,
( H au s man ) ,
7G I nduction c o g n i t i v e d i mension of, 3 5 4
over a. n a.lge b r il. , 2 2 7 ,
3 4 8-:3 4 9
com pared w i t h v i s i o n , 3 5 4 met aphys i c al d i m e n s i o n o f , 3 5 5 two dimensions o f , 353
( E rm a n e t al. ) , 3 8 6 , 3 9 8 ,
Information , loss of i n cogn i t i on , 277, 2 79
399 I-l eri ng t h eory ( of color vision ) , 1 07 H i g h l i g ht i n g and d o w n p l ay i n g .3 2 1
a
1 65
bij ect i ve , 201
b y s y n t act i c
I d e n t i ty, c o n cept o f , 117
as exam p l e o f accom m o d at i o n ,
cl a.ss
H e a r say I I
1 3 2 , 151 , 1 5 6 I d e n t i ty operat o r , 2 0 4
of
forward, 2 0 1
ful l ,
I d e a. l i zed cogn i t i ve m o d e l s ( L akoff ) ,
o f a relat i o n , 1 94
i n vo l ves l oss o f i n fo r m at i o n , 2 7 7
a
I ch kari wom e n , 1 01-102, 1 0 9
I m age
b a c k ward , 201
over
H y d rau l i c s y s t e m s , t heory of as source concept n e t work , 2 5 8
4 07
i n ges t a l t
d efi n i t i o n of, 229 H o p i l an g u age, 100
m e ap
t
h or
,
262, 3 1 2,
recl ai m ed by proj e c t i ve m e t ap h o r ,
277 I N T E G E R ( a l ge b ra ) 2 0 6 , 2 0 9 , 215,
221, 224 , 2 2 6 , 236
447
Su bject Index
Interaction between lexical fields a.ncl content domai n s ( K i t t ay ) , 89 I n t e rpr eti n g S p i n ner's concept net wor k s , 14 1 Intersect ion , of c l as se s , 1 9 1 Intri n s i c de c o m p o s i t i on ( i n Evans ' p rogram ) , 38 1 I nverse of a correspondence, 226 of a fu n c t i o n , 203 of a r e l a t i o n , 1 94 I so m or p hi s m i n B l ack ' s theory, 72 in L a k o ff ' s theory, 82 c o g n i t i ve relation as , 236 defi n i tion of, 230 Isomorph i s m t heorem , F i rst , 23 1 Kernel ( of a h omomor p h i s m ) , 230 K i ne t os c o p e , i nvention of ( E d i s o n ) , 63 K nowledge, b i ologi cal basis of, 1 20 approach to cogn i t i o n , 1 2 4 Lateral g e n i c u l a t e n u c l eu s , 1 0 8 Lat i t u d e and longi t u de, l i nes of ( as exam ples of p r o j ect i o n ) , 133 , 1 68 Lakoffian
Lavoi s i e r ' s t h eory of com b u s t i o n , 2 7 5
La.yercd co g n i t i ve
system and ,
187
n e w i n s i g hts i n , 1 8 6 proj ection i n , 1 82
v i s u al
sys t e m
Learning by
cls ,
1 85
an alog y , 3 73-3 75
Learning, two forms of, 3 74
LEN G T H ( correspondence bet ween algeb ras ) , 2 2 6 , 2 2 7 , 236
l i nguistic
L i n k precon cep t , 1 25 , 1 26 Li teral , 1 4 , 1 9 , 20 fou r sen ses of, 294, 297
L i teral metap hors, 293 Li teral - metaphorical d i chot omy, 2 9 3
Local coheren cy, 1 63 , 302 defi n i t i o n of, 234 L o g i c a l w i d t h ( C a r n ap ) , 324
M acaque mon key, v i s u a l system of, 1 08
M a k i n g the fam i l i ar s t range ( Gor don ) , 6 1 , 2 7 6 , 333, 389, 396, 404
Making t he s t r a n g e fam i l i a r ( G or d o n ) , 60, 2 7 0 , 396 , 4 0 4 M a p , as a concept n et w o r k , 1 5 1 -
1 53 , 1 62 ( He. s e ) , 2 7 0 change, caused by m e t aphor,
M ater i al m o d e l s
Mean i n g
290
Mental models ( H o l l an d e l al. ) , 1 :32 M e n tal spa cs ( Faucon n i er ) , 1 32 Met" ( Fass ) , 3 6 2 , 363 Melaphor
accommodat i on i n , 1 85
m u l t i p l e ' wo rl d s ' ( G ood m an )
Lex i cal d ec i s i o n p a r a d i g m , 4 .5 L e x i c a l fie l d ( K i t t ay ) , 88-89 L ig h t n i n g con d u c t o r , i n v e n t i o n of ( Fr a n k l i n ) , 62 L i n g u i s t i c m e t a p ho rs , s e e M e t a p h o r s ,
'emot ional state as
blot ches of
pai n t ' , 246, 2 5 2 , 256 ' g l ass t e l e p h o n e b oot h as c age of m i se ry ' , 252 ' i d eas are food ' , 82
' l i fe is
a
jou rney ' , 8 3 less is dow n ' ,
' more i s u p '
o ce a n
ii S
81
a h arp ' , 2 4 6 , 2 7 8
' p ai n t br u sh as
a p u m p ' , 60, 85,
274 , 2 7 5 , 2 7 7 , 3 3 :3
Met aphor and Cognition
448
' p ai n t ing a s p u m p i n g ' , 405
' w i l d fl owers as wate r ' , 4 2 , 24 6 , 247, 278, 3 1 0 a s c h a n g e o f re p resen t a t i o n , 7.5 , 401 a s p roj ect i o n , 2 4 9 as y m m et r y of, 1 7 , 1 9 , 254 c o m p a r a t i v e aspect of, 290
open-encledness of m e t ap h o r a n d , 3l l s i m i l a r i t i es bet ween sou rce an d t arget an d , 4 5 , 3 1 0 M e t a p h o r i ca l i n t e r p retat i o n i n C h a p l i n ' s Mod e m Tim es, 2 3 in co n t e m p o r ar y art s , 5 i n D av i d Lean ' s L a wre n ce o f A ra
e m o t i v e force of, 1 9
bia, 24
i n a r t i fi c i a l i nte l l i g e n c e , 3 5 7 i n co g n i t i o n ,
of C h r i s t ' s deat h a n d resu rrec
5
t i on , 22
i n c reat i ve p r o b l e m s o l v i n g , 56
M et a p h o r i c a l q u al i t y , s e e M e t ap h o r -
in le arn i n g a n d ed u c a t i o n , 5 i n n at u ral l a n g u age p r o c e ss i n g sys t e m s , 35 7
M et ap h o rs
asy m m e t ry of, see A s y m m e t r y of metaphors c l ass i fi cat i o n of, 1 c reate ass o c i a t i o n s between word s ,
46 i n contem p o rary art , 6 i n e x t e n d e d contex t s , 4 5 , 3 1 0
i n fi l m s ,
6
i n music, 6
i so l ated , 4 5 ,
st rong t h es i s of, 286 sub j e c t i v i ty of, J 8 see
254
M e t a p h o r i c a l schema ( L akoff ) , 8 3
i n s c i en c e , 5 i n d uces new s t r u c t ur e i n t h e t arg e t , 85 Lako ff ' s d e fi n i t i o n o f, 2 9 7 M ac C o r m ac ' s defi n i t i o n o f , 2 9 7 n at u ral l a n g u ag e p r oc ess i n g a p p r o a c h es t o , 3 6 5 o p e n - e n d ed n ess o f , 3 1 1 p r e d i c t i v e a n al ogy and , 3 1:3 reorgan i zes t h e t a rget , 85
t h eori es of,
i c a l a p t n ess
M e t a p h o r i cal r e l at i o n ,
310
l i n g u i s t i c , 1 3 , 2 4 , 25 , 6 7
T h eo r i es of m e t a p h o r
computat ional m o d e l s of, t heir n o ve l t y, 290
t u r n s i n t o a n o m a l y, 1 7
lose
t u rn s i n to my t h ,
n on - l i ng u i s t i c , 24 , 2.5
288
nsy m metri c , 25
t wo senses of, 297
Metaphoric conten t , deg ree
360
of,
1 3,
op t i o n al , 26
open-endedness of, 2 5 7
1 9 , 23
conven t i on a l e n d of, 2 0 , 2 2
pred i ct. i ve a n alogy, 56 s i m i l ar i ty- based , s e e Simi laritybased m e t ap hors
middle of,
s i m i l a.ri t.y-cre n.t i n g , see S i m i l a ri ty
M et a p hori c - co n t e n t con L i n u u J J J , 2 0 ,
3 1 , 34 23
n o ve l - m e t ap h o r i c a l end of, 20,
23 M e t a p h o r i ca l a p t n ess , 309-3 1 3
creat i ug m e t a .phors
s u b j e c t i v i t y of, 1 6 u n der ly i n g t h e
concept o f m ar-
S u bject In dex
449
ri age, 6 c o n c e p t of, 1 1 6 M i metic symbols, 1 1 4 co n s t r u c t i o n o f, 1 1 7 Model s , 34-3 5 O bj ec t - c o n c e p t s , 1 4 1 conven t i onal i n t erpret a t i o n s of, O bj ec t i ve c r i ter i a of r i g h t ness, J J 5 34, .54 folk and c u l t u ral ( H o l l a n d & Q u i n n ) , nature o f c reated referent ( Haus 1 56 m an ) , 76 pre- t heoret i c , 54 nat u re o f n at u ral s c i en ces , 1 1 2 for q u an t u m mechan i c s , 55 O bjects u n conve n t i o n al i nterpretat i o n s ac q u i re desc r i p t i o n s in cogn i t i ve model , 1 76 of, 35 M O D U L O ( corres p o n d e n c e between co u n terparts of sy m bo l s , 1 60 algebras ) , 224 , 2 2 7 , 2 3 6 i n S p i n n e r ' s e n v i ro n men t , 1 44 Mythology a s com p uter software, O n t o fu n ct i o n , 203 O n t o l ogy 49 Myths, metap h o r i c al i nterp retat i on does n o t e x i s t before concep t u of, 5 al i zat i o n , 1 4 4 e x p e rie n t i a l , 1 3 2 Natural n u mber system ( as a c o n of an e n v i r o n m e n t 1 60 cept network ) , 1 5 1 - 1 5 3 , 1 .55 , O n tology and s t r u c t u re 1 5 6 , 1 62 , 3 1 3 fi xed , ll .S Necessi ty, concept o f ( P i aget ) 1 22 m i n d - i n de p e n de n t , 7 , 9 3 , 1 06 , Negat i ve aftereffects of mot i o n , 96 1 1 1 Network models ( H esse ) , 1 32 objec t i ve , 1 24 New Tes t amen t , 2 6 of abst rad domai n s ( Lakoff ) , ,
,
N e w t o n i an rnech an i c s , I 06 , 2 7 5
N o n - E u c l i d e a n geomet ry, l 1 3 Non- l i n gu i s t i c
m etaphors.
see
M e t a-
phors, non- l i nguistic
N o n determ i n i s m .
see
Copy c a t , n o n
determ i n i s m i n
Novel proj ecti o n i n a m a,ch i ne v i s i o n system , 4 0 1 i n a speech u nders tan d i n g sys tem , 398 N ursery rhymes (M o t h e r
G oose's ) ,
399
fi n i tely genera,ted , perman e n ce,
S p i n ner's
senwr i m otor data
Sf'L , I :JS p re-ex i s t i n g , y;J, 1 24
p reco n cep t u al . 1 11 , 1 2 5 , 1 3 1 O p e ra.t ion ( P i aget ) , for m a l c h ante ter i s ti cs o f , 1 2 1 Opera t i o n al s t r u ct u res , emergence o f , 1 22 O perato r , 2011
constan t , 204 i denti ty, 204 spec i al i z at i o n of, 204
0 - s u balge b r a , 2 1 8 O b j ect
1 25 of
219
O pe rators co m p os i t i o n of,
204
Metaphor a n d Cogn i t ion
450
com p u t ab i l i ty o f, 2 1 7 i n d u ced , 236 of S p i n n e r ' s concept net w o r k s , 141
physi ca l l y real i z a b l e , 1 5 5 represent a c t i o n s of hypot het i cal agen t s , 1 4 6 roles of, 1 .52 O p t i cs , i n fl u e n c ed by t heory of aco u s t i cs , 55
Pai nt b r u s h as a p u m p , ' p a i n t b r u s h as
see a
Metaphor,
pu m p'
P a i n t i ng
as m as k i n g a s u r face , 64 as p u m p i n g , s e e M et ap h o r , ' pai n t i ng a s p u m p i ng ' as s m e a r i n g , 5 9 , 6 1 sen s o r i m o t o r d a. t a set of, 4 0 6 P a i n t i ngs, met a p h o r i cal i n t e r p re t at i o n s o f, 5 P a r ab l e of t h e sowe r , 29 Paradox grue, s e e G r u e pa r a d o x ( G ood Ill a n ) i n B lac k ' s i ntera.c t i o n t h eory, 66 , 73 i n i nteraction t h eo r i es o f m e t a p h o r ,
66 i n i nterac t i o n
view of
7 ) 9 3 , u .s ,
cogn i t i o n ,
1 1 6 , 1 2: 3 , ] 24 '
1 2 7 , 1 28 , 1 3 1 - 1 3 3 , 2 4 5
of creat i o n o f s i m i lari ty, 6 5 , 6 7 , 72, 7 5 , 7 9 , 8 1 , 8 9 , 90, 93 , 1 24 , 1 3 1 , 245, 24 6 , 280 of raven , 344 R ussel l ' s , 1 92 Para l l e l terraced scan ( Copycat ) , 390 Paramo r p h s ( We i tze n fe l d ) , 3 2 8 Pa rt- w hole p reco n cept , 1 2 5 P a rt i t i o n , 1 92 , 2 0 1 , 203
Percep t i on , goal oriented n at u r e of, 1 06 Perspec t i val t heory, s e e Theories of metaphor, perspec t i val t he ory Phenomenal worl d ( K a n t i an ) , 1 60 P h logi ston t h eory, 2 7 5 P honograph , i nven t i on of, 6 3 P hysi ological s t r u c t u res, source of u n i versal s , 1 1 0 P lato n i c concepts, i n Copycat, 386 P leroma ( � u n g ) , 1 58 Poly n o m i al operat i o n s, c l ass of, 2 1 6 , 232 Pos i t i ng s t r u c t u re , 85 Poss i bi l i ty, conce p t of ( P i aget ), 1 22 Power , of a c l a.ss , 1 94 P re - i m age, of a r e l a t i on, 1 96 P reco n ce p ts a s ' u n i versal s ', 1 26 b as i c logi c of, 1 25 genes i s of, 1 26 i n ternal logi c of, 1 25 P redi cat i ve metaphors, 28 P redict i ve anal ogy, 32-34 , 3 6 , 56, 257 com p u t at i o n a l a p p roaches t o , 365375
dark
side
o f,
334
defi n i t i o n of, 3 2 0
di rect
an alogy and, 5 8 fi rst-order general i z at i o n , 325 , 374
general - purpose h eur i s t i c , 3 7 3 in a l c hemy, 3 3 6 i n art i fi c i al i n tel l i gence, 358 in learn i n g, 3 7 3-375 in sports, 35 1 1 1 1 u n d e r s t a n d i n g t e x t - ed i tors , 335
45 1
Su bject In dex 1 33 , 1 68
i n duction and , 3 1 7
measu r i n g t i m e i n h o u r s and
logical p ro b l e m of j u s t i fi c a t i o n ,
m i n u t e s , 1 68
322
p l ay f u l a c t i v i t i es of ch i l d ren ,
m ak i n g t h e fam i l i ar s t r a n ge an d , 61
1 68
ret i n a l i n ve r s i o n of i m age, 1 6 7
metaphor a n d , 3 1 3 p r o b l e m - so l v i ng
h eu ri s t i c ,
33, 31 6,
gr o u p i n g p e rs p e c t i ve o n , 1 74
in
3 2 1 , 3 2 9 , 3 3 2-3 34 , 3 6 5
a
parse r , 394
p roj ect i ve m e t a p h o r an d , 320
i n c o m p u t a t i o n a l syste m s , :394
seco n d-order general i z a t i o n , 327
In m u l t i - l ayered cogn i t i ve sys-
s i m i l ar i ty- b a sed m e t a p hors an d ,
tem , 1 82 I n t h r ee- l ay ere d cog n i t i ve sys-
57
s u gges t i ve m e t a p h or an d , 2 7 0 ,
t e m , 1 82 n ov e l v s . con ve n t i o n al , 395
32 1
syntact i c m e t a p h or an d , 3 2 1
u n d erl i es i n d u ct i o n , 354 vs. as s i m i l a t i o n , 1 34
Pred i c t i ve d i sanalogy, 3 7 5 Preference seman t i cs ( W i l k s ) , 3 6 2
P roject i ve m e t a p hor
P resen t a t i o n al s y m b o l s , 1 1 4
asset t o cogn i l i o n , 2 7 7
P r i m ary s u bj ec t ( of a m e t a p h or ) ,
ex a m p l es o f , 2 7 1
reclai m s lost i n for m at i o n , 2 7 7
1 , 67 P r i m ary system ( of a m et a p h o r ) ,
P ro j ec t i ve m e t a p h o r s , 2 7 1 -2 7 7 i n h i story o f s c i e n ce , 2 7 5
254
Primitives , choices
P ro pe r s u b c l as s , J 9 1
o f , 84
P ri n ci p al subject ( of
a
metaphor ) ,
6 7 , 68
P ro p o r t i o n al a n alogies
com p u t a.t i o n a l mode l s o f, :35 i n H o fs t ad te r ' s m i c roworl d , 3 7 6 ,
Problem sol v i n g
creation o f s i m i l ar i t ies i n , 6 0 i n real-world s i t u a t i o n B , 5 9 , 3 :3 2 P roduct
:384
of geom e t r i c f i g u r e s , 3 0 , :32 , :3 6 , 6 .5 , 2 7 9 , 35 8 , 3 7 7 , 3 7 8
51
o f al gebras , 224
percep t u a l , 3 0 , 3 2 , 5 0 , 5 1
of c l asses , 1 94
symmet ry
P rojec t i o n , a,s
60, 1 64- 1. 68
31
crea.te s i m i l a r i t i es , 50
' to p - dow n ' grou p i n g , 3 9 2
a s rei nterpret i n g concept n e t
P r o t o t y p e e ffec t i n con c e p t n et w or k s ,
1 56
wor k s , 1 4 8 ch anges exper i en t i al o n t o l ogy
of,
verbal , 30
of
e n v i ro n m e n t , 1 3 3
examples of
in mathem a t i c al p roofs , 1 68 l i n e s of lat i t ude a n d l o n g i t u d e ,
P rototy p i c a l i ty, i n Wei n e r ' s m o d e l
of
m et ap h o r , 3 6 1
P to l emaic as tronomy, 275
Q - morph i s m ( H o l l and et
24 1 ,
320
al. ) , 1 66 ,
452
Me i aphor an d Cogn i t ion
Q u a n t i ty, a s t a rget d o m a i n , 82 Q u a n t u m m e c h a n i c s , 49, 6 0 , 1 0 6 p r e- t h e o r e t i c model fo r , 5 5 p r o d u c t of a n a n a l o g y , 50 R a d i a l c at e go r i e s ( Lakoff ) , 1 56 R ad i a l s t r u c t u re , i n c o n c e p t n e t wor k s , 1 5 6 R an do m n es s , of a s a m p l e o v e r s p a c e , :34 6 ove r t i m e , 3 4 7 R e al i t y constrai n s poss i b l e o n t olo g i e s , 1 33 c o n s t r u c t i o n of, 1 1 6
experient i a l , 8 1 e x p e r i e n t i al o n to l o gy of, 1 3 2 o b j e c t i ve, 7 6 , 8 1 , 1 25 o n t o l o g y a n d s t r u c t u r f' o f, 1 32 p r e - c o n c e p t u a l s t r u c t u re of, 8 9 s t r u c t u r e s the e n v i r o n m e n t , 1 4 4 t h ree leve l s of, ] .5 8 R eal m , 2 5 :3
source,
i m age
o f,
i n d u c es a
194
cha i n ,
1 98
i n d u ces g ro u p i ng s , 1 94 in verse of, 194 refl e x i ve , 20 1
sy m me t r i c , 2 0 1 t r ans i t i v e , 2 0 1 Re l at i o n s , co m p o s i t i o n o f , 1 94 Re l a t i v i s m , 89 Re l a t i v i t y , t heory of, 1 1 3 , 2 7 5 Re l i g i o u s symbols, metap horical n at ur e of, 5 Re p r e s en t a t i o n i n a c o g n i t i v e model , 2 3 6 of an object by a co n c e p t , 1 76 Re p re s e n t a t i o n a l l a n g u age s , 405
Rest r i ct i o n , of a cogn i t i ve model , 238
o f i m ag e , as ex am p l e o f p r o j e c t i o n , 1 6 7
Ret i n al i n ve r s i o n R evol u t i o n , R u s se l l ' s
s c i en t i fi c ( K u h n ) , 27.5 paradox , 1 9 2
S - s u b a l ge b r a , 2 1 8
254
fi n i t e l y ge nerated , 2 1 8
t arget , 253
S a l i e n ce
R ed es c r i p t i o n
i n We i n e r ' s m o d e l of m e t aphor ,
c reat es s i m i l a r i t i es . .5 4
i n proport ional a.n alogies,
3 .5 9
u n derl i es c reat i ve m e t a p hors a n d a n al o g i es ,
3.59
:36 1 of objec t s
i n C o pycat , :3 8 7
S a m p l i ng p ri nc i p l e
R e d u c l i o n i s t approa c h to rea l i ty, 106
i n j us t i fy i ng i n d u c t i o n , 344-349
R efi nement o f a cog n i t i v e m o d el ,
in j us t i fy i n g pred i c t i ve ana l ogy ,
323
238 R e fi n em e n t s of
cogn i t i ve models , 241
R e l at i o n
Scale model , of a s h i p , 29 1 S c h e m a i n d u c t i o n , 26:3 , :373, :3 75
codo m a i n o f, 1 94
S c h e m a.s ( I{ a n t ) , ] ] 2
d e fi n i t i o n o f , 1 9 4
S chemas ( P i aget ) ,
d i s c o n n ec t ed , 1 98 d o m a i n of, 1 94 e q u i valence, 2 0 1 fu l l , 1 9 7
1 2 0- 1 2 3 , 1 2 6 , 1 32 ,
151
Schematas ( G o o d m a n ) , 1 5 1 S c o p e of a p r o p o s i t i o n ( I< eynes ) , 326
S u bject In dex
453
Second ary s u b j ect ( of a metaphor ) ,
i n co g n i t i o n , 4 0 , 5 6 p red i c t i ve a n al ogy an d , 5 7
1 , 67
Secon d ary s y s t e m ( of a m e t a p h o r ) ,
S i m i l a r i t y - b a s e d , a c co u n t o f m e t a p h o r ,
254
4 0 , 5 5 , 95 , 333
S e m an t i c d i fferen t i al s c ales , 4 7
S i m i l ari ty-c reat i n g m e t a p h o rs , 1-3 ,
Seman t i c d i s t an ce, 2 8
Semant i c fiel d ,
8-9 , 3 5 , 3 7 , 4 0 , 4 9 , 5 6 , 2 7 1 ,
278-279 , 3.5 7
8 7 , 88
S e m an t i c net , 4 0 0 , 4 0 1 , 4 0 5
a s c h a n ge o f rep resen t a t i o n , 4 0 1
S e m a n t i c prox i m i ty, 74
e m p i r i c a l s t u d ies of, 4 5
Sensori s t i m u l i , 96
i n cogn i t i o n , 5 6 , 6 3
S e n s o r i m o to r d a t a set , J :32 , 1 59
i n fi l m s , 4 3
d e s c r i p t i o n l an gu a g e fo r , 406
i n p rob l e m s o l v i n g , 6 2
for S p e n d e r ' s
paradox o f, 6-5
for
Seascape, 248
S p i n ner , 1 38
p r o b le m o f, 6
i n a p arser , 3 9 3
S i m i l es , 2 6-28
o n t ology o f , 1 32
as sy m m e t r i c co m p a r i s o n s , 28
s t r u c t ur e of, 1 3 2 , 1 .5 9
c rea t i o n o f s i m i l a r i t y a n d , 2 7
S e n so r y v e c t o r
( S pi n n er ) ,
1 36
S e t s v s . c l asses , 1 92
s i m p l e analogies an d , 29 s t a t e m en t s o f l i teral s i m i l a r i ty
S h aw n ee , 8 0
and, 27
S h u s w a p , ' y e l low- w i t h - green ' cate
S i m p l e a n a l og i e s i n n o n - ve r b a l set t i n gs , 4 9
gory i n , 11 0
s i m i l e s an d , 29
Sign s v s . Sym bol s , 1 1 4
S i m p l e a n a l ogy, 29-3 0 , 3 6 , 5 0
S i m i l ar i t i es
b efore an d after t h e m e t a p h o r ,
S i n g l e- i n s t a 1 1 ce ge neral i z il.t i o n , 3 7 3 S l i p n ct
56
creat i o n of, s ee C reat i o n of s i m i -
S M E,
l ar i ty
( Copycat ) ,
see
gine
exper i e n t i a.l ,
Source
79
m i n d - i n d epen dent , 48
( of
m el il p h or ) ,
a
rega rded
pe rcep t i o n of. 2 0
s u p p l i ecl by
by
metap h o r s , 4 7
S i m i l ar i ty met r i c s , 8 0 ,
81
S i m i l arity- based m e t il.phors, 1-:3 , 8 ,
Son rce
as a
co n ce p t
s y s t e m , 68 , 73
tex t , 1 8 networ k , 253, 408,
409 Source domai n , 1
9 , 3 7 , 3 9 , 5 3 , 56-60 , 63 , 24 5 ,
' food ' ,
2 4 6 , 254 , 256-25 7 , 2 79-28 0 ,
'j o u r n ey ' , 83 , 85
3 5 7 , 363
3
' vert i c al i ty ' , 8 1
e p i p h ors an d , 77
Sou r c e real m , 254
in
S o u r c e sem a n t i c f i e l d , 89
art i fi c i al i n t e l l i g e n c e , 358
1. 5
a..ffected by co n t ex t , 1 5
o b j ect i ve , 11 8 , 79 ch an ged
3 8 6 , 4 08
S t r u ct u re- M a p p i ng E n
4 54
Met aphor an d Cogn i t ion
Sov i et U n i o n , 1 0 1 S p ec i al i z at i o n , of an operator, 2 0 4 S peech recogn i t i o n , 4 0 7 S p eech u n derstan d i ng syste m , 386 n ovel p rojec t i o n i n , 398 S p i n ne r , 1 3 5- 1 4 8 changes b i a s o f sen sory o rgan , 1 80
concept networks of, 1 4 1 effectory organ of, 1 3 6 rei n t e r p rets concept networks , 1 48 1 48
sensori motor d a t a. set for , 1 :3 8 sensory o rgan of, 1 3 5 t ransported to a n al i en worl d , 1 47
worl d of, 1 3 8 d e n se fog i n , 1 80 zonal s t r u c t u re of, 1 .58 S p l i t reference ( R i coeu r ) , 74 S t a r of D av i d , 4 , 5. 7 0- 7 3 , 8 1 , 4 0 6 , 407
a s sensor i m o t o r data. set , 4 0 6
( algebra. ) ,
206 , 2 0 9 , 2 1 4 -
2 1 6 , 2 19, 2 2 0 , 2 2 4 , 2 3 6 S t r o n g t h es i s of
89
of of of of of
a descr i p t i o n , 2 1 2 a symbol , 1 5 3 an e n v i ro n m en t , 1 6 0 external wor l d , 7 S p i n n e r ' s concept n e t wo rk s , 141
p re-ex i s t i ng a n d m i n d - i n dependen 1 28
rest r u ct u res conc<"pt networ k s ,
STR ING
creat i o n of, 1 2 7 i n an algeb ra, 2 0 9 o bj ec t i ve , of a content domai n ,
r
m et ap ho ,
2 6-293 ,
296 c h a l l en ges to,
299
t h ree version s of, 287
represen ted as a x i o m s , 84 S t r u c t u re a n d ontology, s e e O n t o l ogy and s t r u c t u re S t r u c t u re ( P i aget ) , for m a l c harac teris t i cs of, 1 2 1 S t r u c t u re M a p p i n g E n g i n e , 3 6 7-3 7 3 S t r u c t u re- m a p p i n g t heory { G e n t n er ) , 367
S t r u c t u re- p rese r v i n g mapping, 85 Su balgebra, 2 1 7 fi n i tely generated , 2 1 8 S u b c l as s , 1 9 1 a concept network , 1 5:3 S u b i d i a r y s u bj ect (of a metaph or ) , 6 7 , 68 S uggest i ve metaphor
S u bn e t work of
exam p l e of, 267 S u gges t i ve metap hors , 266-2 7 0
32 1
S t n1 c t u r a .l cor r e l ation, 8 2 S t r u ct u ral d e s c ri p t i o n , 209 as d i rected a c y cl i c gra.p h , 2 1 1 com p o n e n t s of, 2 1 2 defi n i t i o n of, 2 1 2
Symbolic
S t r u c t u ral descri p t i o n s
S y m b ol i c systems , concept networks
c l ass of, 2 1 1 eval u a t i o n fu n c t i on on , 2 1 2
S t r u c t u re
p red i c t i vc ari a l ogy an d , 2 7 0 , S u rj e c t i ve fu n c t i o n , 203 S y m b ol i c fo r m s , t heory of
( Cassirer) ,
1 13
system ( C ass i re r ) ,
as , 1 32
S y m bo l i s m i n fi l m s , 2 2
11 4
455
Su bject In dex
ad van t a g es
Ta rget concept network , 254 Target content dom a i n ( l\ i t t ay ) , 88 Targe t dom a i n , l ' l i fe ' , 83, 85 ' pai n t i n g ' , 85 ' q u an t i t y ' , 8 2 Tar ge t r eal m , 25 3 eas i e r cog n i t i ve access t o , 26 1 Target sens o r i m o t or data. set , 4 0 7 , 4 08 changed r e p r e s entation of, 409 Ten o r (of a m e t a p h o r ) , 1 , 254 T h e o r i e s of m e t a p h o r comparison t h eo ry, 2-4 d i s c red i ted , 39 e x p l a n ati on of c reat i o n of si m i l a. r i ty, 65 fa.i I u r e of, 65 dead m e t a p h o r t h eory, 294 do m a. i ns-i n t e r a.ct i o n t h eory, 4 La.koffia.n a p p ro ach , 66 l i teral m e a n i n g t h eo r y , 294 , 299 pers p ect i vn. l t h eory, 4, 6 7 , 86 t ra.n s fo r r n a t i o n t h eory, 4 Th eory of evol u t i o n , 5.5 , 60
exam p l e of, 2 5 8
The r m odynam i c s , theory of
of rel i g i o n , 22 Symbols c o m p o n e n t s o f , 153
creat ion of, 1 1 :3 descr i p t i o n s of, 1 .5 3 non- convent i onal i n ter p re t at i o n s o f , 21 of S p i n ner's concept networks ,
141 s t r u c t ur e d set of, 2 1 s t r u c t ur es of, 1 53 types of, 1 1 4 v s . s i gn s , 1 1 4 S y mm e t r i c rel at i o n , 2 0 1 S y mmetry i n i nterac t i o n t heory of m e t aphor B lack , 4 , 7 0 cri t i que by La.koff & Tu rn e r ,
81 H a u s m a n , 5 , 76 i n prop o r t i o n al an a l ogies, :3 0 ,
31 S y n t a ct i c m et a. p h o r , 2 .5 7-2 6 7 , 2 8 0 ,
3 1 2 , 336, 392 , 4 0 9 of, 2 6 1
limits of, 265
a n alogy w i t h flow of fl u i d s , 57 T h i ngs in t h e m sel ves , world of ( 1\ an
p red i ct i ve a n a l ogy a n d , 32 0
Systema.t i c i ty
( Ge n t n e r ) ,
�1 3 1 , 3 3 2 ,
3 3 6 , 3 3 7 , 34 1 , 3 6 7 , 3 7 1 , 3 7 5
Tabletop ( French
& Hofs t adter ) ,
39 1
Ta rget ( of a metaphor ) , 1 4 c ha ng e d
by
contex t , 1 5
determi ned by co n t e x t , 1 8 exp l i c i t m e n ti o n of, 1 5
i n d e p e n d e nt l y s t r u c t u red , 82
o r h i nt e d , 1 6 as a system , 73
not men t i oned not r e g a r ded
referent of, 90 regarded as
a.
system , 68, 7 3
t i an ) , 11 2 , 1 5 8 , 2 7 7 , 2 8 8 , 289 co g n i t i ve access to , !. 5 9 dctc r m i ncs s t r u c t u r e of e n v i ro n ment , 1 60 deter m i nes s t r u c t u re of sen so
r i motor data set, 1 59 r i c h l y c on n e c l e d , 276 Top i c ( o f a. m e t a p h o r ) , 1 , 6 7 , 88 Top i c- less m et a p h o r s , 28 Tran s fo r m at i o n t h e o r y ,
see
T h eo-
r i es of m e t a p h o r , t ra.nsfor-
456
Met a.phor a n d Cogn i t ion m at i on t h eory
h a l l u c i n at i o n s
Tra n s fo r m a t i o n s counterparts of g r ou n d e d
in
operators , 1 6 0
re a l i ty , 1 44
i n S p i n n er ' s e n v i ro n m en t , 1 4 4 Tra n s i t i v e re l a t i o n , 2 0 1
o f ( To u r a n g ea u & S t e rnb er g ) 310
( Co py c at ) , 3 8 7 Wor l d ( G oodman ) , 1 1 5 Wor k s pace
U n co n v en t i o n al i n te r p ret a t i o n , 1 5-
1 9 , 2 5 , 2 7 , 2 9 , 36
of.
1
ex-
p e r i e n ce , 24 9 a s r e p res e n t i n g i n tern a l l y , 249 metaphorical d e s c r i p t i o n , 25 1 n o n - metaphor i c a l descri p t i o n , 24 9 v s . correc t n ess , 3 0 5 n i o n , of c l a s s es , 1 9 1 U n i q ueness co n d i t i on ( H a u s m an ) , 4 , 75 U n i versal A l gebra. 9,
1 90
U n i versal k n o w l e d g e s t r u c t u re , 1 3 1 U n i ve r sal s , 94 , 1 06 i n color
categories , J 0 7
U z b e k i s t an , L O J
( o f a metap h or ) , 1 , 88, 6 7 , 254 , 3 1 1 Vert ical i ty, as source doma i n , V i s u a l cortex , 1 0 8 V i s ual i ll u si o n s , 1 00 , 1 0 1 Veh i c l e
effe c t o f c u l t u ral b n.c k g rou n d ,
1 04 V i s u a l s y s tem
as a l ayered co g n i t i ve s y s t e m , 1 85
You n g- H e l m h o l t z t heory ( of color
vision ) , 1 0 7
6
U n d e r s t an d i n g as i m agi n i n g a p e r c e p t u a l
o f m a caq ue m o n key, 1 08 V i v i d ness t h es i s ( O rtony ) , 25 1 Voca b u l ary, 84 W i t h i n - d o m a i n s i m i l a r i ty , c r i t e r i o n
Tra.nssu b s t an t i at i on doct r i n e , 5 Tree series, by . 1 o n d r i a n , 6 :3 T r u t h v s . c o rr e c t n ess , 3 0 3 Ty p e , of a n operator, 1 6 1
s u b j e ct i v i t y
a n d pa.ra.doxes i n ,
339
ZO R B A - l
( I< I i n g ) , 3 6 5 , 366
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