The psychology of deductive reasoning 9781315819631, 1315819635, 9781317820451, 1317820452, 0710009232

Table of contents :
Content: pt. 1. Elementary reasoning tasks --
pt. 2. Syllogistic reasoning --
pt. 3. Propositional reasoning --
pt. 4. Discussion.

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PSYCHOLOGY

REVIVALS

The Psychology of Deductive Reasoning Jonathan St. B.T. Evans

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Psychology Revivals

The Psychology o f D eductive Reasoning

O rig in a lly p u b lis h e d in 1 9 8 2 , th is was an extensive an d u p -to -d ate review o f research in to th e psychology o f d e d u ctiv e reasoning, Jo n a th a n Evans p resents an altern ativ e theoretical fram ew ork to th e ratio n alist approach w hich had d o m in a te d m u ch o f th e p u b lish e d w ork in th is field a t th e tim e. T h e review falls in to th ree sections. T h e first is concerned w ith ele­ m en ta ry reasoning tasks, in w h ic h response latency is th e p rim e m ea­ sure o f in terest. T h e second a n d th ird sections are concerned w ith syllogistic an d pro p o sitio n al reasoning respectively, in w hich in terest has focused on th e e xplanation o f freq u en tly observed logical errors. In an e x te n d ed discussion it is a rg u ed th a t reasoning processes are c o n te n t specific, an d give little in d icatio n o f th e o peration o f any u n d e rly in g system o f logical com petence. Finally, a dual process th eo ry o f reason­ ing, w ith broad im p lica tio n s a n d conn ectio n s w ith o th e r fields o f psy­ chology, is elaborated a n d assessed in th e lig h t o f recen t evidence.

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T he Psychology o f D eductive Reasoning

J o n a th a n St. B .T . E v an s

V p Psychology Press I Taylor& Francis Croup LONDON AND NEW YORK

First p u b lish ed in 1982 by R o u d e d g e & K eg an Paul Lrd T h is e d itio n first p u b lish ed in 2 0 1 4 by Psychology Press 2 7 C hurch R oad, H ove. B N 3 2FA an d by Psychology Press 711 T h ird A venue, N e w Y ork, N Y 10017 Psychology Press is an imprint o f the Taylor & Francis Group, an informa business © Jo n a th a n St. B .T. Evans, 1982 A ll rig h ts reserved. N o p a rt o f th is book m ay be re p rin ted or reproduced or u tilise d in any form or by any electronic, m echanical, or o th e r m eans, now k now n or hereafter invented, in clu d in g photo co p y in g an d recording, or in any inform ation storage o r retrieval system , w ith o u t perm ission in w ritin g from th e publishers. P u b l i s h e r ’s N o te T he p u b lish er has g o n e to g re a t len g th s to ensure the q u a lity o f th is re p rin t bu r p o in ts o u t th a t som e im perfections in th e original copies m ay be apparent. D is c la im e r T he p u b lish er has m ade every effort to trace co p y rig h t holders and welcom es correspondence from those they have been un ab le to contact. A L ibrary of C ongress record exists u n d e r ISB N : 0 7 1 0 0 0 9 2 3 2 ISBN : 9 7 8 -1 -8 4 8 7 2 -3 1 5 -3 (hbk) ISBN : 9 7 8 -1 -3 1 5 -8 1 9 6 3 -1 (ebk)

The psychology of deductive reasoning

Jonathan St. B. T. Evans

Routledge & Kegan Paul London, Boston and Henley

First published in 1982 by Roulledge & Kegan Paul Ltd 39 Store Street, London WC1E 7DD, 9 Park Street, Boston, Mass. 02108, USA, and Broadway House, Newtown Road, Henley-on-Thames, Oxon RG9 1BN Set in Baskerville by Input Typesetting Ltd, London and printed in Great Britain by The Thetford Press Ltd Thetford, Norfolk © Jonathan St. B. T. Evans, 1982 No part o f this book may be reproduced in any form without permission from the publisher, except for the quotation o f brief passages in criticism Library o f Congress Cataloging in Publication Data Evans, Jonathan St. B. T., 1948The psychology o f deductive reasoning. (International library o f psychology) Includes bibliographical references. 1. Thought and thinking. 2. Logic. 3. Reasoning (Psychology) I. Title. II. Series. BF455.E931982 153.4'33 81-13991 ISBN 0-7100-0923-2

AACR2

Contents

A ck n o w led g m en ts 1 In tro d u c tio n

Part I: Elementary reasoning tasks 2 T h e o re tic a l b a c k g ro u n d 3 S entence verificatio n 4 T ra n s itiv e inference

5 6

7 8 9 10

vii 1

9 11 24 49

Part II: Syllogistic reasoning

71

A n in tro d u c tio n to syllogistic re aso n in g T h e e x p e rim e n ta l psychology o f syllogism s

73 82

Part III: Propositional reasoning

113

A n in tro d u c tio n to p ro p o sitio n a l re aso n in g C o n d itio n a l re aso n in g T h e VVason selection task D isju n ctiv e re aso n in g

115 128 157 189

Part IV: Discussion 11 O n e x p la in in g the re su lts o f reaso n in g e x p erim e n ts 12 D u a l processes a n d beyond R eferences N am e index S ubject index

209 211 234 258 273 276

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Acknowledgm ents

It is not possible to identify everyone w ho h a s influenced m y th in k ­ ing a b o u t th e psychology o f reaso n in g , a n d th u s c o n trib u te d in d i­ rectly to the w ritin g o f this book. T h e re is no d o u b t, how ever, th a t w ith o u t P e te r W aso n , w ho stim u la te d a n d n u rtu re d m y early in te r­ est in the field, the book w ould nev er have been w ritte n . M y ideas owe m u ch to the m an y discussions I have had w ith him over the years, a n d also to th e colleagues a n d re sea rc h s tu d e n ts w ho have sh a re d m y in te re s t in re aso n in g re sea rc h a t P ly m o u th P olytechnic. I w ould especially w ish to acknow ledge th e c o n trib u tio n s o f Paul P o llard , Steve N e w ste ad , K e n M a n k telo w a n d Phil Brooks.

F ew p e rso n s c a re to stu d y logic, b e c a u s e e v e ry o n e co n ceiv es h im s e lf to be p ro fic ie n t e n o u g h in th e a r t o f re a s o n in g a lre a d y . (C h a rle s S a n d e rs P eirce) M e n m a y a rg u e b a d ly b u t th ey re a so n w ell, th a t is, th e ir p ro fessed g ro u n d s a re n o su ffic ie n t m e a s u re o f th e ir re al ones. (C a rd in a l N e w m a n ) I ’d be a d o n k e y , a m o n k e y o r a b e a r, o r a n y th in g b u t th a t v a in a n im a l w h o is so p r o u d o f b e in g ra tio n a l. (J o h n W ilm o t, E a rl o f R o c h e s te r)

Introduction

In one sense th is book is only a b o u t d e d u ctiv e reaso n in g . In a n o th e r sense it is a b o u t lan g u a g e c o m p re h en sio n , m en ta l im ag ery , lea rn in g processes, m em o ry o rg a n isa tio n a n d the n a tu re o f h u m a n th o u g h t. T h e first sense is d efined by th e paradigms em ployed; the second by n a tu re o f th e psychological processes w hich the p a ra d ig m s evoke. W e will s ta rt w ith a b rie f c o n sid e ra tio n o f the n o tio n o f d e d u ctiv e re aso n in g as a p h ilo so p h ic a l c o n ce p t, a n d th en p roceed to p sy c h o ­ logical issues. O n e ro u g h d e finition o f d e d u ctiv e th o u g h t is th a t it leads from th e g e n era l to th e p a rtic u la r, e.g. All sw ans a re w hite, T h is b ir d is a s w a n

T h ere fo re, th is b ird is w hite. A n inductive inference, o n th e o th e r h a n d , leads from the p a rtic u la r to the g eneral: All the sw ans I have ever seen a re w hite, T h e re fo re all sw ans a re w hite. T h is inference is n o t v alid, n o r is an y o th e r in d u ctiv e inference. An a rg u m e n t is v alid if a ssu m p tio n s w hich are tru e c a n n o t lead to conclusions w hich are false. H o w ev e r m an y w hite sw ans I have seen, th ere m ay be som e b lack ones a ro u n d . T h e v a lid ity o f a logical a rg u m e n t is n o t affected by w h e th e r its prem ises a n d c onclusions a re, in fact, tru e o r false. T h e follow ing a rg u m e n t is v alid , even th o u g h its conclusion is obviously false: 1

2

Introduction All c ats a re fish. All fish hav e gills, T h erefo re, all c ats have gills.

T h is v alid a rg u m e n t p e rm its a false conclusion because one o f its a ssu m p tio n s is false. In v a lid a rg u m e n ts m ay also lea d to tru e conclusions: I f 2 + 2 = 4 th en dogs chase cats, D ogs chase cats, T h erefo re, 2 + 2 = 4. D ed u ctiv e reaso n in g is tau to lo g ical. I t a d d s no new know ledge, b u t sta te s necessary c o n seq u en ces o f th a t w hich is a lre a d y a ssu m e d . H ow ever, logical system s a d o p t c e rta in p rin cip les as a x io m a tic, such as the law o f n o n -c o n tra d ic tio n . A c o n tra d ic tio n is the sim u l­ tan eo u s a sse rtio n th a t som e p ro p o sitio n p a n d its n e g atio n not p are both tru e. T h e a v o id a n ce o f su c h c o n tra d ic tio n s is fu n d a m e n ta l to m ost system s o f logic. A logical system n o rm ally has a set o f p rin cip les o r rules o f inference w hich provide tec h n iq u e s for m aking v alid d e d u c tio n s o f c o n clu ­ sions from a ssu m p tio n s o r prem ises. M a th e m a tic s can be re g ard e d as a se t o f logical system s, in w hich sym bols a re m a n ip u la te d . F o r exam ple, the solu tio n o f sim u lta n e o u s e q u a tio n s s ta rts w ith the e q u atio n s (prem ises) a n d , by a p p lic a tio n o f rules, d e d u ce s the necessary n u m erica l v alues o f the a lg e b ra ic v a ria b le s as the co n ­ clusion. A good e x am p le o f a set o f logical a rg u m e n ts is E u c lid ’s geom etry, in w hich a set o f theorems (conclusions) a re d e d u c e d from a set o f axioms (prem ises). W e a re not c o n ce rn ed in this book w ith m a th e m a tic a l logic, b u t ra th e r w ith th e d e d u c tio n o f c onclusions sta te d as v e rb al p ro p o si­ tions. A n u m b e r o f p h ilo so p h ers, from A risto tle o n w a rd s, have been concerned w ith dev isin g system s o f logic to achieve this. A ssu m in g th a t it is possible to an aly se th e logical stru c tu re o f n a tu ra l lan g u a g e a rg u m e n ts, we m ig h t ask w hy it is necessary to d o so. O n e a re a in w hich logical a rg u m e n t seem s to be essential is in the c o n stru ctio n a n d testin g o f scientific theories. L ogic facilitates this process in two w ays. F irstly , it p ro v id es a check on the in te rn a l consistency o f a theory; it sh o u ld n o t be possible to d e d u c e a c o n tra d ic tio n from the

Introduction

3

a ssu m p tio n s o f th e th eo ry . Secondly, d e d u ctiv e logic is involved in testin g e m p irica l p re d ic tio n s o f scientific theories. Philo so p h ers o f science tra d itio n a lly view ed science as a process o f m aking inductive generalisations from e x p erim e n tal o b se rv atio n s. H ow ever, as o b serv ed e arlie r, such in d u ctiv e inferences c an nev er be v alid, so is it no t u n sa tisfac to ry for science to be based on an invalid ty p e o f logic? T h e m o d ern p h ilo so p h e r K a rl P o p p e r (e.g. 1959) h as resolved this d ile m m a by a sse rtin g th a t th e p u rp o se o f science is n o t th e verificatio n b u t th e falsification o f theories. F a lsi­ fication can be ach iev ed by d e d u ctiv e logic. I can nev er prove the s ta te m e n t ‘All sw ans a re w h ite ’ to be tru e , b u t I only need to observe one b lack sw an to prove th a t it is false. T h e logical n a tu re o f scientific th eo ry testin g is as follows: 1 2 3 4

S tate theory. D educe logically necessary a n d e m p irica lly testa b le pred ictio n s. T e st p re d ic tio n s by e x p e rim e n t o r o b se rv atio n . R e -ev a lu a te theory.

I f a th e o ry ’s p re d ic tio n s fail, i.e. a re not b o rn e o u t by em p irical o b se rv atio n , th en we h a v e a c o n tra d ic tio n betw een p re d ic tio n an d observ atio n . A ssu m in g th e e x p e rim e n t w as p ro p e rly c o n d u cted , this m eans th a t a t lea st one a ssu m p tio n o f the o rig in al theory m ust have been in co rre ct. C o n se q u e n tly , th e th eo ry m u st be e ith e r revised o r a b a n d o n e d . I f the p re d ic tio n is con firm ed , th is does n o t necessarily m ean th a t th e theory is correct. P o p p e r a rg u es th a t a th eo ry m u st be open to e m p irica l falsification in o rd e r to be called a scientific theory, a n d th a t a good th eo ry will m ake risky p re d ic tio n s, i.e. p re d ic t th in g s th a t w ould n o t be likely a priori. S cience, as P o p p e r sees it, consists o f a lte rn a tin g co n je ctu re s an d re fu ta tio n s. B ad th eo ries a re w eeded o u t, a n d good ones su rv iv e by a kind o f n a tu ra l selection. W e m ay a g ree w ith P o p p er, th en , th a t d e d u ctiv e logic is fu n d a m e n ta l in science. W e m u st be ab le to deduce conclusions a n d to e lim in a te c o n tra d ic tio n s. Is d e d u ctiv e logic a necessary a n d n a tu r a l p a rt o f h u m a n th o u g h t, how ever? T h e answ er d e p e n d s u p o n w h e th e r o r n o t one a d o p ts a rationalist view o f m an. In th e ra tio n a list a p p ro a c h (e.g. K elly, 1955) m a n is seen as a kind o f sc ien tist in his ev ery d ay life. A ccording to this m odel, people are c o n tin u ally involved in c o n stru c tin g theories, d eriv in g p re d ic ­

4

Introduction

tions, collecting ev idence a n d th e like in all asp e cts o f life, in clu d in g , for exam ple, th e d e v elo p m en t o f in te rp e rs o n a l re la tio n sh ip s. A ra tio n al m an w ould n eed , a n d be exp ected to possess, som e system o f d e d u ctiv e logic. T h e behaviourist view (e.g. S k in n er, 1972), on the o th e r h a n d , sees m a n ’s b e h a v io u r as u n d e r the c ontrol o f his e n ­ v iro n m e n t, a n d d e te rm in e d by his p e rso n al histo ry o f rein fo rcem en t. T h is a p p ro a c h does n o t re q u ire the a ssu m p tio n o f an y in te rn alise d logical system . B e h av io u r will a cc o rd w ith logical p rin cip les if a n d only if th e a p p ro p ria te re in fo rc em e n t contin g en cies hav e been applied. T h e re a re, o f course, m an y in te rm e d ia te positions, b u t it will be useful to keep sig h t o f these ex trem es. R a tio n a lism , in p a rtic u la r, is m anifest in m an y o f th e a p p ro a c h e s to re aso n in g re sea rc h th a t will be review ed. T h is view p o in t h a s im p lica tio n s beyond th e a ssu m p ­ tion o f logical com p eten ce. F o r e x am p le, it m ay lead to th e a s­ su m p tio n th a t th o u g h t processes a re a v ailab le to in tro sp ec tio n , a n idea th a t will be c ritically ex am in ed in the la te r p a rt o f this book. I t is even su p p o sed by som e th a t a system o f logical th o u g h t is in n ately d e te rm in e d . R ecen t books o n th e psychology o f reaso n in g have h a d a d istin c t b ias to w a rd s the ra tio n a list a p p ro a c h (F alm agne, 1975; R evlin a n d M a y e r, 1978). In c o n tra st, this book will em phasise n o n -ra tio n a l asp e cts o f h u m a n reaso n in g , in th e con tex t o f a review o f the re ce n t lite ra tu re in the field. All the e x p e rim e n ta l re se a rc h to be review ed c an be seen, in one sense, as a ssessing p e o p le ’s c o m p e ten c e to solve logical tasks. P a rt I o f the book is co n ce rn ed w ith relatively sim ple tasks w here e rro r ra te s a re g en erally low. In th e m o re com plex tasks in volving syllo­ gistic re aso n in g (P a rt I I ) , a n d p ro p o sitio n a l re aso n in g (P a rt I I I ) , how ever, logical e rro rs a b o u n d in all stu d ies. T h is m ig h t, in itself, lead one to a b a n d o n ra tio n alism ; b u t ra tio n a lists a re n o t so easily d e te rred . R a tio n a lity is seen as su b jectiv e to the in d iv id u a l. In th e field o f d ecision-m aking, for e x am p le, ra tio n a l m a n is su p p o sed to choose in su c h a w ay as to m ax im ise p e rso n al g a in (see Lee, 1971). O b ­ jectiv ely , m an y decisio n s a p p e a r ‘ir ra tio n a l’, b u t can be ex p la in ed as ra tio n a l by a ssu m in g su b jectiv e d isto rtio n s in th e a ssu m p tio n s w hich the d e cisio n -m ak e r holds. Som e d iscussion o f d ecision re­ search a n d its a p p lic a b ility in th e e x p la n a tio n o f re aso n in g d a ta is given in C h a p te r 11. In reaso n in g , as in d e cisio n -m ak in g , ‘ra tio n a l’ e x p la n atio n s c an be offered for a p p a re n tly irra tio n a l, i.e. illogical,

Introduction

5

p erfo rm an ce. H e n le (1962) pro p o sed th a t su b je cts in te rp re t the prem ises o f re aso n in g a rg u m e n ts in a p e rso n al w ay. T h e y m ay a lte r, a d d o r d ro p p rem ises. She c o n te n d s, how ever, th a t su b je c ts’ co n ­ clusions follow logically from th e ir re in te rp re te d version o f the p ro b ­ lem . T h is highly influ en tial p a p e r is discu ssed in d e ta il in C h a p te r 5, an d th e m erits o f ‘H e n le ism ’ a re su b seq u e n tly ex am in ed w ith reference to b o th syllogistic a n d p ro p o sitio n a l reaso n in g . In this book, it will n o t be a ssu m e d , a priori, th a t ‘re a so n in g ’ is necessarily g oing on in re a so n in g e x p erim e n ts. T h is brin g s us back to the p o in t o f th e o p e n in g p a ra g ra p h o f th is c h a p te r. T h e book review s resea rc h w hich h a s involved d e d u ctiv e re aso n in g p a r a ­ digm s. O u r co n cern is w ith th e psychological e x p la n a tio n o f p e r­ form ance o n such tasks, a n d th e w id er im p lica tio n s th a t follow. O n e d isa d v a n ta g e o f th e psychology o f re aso n in g is th e re la tiv e isolation o f the field from o th e r w ork in cognitive psychology. A fu rth e r aim o f the p re sen t book is to re la te re aso n in g re se a rc h to g e n era l issues in the stu d y o f cognition. A t this p o in t, it w ould be helpful to define the c rite ria by w hich w ork h as b een in clu d e d in th e review th a t form s th e m ajo r p a rt o f this book. A d e d u ctiv e re aso n in g task involves m ak in g a n inference from in fo rm a tio n w h ich is given. I f th e task re q u ire s access to m em ­ ory o f th in g s w h ich a re n o t p re se n te d , th en it is n o t sim ply a reaso n in g task. T h is m ea n s, for e x am p le, th a t p ro b lem s w hich d ra w on sem an tic m em ory for th e ir so lu tio n a re in ad m issib le. F o r sim ila r reasons, th e in te re stin g a re a o f p ra g m a tic inference (see, for e x a m ­ ple, H a rris a n d M o n a c o , 1978) is n o t in clu d e d . M a n y o f th e com plex re aso n in g tasks discu ssed in P a rts I I a n d I I I em ploy a b s tra c t m a ­ terials su c h as le tte rs a n d n u m b e rs, a lth o u g h th e use o f th e m a tic c o n te n t in logically e q u iv a le n t task s is also co n sid ered in som e detail. E ven in the la tte r case, how ever, in stru c tio n s to th ese tasks will alw ays in d ic a te th a t su b je cts sh o u ld e v a lu a te the valid ity o f a rg u m e n ts on the basis o f w h a t is p re sen te d . T h e lim ita tio n is, o f course, o n e o f p a ra d ig m s n o t processes. S ubjects m ay well be influenced by tra n s fe r o f lea rn in g from o th e r situ atio n s, a n d a n u m b e r o f the e x p la n a tio n s to be co n sid ered a re along these lines. B oth ra tio n a lists a n d n o n -ra tio n a lists a c c o u n t for reasoning e rro rs in term s o f som e lea rn ed ten d en cies, re la tin g to the in te rp re ta tio n o f sen ten ces, o r o th e r factors. T h e n o n -ra tio n a list, how ever, h a s b o th m ore to e x p lain (rig h t as well as w ro n g answ ers)

6

Introduction

a n d m o re d ev ices w ith w h ic h to fo rm u la te e x p la n a tio n s (e.g. re ­ sponse b iases). T h e task s u se d d o , o f c o u rse, re q u ire so m e lin g u istic k n o w led g e for th e ir so lu tio n . F o r e x a m p le , n e g a tio n h a s th e logical p r o p e rty o f re v ersin g t r u th v a lu e : if p is tru e th e n not p is false, a n d vice v e rsa. S tu d ies o f se n te n c e v e rific a tio n (C h a p te r 3) re v ea l th a t n e g a tio n serves th is fu n c tio n in la n g u a g e a s w ell, b u t lin g u istic n e g a tio n is m ore c o m p lic a te d . O t h e r re a so n in g ta sk s in v o lv e se n te n c e s su c h a s A ll A are B , I f p then q a n d Either p or q. O b v io u sly , su b je c ts c a n o nly a tte m p t to solve su c h ta sk s if th e y u n d e rs ta n d th e m e a n in g o f c o n n ec tiv e s su c h a s ‘I f . . . th e n . . A g a in , w e sh a ll see th a t th e lin g u istic in te rp r e ta tio n o f su c h c o n n e c tiv e s is a good d e a l m o re c o m p lic a te d th a n th e c o rre s p o n d in g re la tio n s in s ta n d a r d tex tb o o k s o f logic. T h e a im s o f th e p re s e n t book a re tw ofold. T h e first a im is to p ro v id e a c o m p re h e n s iv e rev iew o f re se a rc h in v o lv in g d e d u c tiv e re a so n in g task s. T h e e x p a n s io n o f th e field in re c e n t y e a rs n e ce ssi­ ta te s th is a r d u o u s exercise. I t is a ssu m e d th a t th e re a d e r is fa m ilia r w ith b a sic w o rk in e x p e rim e n ta l a n d c o g n itiv e p sy c h o lo g y , b u t th e book is o th e rw is e se lf-c o n ta in e d . I n P a r t I I , a c h a p te r is d e v o te d to d isc u ssio n o f b a sic issu es in th e stu d y o f la n g u a g e a n d im a g e ry , w h ich a re n e c e ssa ry for u n d e rs ta n d in g o f th e w ork rev iew ed in C h a p te rs 3 a n d 4. P a r ts I I a n d I I I e a c h c o n ta in a n in tro d u c to ry c h a p te r w h ic h e x p la in s th e b a sic s o f th e lo g ical sy ste m s used in th e re a so n in g task s w ith w h ic h they a re c o n c e rn e d . T h e se c o n d a im is to p ro v id e a v ia b le th e o re tic a l a lte rn a tiv e to r a tio n a lis t th e o rie s o f h u m a n re a so n in g , a n d to re la te th e s tu d y o f logical re a s o n in g p e rfo rm a n c e to the m a in field o f c o g n itiv e p sy ­ chology. T h e D isc u ssio n is c o n c e rn e d w ith th is la tte r o b jec tiv e . In C h a p te r 11 it will be a rg u e d th a t a m a jo r c h a n g e o f a p p ro a c h is n eed ed to th e p sy c h o lo g y o f re a so n in g . F ro m c o n s id e ra tio n o f th e m a te ria l review ed in P a r ts I to I I I o f th is book, it a p p e a r s th a t th e re is little e v id e n c e for th e in flu e n ce o f a g e n e ra l sy ste m o f logical c o m p e te n c e , a n d th a t th e th o u g h t p ro c esses in v o lv ed a re h ig h ly content dependent. It is a lso a rg u e d th a t re a so n in g e x p e rim e n ts a re best v iew ed a s sp e c ia lise d p ro b le m -so lv in g o r d e c isio n -m a k in g task s, a n d e x p la n a tio n s fo r v a rio u s p h e n o m e n a a re offered in line w ith these c o n sid e ra tio n s. I n C h a p te r 12, a tte n tio n is fo cu sed o n th e d u a l p rocess th e o ry o f re a so n in g (VVason a n d E v a n s , 1975) a n d its s u b ­ se q u e n t d e v e lo p m e n t. I n th is re sp e c t, re a so n in g p h e n o m e n a a re

Introduction

1

re la te d to d iv erse w ork in social psychology, m em o ry th eo ry a n d the d ifferential fu n c tio n o f th e tw o h em isp h e res o f th e b ra in . W h ilst som e o f these la te r suggestions m ay be ra th e r sp ecu lativ e, I w ould m a in ta in th a t it is for its c o n trib u tio n to cognitive psychology th a t psychology o f re aso n in g - a n d th is book - m u st be ju d g e d . F inally, a p o in t a b o u t style is in o rd e r. L ike all w riters o f the E nglish lan g u a g e, I w as co n fro n ted w ith the p ro b lem th a t th ere a re no generic p ro n o u n s w hich a re n e u tra l w ith re sp ec t to sex. F or stylistic re aso n s I hav e re ta in e d th e o ld -fashioned ‘h e ’, ‘h is’, etc., in preference to su c h devices as ‘h e /s h e ’, ‘(s)h e ’, etc. T h is in no w ay im plies th a t th e peo p le referred to (e.g. e x p erim e n tal su b jects) a re m ore likely to be m ale th a n fem ale.

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Part I

Elementary reasoning tasks

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Theoretical background

In P a rt I the focus is on relatively sim ple tasks in volving sentence verification (C h a p te r 3) a n d tra n sitiv e inference (C h a p te r 4). T h ese are c onsidered first b eca u se o f th eir c o m p a ra tiv e sim plicity. P e r­ form ance on th e com plex tasks discussed in P a rts I I a n d I I I is subject to high e rro r ra te s w hich p ro v id e the m ain basis for s ta t­ istical an aly sis. By c o n tra st, p e rfo rm a n ce on the tasks review ed in P a rt I is g e n era lly su b je ct to low e rro r ra te s, so th a t th e laten cy o f response becom es th e m ain m ea su re o f in te rest. T h e se tasks are also th o u g h t to give relatively d ire c t in fo rm a tio n a b o u t th e m a n n e r in w hich sim ple se n ten c es a re c o m p re h en d e d o r represented in m em ory. In g e n era l, it is im p o rta n t in stu d y in g an y pro b lem -so lv in g task to ask how the in fo rm a tio n given is re p re se n te d in te rn ally by the subject. O n e m u st b e a r in m in d th a t the su b je ct re sp o n d s to the pro b lem as he u n d e rs ta n d s it, w hich is n o t necessarily th e w ay th a t the e x p e rim e n te r in te n d s o r a logic textbook in stru c ts. H o w e\'e r, an in terest in th e re p re se n ta tio n o f sen ten ces a n d o th e r form s o f infor­ m atio n is also th e co n ce rn o f p sy ch o lin g u ists, m em o ry re sea rc h ers an d o th e r cognitive psychologists. It is, th erefo re, necessary to es­ tab lish a g e n era l th eo re tic al c o n te x t w ith in w hich to assess the research review'ed in th e follow ing tw o c h a p te rs. P a rtic u la rly re l­ ev an t is th e d e b a te a b o u t the relativ e s ta tu s o f th eo ries p ro p o sin g th a t se n ten c es (a n d p ictu res) are re p re se n ted by u n d e rly in g a b stra c t propositions, a n d those w hich p o stu la te the use o f mental images. W e will first c o n sid er the n a tu re a n d orig in o f these types o f theory, a n d th en a tte m p t to identify th e issues o f conflict w hich arise.

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12

Elementary reasoning tasks

Propositional representations P ro p o sitio n al tre a tm e n ts o f sen ten ce c o m p re h en sio n a ssu m e th a t the u n d e rly in g m ea n in g is re p re se n te d in a n a b s tra c t se m a n tic code, consisting o f a set o f p ro p o sitio n s. T h e idea o f such u n d e rly in g re p re se n ta tio n owes m u ch to th e w ork o f th e lin g u ist N o a m C h o m ­ sky (1957, 1965, 1968). C h o m sk y a rg u e d th a t o n e ’s a b ility to p ro ­ duce a n d to u n d e rsta n d u tte ra n c e s could n o t be a c q u ire d by the p rinciples o f le a rn in g th eo ry (see C h o m sk y , 1959), b u t m u st be generative in n a tu re , in o rd e r to a c c o u n t for a lan g u a g e u se r’s p o te n ­ tial to p ro d u c e o r u n d e rs ta n d a n in fin ite n u m b e r o f different u tte r ­ ances. Specifically, he pro p o sed th a t th e surface structure o f a sen ten ce - as it a ctu ally a p p e a rs - m u st be g e n e ra te d from a n u n d e rly in g deep structure by use o f tra n s fo rm a tio n a l rules. T h e d e ep s tru c tu re consists o f a set o f base strin g s o r p ro p o sitio n s plus tra n sfo rm a tio n a l m ark ers. T h e se m ark e rs can be re g a rd e d as in stru c tio n s for g e n e r­ a tin g the surface stru c tu re from th e d e e p stru c tu re . T ak e, for ex am p le, the se n ten c e, ‘T h e big boy d id n o t hit the g irl’. T h e e le m en tary p ro p o sitio n s o f the d e ep s tru c tu re c o rre sp o n d to sim ple a sse rtio n s o f fact: T h e boy is big. T h e boy b it the girl. B oth the c o m b in a tio n o f these p ro p o sitio n s a n d the n e g atio n o f the second p ro p o sitio n a re achieved by ‘tra n s fo rm a tio n s’. T h e idea th a t neg ativ e se n ten c es (also passives, etc.) hav e g re a te r tra n s fo r­ m atio n al com plexity th a n affirm ativ es h a s stim u la te d som e p sy c h o ­ logical re sea rc h (see C h a p te r 3). E a rly psychological in te re s t in C h o m sk y ’s theo ries (e.g. M iller, G a la n te r a n d P rib ra m , 1960) w ere in fact, focused on th e syntactic a sp e ct o f C h o m sk y ’s theories, e.g. tran sfo rm a tio n a l rules, ra th e r th a n th e semantic asp e ct o f how m e a n ­ ing m ay be o b ta in e d from a d e ep stru c tu re re p re se n ta tio n . In d e e d , in his o rig in al fo rm u la tio n C h o m sk y (1957) a p p e a re d to be m ain ly in te rested in sy n ta ctic m ec h an ism s w hich he co n sid ered a t th a t tim e to be in d e p e n d e n t o f m eaning. Psychologists such as G eo rg e M ille r w ere, a t one tim e, in te re ste d in testing th e ‘p sychological re a lity ’ o f C h o m sk y ’s 1957 theory. T h e questio n asked w as, in effect, w h e th e r the psychological ‘ru le s’ o f sentence c o m p re h en sio n c o rre sp o n d in som e w ay to C h o m sk y ’s

Theoretical background

13

linguistic rules. T h e p ra c tic a l p ro b lem from th e psy ch o lo g ist’s p o in t o f view co n ce rn s testa b ility , a lth o u g h th e re is th e m ore general q uestio n o f w h e th e r a theory can sim u lta n eo u sly fun ctio n as b oth a linguistic a n d a psychological theory. O n e difficulty, discussed by C hom sky him self, lies in th e d istin c tio n betw een lin g u istic competence an d linguistic performance. A lan g u a g e u s e r’s c o m p eten ce is revealed by his in tu itiv e a b ility to d istin g u ish g ra m m a tic a lly legal from illegal u tte ran c e s. In p ra c tic e such c o m p eten ce w ould alw ay s be subject to d isto rtio n by p e rfo rm a n ce factors su c h as m em ory lapses, o r a change o f m in d o c c u rrin g halfw ay th ro u g h u tte rin g a sentence. T h u s c o m p e ten c e a n d p e rfo rm a n ce w ould no t c o rre sp o n d exactly; an d C h o m sk y a rg u e d th a t the task o f g e n era tiv e g ra m m a r is to describe c o m p e ten c e, n o t p e rfo rm a n ce . W h ile linguistically necess­ ary, th e d istin c tio n b etw een c o m p e ten c e a n d p e rfo rm a n ce severely restricts th e e m p irica l falsifiability o f a linguistic theory. A ny d e v ia ­ tion from th e th e o ry ’s p re d ic tio n s m ig h t be a ttrib u te d to som e kind o f p e rfo rm a n ce factor. In the revised version o f his theory (1965), C h o m sk y in tro d u c ed a se m an tic c o m p o n e n t, w hich o p e ra te d on the d e ep stru c tu re re p ­ re sen ta tio n to g e n e ra te m ea n in g . S u b se q u e n t tre n d s in p sy c h o lin ­ guistics hav e c o n tin u e d to show a c h a n g e o f e m p h a sis from sy n ta ctic to sem an tic a sp e cts o f lan g u ag e. T h e re h a s also been a tre n d to­ w ard s c o n sid e ra tio n o f c o n n ec te d p ro se ra th e r th a n isolated se n ­ tences. Som e o f th e m o d e rn w ork is based largely on th eo re tic al analysis (e.g. M ille r a n d J o h n s o n -L a ird , 1976) w ith a co n sid era b le in te rest in th e fo rm u la tio n o f lan g u a g e p rocessing th eo ries in the form o f c o m p u te r p ro g ra m s (e.g. W in o g ra d , 1972; S h an ck , 1972). W e will, how ever, confine o u r in te re st to theo ries w hich lend th e m ­ selves to re ad y e m p irica l test. T h e n o tio n th a t lan g u a g e is u n d e rsto o d by reference to u n d e rly in g pro p o sitio n s is now w id e sp rea d in b o th c o m p u te r sim u la tio n m odels a n d in g e n era l p sy c h o lin g u istic a n d m em o ry theories. M o d e rn p ro p ­ ositional a n aly sis is, how ever, q u ite d e ta c h e d from C h o m sk y ’s lin ­ guistic theories. T h is is illu stra te d by the re m a rk a b le ab se n ce o f term s su ch as ‘g e n era tiv e g ra m m a r’ a n d ‘tra n s fo rm a tio n ’ in the subject in d ex o f th e re ce n t text o n p sy ch o lin g u istics by C la rk a n d C lark (1977). T h e re a re now a n u m b e r o f fo rm u la tio n s o f p ro p o si­ tional theo ries w h ich differ w ith re sp ec t to how the p ro p o sitio n s are w ritte n a n d th e n a tu re o f th e m ec h an ism s p ro p o se d to u n d e rlie them . K in ts c h ’s (1974) th eo ry is p rim a rily a p p lie d to se m an tic

14

Elementary reasoning tasks

m em o ry , w hile H . C la rk (see, for e x a m p le , C la rk a n d C la rk , 1977) h a s a p p lie d his p ro p o sitio n a l th e o ry to v e rifica tio n a n d re a so n in g tasks. C la r k ’s w ork in th ese a re a s will be c o n sid e re d in C h a p te r s 3 a n d 4. A n d e rs o n ’s (1976) A C T sim u la tio n m o d el, w h ic h o p e ra te s on a p ro p o s itio n a l n e tw o rk , is a p p lie d to p ra c tic a lly e v e ry th in g (for A C T ’s p re d e c e s so r H A M see also A n d e rso n a n d B ow er, 1973). C la r k ’s th e o ry is c o n c e rn e d w ith th e m a n n e r in w h ic h p e o p le p ro cess th e lin g u istic s tr u c tu r e o f in d iv id u a l se n te n c e s. H e s ta r ts w ith th e n o tio n t h a t se n te n c e s a re b ro k e n d o w n in to constituents. H is a n aly sis o f c o n s titu e n t s tru c tu r e is e sse n tia lly sim ila r to C h o m s k y ’s tre a tm e n t o f su rfa c e s tru c tu re . H e d e fin e s a c o n s titu e n t a s ‘ . . . a g ro u p o f w o rd s th a t c a n be re p la c e d by a single w o rd w ith o u t a c h a n g e in fu n c tio n a n d w ith o u t d o in g v io le n c e to th e re st o f th e se n te n c e ’ (C la rk a n d C la rk , 1977, p. 48 ). T h e p ro p o sitio n s u n d e rlie th e c o n stitu e n ts , a n d b o th h a v e a h ie ra rc h ic a l s tru c tu re . P ro p o s i­ tio n s th em se lv es a re w ritte n in th e fo rm o f a lg e b ra ic fu n c tio n s, in w h ich a m o d ifie r is follow ed, in p a re n th e s e s , by th e o b je c t o r o b jec ts it m odifies, e.g. ‘J o h n w a lk s’ w o u ld be w ritte n : W a lk ( J o h n ). C la rk is n o t, h o w e v er, p o sin g sim p ly a lin g u istic s tru c tu re , b u t a lso a p sy c h o lo g ic al s tru c tu re . F o r e x a m p le , th e lis te n e r is s u p p o s e d to c o m p re h e n d la n g u a g e by b re a k in g se n te n c e s d o w n , firstly in to c o n ­ s titu e n ts, a n d se c o n d ly in to u n d e rly in g p ro p o sitio n s . P ro p o s itio n a l th e o rie s, h a v e , h o w e v er, a m u c h b ro a d e r ra n g e o f a p p lic a tio n th a n su g g e ste d by th e e x a m p le s giv en . A p ro p o s itio n a l a n aly sis c a n be m a d e o f w hole tex ts r a th e r th a n in d iv id u a l se n te n c e s (see K in ts c h , 1974). I t c a n a lso b e a p p lie d to k n o w le d g e a c q u ire d by n o n -lin g u istic m e a n s. W e sh a ll see la te r, for e x a m p le , th a t p r o p ­ o sitio n a l th e o rie s h a v e b e en offered for th e e x p la n a tio n o f p ic to ria l re p re s e n ta tio n s . In c u rre n t u sa g e p ro p o sitio n s a re re g a rd e d as abstract (h e n ce n o t v e rb a l). T h e y a lso h a v e a useful p ro p e rty o f truth value - th e y m a y be tru e , false o r in d e te rm in a te . I t is a rg u e d by som e th a t all k n o w le d g e c a n be re p re s e n te d as a se t o f v e rifiab le p ro p o sitio n s. W h e th e r o r n o t th is is a n a d e q u a te c h a ra c te ris a tio n o f h u m a n k n o w le d g e is, h o w e v er, a m a tte r for c o n sid e ra b le d e b a te . M a n y a u th o rs fa v o u r th e view th a t so m e fo rm s o f re p re s e n ta tio n a re a ch iev e d in th e fo rm o f m e n ta l im a g e s, a view th a t w ill n o w be e x am in ed .

Theoretical background

15

Mental imagery T h e to p ic o f m e n ta l im a g e ry h a s h a d a n in te re s tin g h isto ry in p sychology. A fa sh io n a b le to p ic in th e la te n in e te e n th a n d e a rly tw e n tie th c e n tu rie s w h e n th e in tro s p e c tiv e m e th o d w a s re sp e c ta b le , it w as b a n is h e d by th e a d v e n t o f W a ts o n ’s b e h a v io u ris m . In re c e n t y e ars, h o w e v er, im a g e ry h a s m a d e a se n sa tio n a l c o m e b a c k in to p sy c h o lo g ic al stu d y , rid in g on th e b a n d w a g o n o f ‘c o g n itiv e p sy ­ c h o lo g y ’. In d e e d , it is h a r d n o w to th in k o f a tr e n d ie r o r m o re in te n siv e ly re se a rc h e d a sp e c t o f c o g n itio n . H o w e v e r, th e re is som e c o n sid e ra b le co n fu sio n in th e use o f th e te rm ‘im a g e ry ’. F o r som e it m e a n s a su b je c tiv e e x p e rie n c e o f m e n ta l p ic tu re s , w h e re a s o th e rs use it to d e s ig n a te a n o p e ra tio n a lly d e fin e d c o g n itiv e pro cess. G a lto n (1883) is fre q u e n tly c ite d as o n e o f th e e a rlie st serio u s in v e s tig a to rs o f m e n ta l im a g e ry . H o w e v e r, it sh o u ld be p o in te d o u t th a t h is s tu d y w a s e n tire ly in tro s p e c tiv e in n a tu re , a n d n o t n e ce ss­ a rily c o n n e c te d w ith all c u rre n t use s o f th e te rm im a g e ry . T h e use o f su b je ctiv e re p o rt te c h n iq u e s im p lie s th a t im a g e ry is a m e n ta l e x p erien c e . I t m ig h t be d e fin e d a s a n e x p e rie n c e w h ic h re sem b les th a t o f a p e rc e p tio n in th e a b se n c e o f a n a p p r o p ria te stim u lu s. F a m ilia r e x a m p le s w o u ld be v isu a lisin g a face, o r h e a rin g a tu n e ‘in y o u r h e a d ’. P e rk y (1910) c la im e d t h a t su b je c ts c o u ld be tric k e d in to c o n fu sin g a p e rc e p tu a l e x p e rie n c e w ith a n im a g in a l o n e , a n d Segal h a s, u n d e r sp e c ia l c o n d itio n s, b e e n a b le to re p e a t th is re su lt in re c e n t tim e s (for a review see S eg al, 1971). M o st p e o p le , h o w e v e r, w o u ld a g re e t h a t th e a im o f c o g n itiv e p sychology is n o t to s tu d y m e n ta l e x p e rie n c e a s su c h , b u t to in v es­ tig a te processes w h ic h m e d ia te b e h a v io u r. Im a g e ry h a s b e en c la im e d to c o n s titu te su c h a c o g n itiv e p ro c ess, a lth o u g h , a s w e sh a ll see, th is v iew p o in t is h ig h ly c o n tro v e rsia l. A goo d e x a m p le o f th e p ro c ess a p p ro a c h o c c u rs in 'm e n ta l r o ta tio n ’ stu d ie s (e.g. S h e p a rd a n d M e tz le r, 1971; C o o p e r a n d S h e p a rd , 1973; C o o p e r, 1975). In th ese stu d ie s su b je c ts a re re q u ire d to m a k e sa m e /d iffe re n c e ju d g m e n ts a b o u t tw o fig u res w h ic h a re r o ta te d w ith re sp e c t to o n e a n o th e r. T h e g e n e ra l fin d in g is t h a t o n p o sitiv e ju d g m e n ts (i.e. w h e n th e tw o figures m a tc h ) th e re a c tio n tim e in c re a s e s lin e a rly w ith th e d e g ree o f a n g u la r d is p la c e m e n t o f th e figures. T h is fin d in g is c o n siste n t w ith th e n o tio n t h a t th e su b je c t m e n ta lly r o ta te s o n e o f th e p ic tu re s , a t a c o n s ta n t a n g u la r velo city , a n d th e n m a tc h e s it a g a in s t the o th er.

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Elementary reasoning tasks

T h e in tro sp ec tiv e o r e x p erien tial d e fin itio n o f im ag ery clearly has a stro n g influence on som e cognitive psychologists. F o r ex am p le, one line o f w ork is co n ce rn ed w ith in v estig a tin g th e p ro p e rtie s o f visual im ages by ask in g su b je cts to ‘s c a n ’ th em . (e.g. K osslyn, 1975; 1978). A lth o u g h som e objectiv e b e h a v io u ra l m easu res such as re­ action tim es a re em p lo y ed , this w ork rests u p o n th e a ssu m p tio n th a t the su b je ct p erceives a n d re sp o n d s to in stru ctio n s a b o u t an in n e r m en ta l p ic tu re , av ailab le only to his p e rso n al experience. In these e x p erim e n ts su b je cts a re a sk ed to d e sc rib e a n d m ea su re aspects o f th e ir im ages as i f they w ere p e rce p ts. F o r e x am p le, K o s­ slyn (1978) re p o rts th a t a fte r being asked to visualise a n object, subjects, ‘w ere re q u e ste d to im a g in e th a t they w ere m oving to w a rd s the object, a n d asked w h e th e r it seem ed to loom la rg e r as they m oved c lo ser’. A scep tic o f th e ‘m e n ta l p ic tu re ’ a p p ro a c h m ig h t suggest th a t su c h in stru c tio n s c o n ta in c le a r d e m a n d c h a ra c te ristic s to evoke subjective re p o rts in th e term s fav o u red by th e th eo re tic al position o f th e e x p erim e n ter. C ritic ism s o f the m en ta l p ic tu re a p p ro a c h a re not, how ever, re ­ stricted to the p ro b lem s o f in tro sp ec tiv e re p o rts. T h e g e n era l p ro b ­ lem o f in tro sp ec tiv e re p o rts is d iscu ssed in C h a p te r 12. Several logical difficulties a rise in su ch a cc o u n ts as we shall see in th e next section.

Images versus propositions A n im p o rta n t d e b a te h a s dev elo p ed recen tly a b o u t the s ta tu s o f m en ta l im ag ery as a n e x p la n a to ry c o n stru c t. T h e K osslyn k ind o f a p p ro a c h is so m etim es referred to as th e ‘im agery p o sitio n ’. T h is definition is not too helpful, since the term ‘im a g e ry ’ is not in p ractice re stric te d to the v o c ab u lary o f those a d o p tin g th is a p ­ p roach. As A n d e rso n (1978) p u ts it, ‘N o one seem s to d e n y th a t there is a p h e n o m e n o n called mental imagery. O n th e o th e r h a n d there is c o n sid era b le d e b a te o ver w h e th e r th ere is a useful re p re ­ se n tatio n al c o n stru c t called a n image.' P ylyshyn (1973), a leading critic o f th e so-called ‘im a g e ry p o sitio n ’ has c h a ra c te ris e d it as em ploying a picture-metaphor - su b je cts a re su p p o sed to ‘see’ a n im age as i f it w ere a p ictu re. A lth o u g h im ag ery th eo rists have p ro tested th is to be a ‘s tra w m a n ’ (P aivio, 1976, K osslyn a n d Pom eranz, 1977), it does seem a fair d e sc rip tio n . F o r e x am p le, K osslyn

Theoretical background

17

a n d P o m e ran z (1977) also a sse rt th a t ‘som e o f the o p e ra to rs . . . th a t a re used in a n a ly sin g p e rce p ts a re also a p p lie d to im a g e s’, a n d ‘the q u e stio n o f how know ledge can be d erived from im a g e ry is q u ite sim ila r to the q u e stio n o f how know ledge is d eriv ed from ongoing sen so ry a c tiv ity .’ A n d erso n (1978) h as also c o n clu d ed th a t, ‘it seem s th e p ic tu re m e ta p h o r is th e im ag ery th e o ry .’ T h e critics o f th is a p p ro a c h g en erally pre fe r to a cc o u n t for the re p re se n ta tio n o f all form s o f know ledge in term s o f pro p o sitio n s (e.g. A n d e rso n a n d Bow'er, 1973; P yly sh y n , 1973). P ylyshyn, for exam ple, re g a rd s m e n ta l im a g e ry as a n epi-phenomenon. H e arg u es th a t it is n o t a process, b u t the resu lt o f a process. H e p roposes th a t n e ith e r the in fo rm a tio n c ap a c ity o f the b ra in n o r th e p ro b lem s o f o rg anising re trie v a l wro uld p e rm it in fo rm a tio n to be sto re d as visual im ages. Since th ey m u st be c o n stru c te d from som e u n d e rly in g a b stra c t (o r p ro p o sitio n a l) re p re se n ta tio n , th en it is th e n a tu re o f these re p re se n ta tio n s th a t sho u ld serve to e xplain th e m ed ia tio n o f b eh av io u r. P ylyshyn also a tta c k s the use o f the p ic tu re m e ta p h o r by im agery th eo rists on several g ro u n d s. F o r exam ple, 1 T h e m e ta p h o r lead s to a false an alo g y betw een p e rce p tio n a n d im agery. T h u s th e im ag e w hich is th e c o n seq u en ce o f p e rce p tu a l processing is tre a te d as if it w ere a stim u lu s to be processed. 2 A dvocates o f the ‘im a g e ry p o sitio n ’ are u n d u ly in fluenced by in tro sp ectiv e d a ta . In line w ith c o n sid e ra tio n s o f o u r prev io u s sec­ tion, P ylyshyn p o in ts o u t th a t term s like ‘im a g e ’ a re used in q u ite different senses w h en a p p lie d to in fo rm a tio n processing th a n w hen applied to conscious ex perience. H e a d d s, ‘T h e recen t lite ra tu re a b o u n d s in ex am p les w h ich reveal th a t th e in v estig a to r tacitly a s­ sum es th a t w h a t is fu n c tio n al in cog n itio n is a v ailab le to in tro sp e c ­ tio n .’ U n fo rtu n a te ly , P y ly sh y n ’s a sse rtio n is q u ite co rrect. 3 Im a g e ry th eo rists m ake bogus use o f o p e ra tio n a l definitions. D ifferent co n v erg in g o p e ra tio n s to d e m o n s tra te th e im p o rta n c e o f im agery in, for ex am p le, v e rb al le a rn in g (P aivio, 1971) logically define different c o n stru c ts. ‘T h e u n ity o f these c o n stru cts, a n d c o n ­ se q u e n tly , the n o tio n o f im ag ery , re sts o n a m e ta th e o re tic a l a s­ su m p tio n . T h is a ssu m p tio n , in tu rn , rests on the pe rsu asiv en e ss o f subjective ex p erien ce a n d th e o rd in a ry inform al m e a n in g o f the w ord image.' W hile I th in k th a t th ese c riticism s a re so u n d a n d a m n o t co n ­ vinced by th e a tte m p ts o f K osslyn a n d P o m e ran z (1977) to refute them , I d o n o t th in k th a t P y ly sh y n ’s p a p e r e ith e r d estro y s the

18

Elementary reasoning tasks

im agery p osition e n tirely , o r e stab lish e s the p ro p o sitio n a l position. W hile the m a lp ra c tic e s he cites a re certain ly asso ciated w ith m an y im agery th eo rists, they a re n o t an in ev itab le co n seq u en ce o f a ssu m ­ ing p ictorial re p re se n ta tio n . A n d erso n (1978) a tte m p ts to u n d e rm in e m u ch o f the basis o f the p ictu re-p ro p o sitio n a rg u m e n t. H e a rg u es tw o essential po in ts. H e claim s th a t no th eo ry a b o u t the n a tu re o f the representation o f know ­ ledge can be assessed in d e p e n d e n tly o f a ssu m p tio n s a b o u t th e pro­ cess. T h u s it is m ean in g less for people like P ylyshyn a n d K o ssly n to argue a b o u t w h e th e r re p re se n ta tio n s a rc in th e form o f p ictu res or pro p o sitio n s, w ith o u t also specifying process a ssu m p tio n s. A ny cog­ nitive theory m u st be specified as a representation-process pair. Sec­ ondly, he claim s th a t an y p ic tu re theory can be fo rm u la ted as a p ro p o sitio n al th eo ry an d vice versa. H e arg u es, for e x am p le, th a t it is a sim p le m a tte r to p ro d u c e a p ro p o sitio n a l m odel to a c c o u n t for the m en ta l ro ta tio n studies: T h e m odel w ould involve a p ro p o sitio n a l d e sc rip tio n o f an o bject a n d its o rie n ta tio n in space. J u s t as K osslyn an d S ch w artz (1977) c o m p u te a series o f sm all ch an g es in th eir im age, so a series o f sm all ch an g es can be c o m p u te d in the p ro p o sitio n a l re p re se n ta tio n . T h e force o f A n d e rso n ’s a rg u m e n t is b ro u g h t hom e by th e co n ­ sid e ratio n th a t if it w ere not possible to re p re se n t such a m odel in term s o f p ro p o sitio n s, th en one could no t w rite a c o m p u te r p ro g ram to sim u la te it. A n d e rso n ’s tw o p o in ts a re not, o f course, in d e p e n d e n t. T h e p o in t a b o u t m en ta l ro ta tio n is th a t it is a h y p o th esis a b o u t a process an d not a re p re se n ta tio n . T h e only asp e ct th a t the p ictu re re p re se n ta tio n m ight seem to a d d to th a t o f the p ro p o sitio n s is in its in tu itiv e c o rresp o n d en ce to o u r su b jectiv e ex perience. A n d e rso n dism isses this c o n sid era tio n as follows: T h e in tro sp ec tiv e re p o rts a re d a ta th a t re q u ire e x p la n atio n s like any o th e r d a ta . H o w ev er, th ere is no reason to su p p o se th a t the best re p re se n ta tio n to a c c o u n t for v e rb al re p o rts o f p ictu re-lik e p ro p e rties is a p ic tu re . A c o m p u te r p ro g ra m could be w ritte n to deliver such re p o rts from a p ro p o sitio n a l d a ta base.

Theoretical background

19

A n d e rso n ’s a rg u m e n ts hav e com e u n d e r c o n sid era b le criticism (e.g. H a y e s-R o th , 1979; P ylyshyn, 1979; J o h n s o n -L a ird , 1979), a lth o u g h he h a s stu c k reso lu tely to his positio n in rep ly in g to som e o f these p a p e rs (A n d e rso n , 1979). In p a rtic u la r, his critics d isp u te the assertio n th a t th e p o stu la te d fo rm at o f re p re se n ta tio n h a s no functional conseq u en ces. A t th e tim e o f w ritin g th e im ages v. p ro p ­ ositions d e b a te is bein g c o n d u cted in a m a n n e r w h ich is b o th p h ilo ­ sophically d e ep a n d tech n ically com plex, a n d show s no im m e d ia te signs o f reso lu tio n . I will sim ply offer som e te n ta tiv e conclusions: 1 D ifficulties arise in th e a p p lic a tio n o f the im ag ery c o n stru ct, especially w'hen explicit o r im p licit re lian c e is p laced u p o n the subjective ex p erien ce o f m en ta l p ictu res. 2 Im ag e ry re p re se n ta tio n s m ay be view ed as a form o f s tru c tu ra l a nalogue o f the e x te rn a l w orld. H ow ever, it is claim ed by som e th a t the in fo rm a tio n they c o n ta in can be en tirely d e sc rib e d by a p ro p ­ ositional re p re se n ta tio n . 3 I t is im p o rta n t to d istin g u ish b etw een the format o f a re p re se n ­ tatio n (im age versus p ro p o sitio n ) a n d its in fo rm a tio n -p ro c essin g s tru c tu re . T h e re la tiv e value o f e ith e r type o f form at, a n d even the possibility o f d istin g u ish in g th em is a m a tte r o f u n reso lv ed d e b ate. In view o f th is last c onclusion, it is im p o rta n t to ask w h e th e r there are s tru c tu ra l differences betw een th e types o f p ro p o sitio n a l a n d im ag ery th eo ries th a t hav e been p ro p o se d , a p a r t from the a ssu m p tio n s a b o u t fo rm at. T h e re is, in d ee d , a g en eral stru c tu ra l issue, w hich is o f c o n sid era b le relev an ce to th e u n d e rsta n d in g o f reaso n in g d a ta in b o th th is a n d la te r p a rts o f th e book. T h is issue is ex p lain ed in th e follow ing section.

Dual coding versus central processing T h o se fav o u rin g th e n o tio n o f im a g in al re p re se n ta tio n hav e ten d e d to a d o p t m u ltip le pro cessin g a p p ro a c h e s to cognition, w hile p ro p ­ o sitional th eo rists hav e ten d e d to w a rd s a single process position. F or ex am p le, P aivio (1971) p ro p o se d a d u a l c o d in g th eo ry to acco u n t for v e rb al le a rn in g d a ta . H e a rg u e d th a t w o rds m ay be en tered in to one o f tw o codes w h ich a re visual a n d verbal in n a tu re . H e p ro p o sed th a t the lo n g -esta b lish ed su p e rio rity o f le a rn in g c o n ­ crete over a b s tra c t w ords is d u e to the fact th a t w hile th e la tte r have access only to th e v e rb al code, th e fo rm er also hav e access to

20

Elementary reasoning tasks

the visual code w hich h a s stro n g m n em o n ic p ro p e rties. F u rth e r evidence for the d u a l-c o d e h y p o th esis is o b ta in e d th ro u g h the use o f v a rio u s ‘co n v erg in g o p e ra tio n ', such as in stru c tio n s to a d o p t a n im agery stra te g y , w h ich fa cilitate th e le a rn in g o f co n cre te w ords. (F o r a re ce n t ex am p le o f th e use o f th is te c h n iq u e see R ic h a rd so n , 1978.) P ro p o sitio n al th eo rists such P yly sh y n , on the o th e r h a n d , hav e tended to a single c oding a p p ro a c h . As K ie ra s (1978) p u ts it, M ost o f th e d e b a te on th e n a tu re o f im ag ery h as c en tere d on a n ex trem e form o f th e p ro p o sitio n a l position. T h e ex trem e position takes a cue from the a b s tra c t n a tu re o f p ro p o sitio n s an d in sists th a t all h u m a n know ledge is itself a b s tra c t a n d re ta in s no tra c e o f its o riginal so u rce m od ality . From th e c o n sid era tio n s o f the p rev io u s section, th ere is obviously no reason w hy a p ro p o sitio n a l theory need be cast in this form , a n d K ie ras h im self goes on to c o n sid er p ro p o sitio n a l theo ries wrhich d o re ta in in fo rm a tio n a b o u t source m od ality . W h a t th o u g h o f the ev idence for d u a l v ersus single codes or processes? T h e m n em o n ic type ev idence com es u n d e r fire from P y ly sh y n ’s p o in t 3. I f th e re is no logical p a th from the vario u s o p e ra tio n a l d efin itio n s to a unified im a g e ry c o n stru c t, th e n the results o f each se p a ra te p a ra d ig m m ay be o pen to a lte rn a tiv e ex­ p lan a tio n s. A n d erso n (1978) suggests th a t such evidence is w e ak ­ ened by re ce n t e x p erim e n tal findings, w hich d e m o n s tra te the im p o rta n c e o f th e type a n d level o f se m a n tic p rocessing a d o p te d w ith e ith e r ty p e o f m a te ria l in e sta b lish in g m em ory stre n g th . T h e n o tio n o f d u a l codes is ra th e r sta tic , a n d o sten sib ly m o re a h yp othesis a b o u t re p re se n ta tio n th a n a b o u t process. P aivio (1975) has, how ever, ex te n d ed the n o tio n to th o u g h t processes. T h is ex­ ten d e d th eo ry will be d iscu ssed in C h a p te r 12, w h ereas the p re sen t discussion will focus o n th e a rg u m e n t for d u a l coding. P o te n tia lly the stro n g e st ev idence for such a po sitio n , a n d the w ork w hich causes m o st p ro b lem s for p ro p o sitio n a l th eo rists, arises from the selective in terferen ce stu d ies (B rooks, 1967; 1968; A tw ood, 1971; S althouse, 1974; 1975). W h a t these stu d ies a p p e a r to show is th a t if a subject is asked to c a rry o u t tw o c o n c u rre n t tasks, one involving im agery a n d th e o th e r p e rce p tio n , th en th e re is m ore in te rfere n c e if the tw o tasks involve th e sa m e m o d ality . T h is evidence, if so u n d ,

Theoretical background

21

refutes a n e x tre m e p ro p o sitio n a l th eo ry in w hich it is assu m e d th a t all m en ta l o p e ra tio n s a re p e rform ed o n a n a b s tra c t code w hich contains no reference to a p e rc e p tu a l m od ality . A n d erso n (1978) h as suggested th a t su ch resu lts a re a n a rtifa c t, a n d th a t in terferen ce arises from sim ila rity o f content ra th e r th an m odality. I d o n o t th in k th a t all the evidence can be e x p la in ed in this w ay, how ever, p a rtic u la rly th a t o f B rooks. C o n sid e r, for ex­ am ple, one o f the e x p erim e n ts in his 1967 p a p er. S u b jects w ere req u ire d to le a rn a v e rb al list w ith e ith e r a c le a r v isu a l-sp atial reference o r else a c o n tro l ‘n o n se n se ’ list. In th e sp a tia l list, se n ­ tences referred to a 4 X 4 grid o f sq u a re s a n d c o n ta in ed in stru ctio n s such as In th e s ta rtin g sq u a re p u t a 1. In the nex t sq u a re to th e rig h t p u t a 2. In the n ex t sq u a re u p p u t a 3, etc., e tc ., etc. W ith no n sen se m a te ria ls sp a tia l ad jectiv es such as ‘u p ’ an d ‘d o w n ’ w ere re p la ce d by adjectiv es such as ‘q u ic k ’ a n d ‘slow ’, th u s p re su m ab ly p re c lu d in g th e p ossibility o f c o n stru c tin g a sp a tia l im ­ age as a m n em o n ic device. T h e tests w ere p re sen te d for lea rn in g e ith e r a u ra lly , o r else a u ra lly and visually. T h e m ean n u m b e r o f errors m ad e in le a rn in g is show n in T a b le 2.1. W e see th a t a cross-over in te ra c tio n o c cu rre d . W h en su b je cts w ere re ad in g , as well as listen in g , they d id w orse on the sp a tia l th a n no n sen se m a ­ terial; the reverse w as tru e w h en they listened only. B rooks c o n ­ cludes th a t th e use o f th e visual p e rc e p tio n system interferes w ith im a g in al c oding o f th e sa m e m od ality . H e h as also claim ed in te r­ ference w ith th e p e rc e p tu a l m o d ality used in resp o n se o u tp u t, a n d fu rth e r ge n era lise d h is evidence to a u d ito ry as well as visual im agery (Brooks, 1968).

T A B L E 2.1 Results o f Brooks (1967) Experiment I (Mean number o f errors)

L istening L istening and read in g

S patial m aterial

N onsense m aterial

1.2 2.8

2.3 1.3

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Elementary reasoning tasks

T h o u g h w idely a cc ep te d a n d q u o te d , B rooks’s resu lts hav e re­ cently com e u n d e r a tta c k from P hillips a n d C h ristie (1977). T h e y criticise Brooks for n o t u sin g blank controls, i.e. c o n d itio n s u n d e r w hich no in te rferin g task is given. T h e y also re p o rt e x p erim e n ts w hich fail to re p ro d u c e his m o d ality re la te d in terferen ce effects. It should be n o ted , how ever, th a t th e ir ‘im a g e ry ’ task w as very differ­ ent from his. P hillips a n d C h ris tie ’s su b je cts w ere asked to m em orise a novel visual p a tte rn . E q u a tin g th is w ith B rooks’s task o f co n ­ s tru c tin g sp a tia l im ages is a good e x am p le o f the overin clu siv e use o f the term ‘im a g e ry ’ o f w hich P ylyshyn c o m p la in s. N ev erth eless, B rooks’s finding m ay h a v e less g e n era lity th a n w as on ce th o u g h t. In conclusion, th e re m ay be som e a d v a n ta g e s in p ro p o sin g th a t a lte rn a tiv e form s o f re p re se n ta tio n a re a v a ila b le to th e in fo rm a tio n processor. Is th e issue really in d e p e n d e n t o f assu m e d fo rm a t, how ­ ever? I f m o d ality specific interferen ce effects a re su b s ta n tia te d , th en it is h a rd to reconcile th em w ith a g e n era l p ro p o sitio n a l theory o f m em ory. E ven if in p u t m o d ality is in clu d e d in th e p ro p o sitio n a l re p re se n ta tio n , it is h a rd to see w hy su c h m em ory should suffer interference from a p e rc e p tu a l task. O n the o th e r h a n d , if an a nalogue (im agery) re p re se n ta tio n is p ro p o se d , it is perfectly re aso n a b le to suggest th a t it w o u ld em ploy som e o f th e m ec h an ism s used in the p e rc e p tu a l system o f th e c o rre sp o n d in g m od ality .

Conclusions I t should be cle ar from th e w ork review ed in this c h a p te r th a t the stu d y o f lan g u a g e, m em ory a n d th o u g h t a re beco m in g increasin g ly in te rco n n e c te d . C h o m sk y m a d e a n in v a lu a b le c o n trib u tio n to p sy ­ chology by stim u la tin g th e d e v elo p m en t o f psych o lin g u istics. T h e field o f p sy ch o lin g u istics h a s dev elo p ed since to w a rd s a g re a te r concern w ith how u n d e rly in g m e a n in g is re p re se n te d a n d used. M em ory re sea rc h , alw ays v e rb al in e m p h a sis, h a s m oved from the stu d y o f in d iv id u a l w ords to sen ten ces a n d c o n n ec te d prose. T h u s the tw o fields hav e firm ly co n n ec te d a n d th e p ro p o sitio n a l th eo ries arise at th eir in te rse ctio n . T h e use o f th e im a g e ry c o n stru c t gives rise to a n u m b e r o f th e o r­ etical p ro b lem s, especially w ith re g a rd to its a sso c iatio n w ith s u b ­ jec tiv e m en ta l ex perience. N ev erth eless, th e c o n stru c t has been used as a m n em o n ic device in v e rb al le a rn in g a n d m em ory, a n d as the

Theoretical background

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basis o f p e rfo rm a n ce o f v a rio u s cognitive tasks. A n d e rso n 's view th a t th e d e b a te betw een im a g e ry a n d p ro p o sitio n a l th eo rists has confused re p re se n ta tio n a n d p rocess is a cc ep te d . It is a m a tte r o f c u rre n t d e b a te w h e th e r o r no t th e fo rm at o f re p re se n ta tio n s (im ag inal v. p ro p o sitio n a l) can be d istin g u ish e d . A n im p o rta n t stru c ­ tu ra l issue co n ce rn s th e d istin c tio n betw een the use o f a single se m an tic code, a n d tw o (o r m ore) types o f code specialised for processing different types o f in fo rm a tio n . W ith these c onclusions in m in d , w e sh all now c o n sid er th e findings o f e x p erim e n ters on e lem en tary v erification a n d re aso n in g tasks.

Sentence verification

T h is c h a p te r is c o n cern ed w ith the w ay in w hich people verify (decide the tru th o r falsity of) relativ ely sim p le sentences, in re la tio n to a situ a tio n th a t th ey p u rp o rt to d e sc rib e . M a n y o f the e x p erim e n ts involve se n te n c e -p ic tu re co m p a riso n . F o r ex am p le, su b je cts m ay be told th a t ‘T h e s ta r is a b o v e the p lu s ’ a n d show n a p ic tu re o f e ith e r a s ta r above a p lu s o r vice v ersa. T h e su b je cts a re re q u ire d to m ake a tru e/false ju d g m e n t a n d th e ir late n cy o r resp o n se tim e is m ea su re d . S u ch tasks are freq u en tly c o m p lica te d by the in tro d u c ­ tion o f n egatives, e.g. ‘T h e plus is n o t above the s ta r .’ V erificatio n tasks involving logically com plex se n ten c es su c h as u n iv ersals {All A are B ) o r c o n d itio n als ( I f p then q) will be co n sid ered in late r sections o f the book. A lth o u g h such v erification tasks a re often referred to as sim ple ‘re aso n in g ’ p ro b lem s, they d o n o t a c tu a lly re q u ire d e d u ctiv e re a so n ­ ing as defined in C h a p te r 1. S u b jects a re n o t re q u ire d to u n d e rsta n d th e c o n cep t o f v a lid ity , i.e. th a t th e tr u th o f one o r m o re sta te m e n ts logically n e cessitates the tru th o f a n o th e r. T h e y m erely have to decide w h e th e r o r n o t a d e sc rip tio n is a cc u ra te . I t is, how ever, essential to review p e rfo rm a n ce on su c h tasks in a book such as this. F o r one th in g , th e tasks pro v id e in fo rm a tio n a b o u t p e o p le ’s a bility to re p re se n t a n d p rocess linguistic stru c tu re s th a t are in ­ volved in bona fide d e d u c tiv e reaso n in g p ro b lem s. T h u s , the stu d ies review ed in th is c h a p te r tell u s a b o u t p e o p le ’s a b ility to process negatives, w hich a re freq u e n tly involved in com plex re aso n in g tasks. S im ilarly, the m a n n e r in w hich people verify c o n d itio n al sentences is o f vital relev an ce to th e u n d e rsta n d in g o f c o n d itio n al re aso n in g p e rfo rm a n ce (see C h a p te r 8). I t will also em erge th a t the types o f th eo re tic al m odel w hich can be p ro p o sed to a c c o u n t for su b je c ts’ 24

Sentence verification

25

strateg ies on v erification tasks a re o f essentially sim ila r stru c tu re to those a p p lic a b le to tasks in volving g e n u in e d e d u ctio n . In a d e d u c ­ tive task one m u st c o m p a re th e re p re se n ta tio n o f tw o (o r m ore) prem ises a n d d e d u c e a conclusion. In a v erification task on e c o m ­ pares th e re p re se n ta tio n s o f a sen ten ce a n d (say) a p ic tu re a n d decides w h e th e r o r not they m atch . Before co n sid erin g p a rtic u la r e x p erim e n ts a n a rb itra ry b u t necessary lim ita tio n m u st be p laced on th e m a te ria l to be d iscussed. It w as in d ic a te d in C h a p te r 1 th a t only tasks in w hich all the inform ation re q u ire d for th eir solution is p re sen te d to the subject w ould be co n sid ered . T h e re a re m an y stu d ies o f sen ten c e verifica­ tion w here th is is n o t th e case. In such e x p erim e n ts th e su b je ct verifies a se n ten c e not a g a in st a p ic tu re o r som e o th e r p resen ted m ate ria l, b u t a g a in st his ow n know ledge o r se m an tic m em o ry (e.g. ;A c an a ry is yellow - tru e o r false?’). C o n sid e ra tio n o f su c h stu d ies an d th eir a tte n d a n t th eo ries w ould be a n in te re stin g b u t u n ju stifi­ able d iv ersio n from th e p u rp o se o f th is volum e. W e will c o n sid er the lite ra tu re in histo rical o rd e r. E arly e x p eri­ m ents w ere c o n ce rn ed w ith in v estig a tin g th e effect o f sy n ta ctic v a r­ iables, p a rtic u la rly n e g atio n . A s re sea rc h d eveloped p eople becam e increasingly a w a re o f th e im p o rta n c e o f se m an tic factors. In the early 1970s in fo rm a tio n -p ro c essin g m odels based on p ro p o sitio n a l re p re se n tatio n w ere dev elo p ed , a n d hav e ten d e d to d o m in a te the su b seq u e n t lite ra tu re .

Syntactic factors in sentence verification T h e e arlie st sy ste m atic stu d ies o f th e p rocessing o f positive an d negative sta te m e n ts w ere c a rrie d o u t by W aso n (1959, 1961). T h e basic sy n ta c tic fu n c tio n o f th e n eg ativ e w ith w hich he w as co n cern ed is its reversal o f tr u th value. E ssen tially , if an y p ro p o sitio n p is tru e, th en it follows th a t not p is false; sim ilarly if not p is tru e th en p m ust be false. T h is essential p ro p e rty o f n eg atio n m akes it fu n d a ­ m en tal to an y system o f form al logic, a n d hence o f co n sid era b le relevance to th e stu d y o f reaso n in g . W aso n set o u t to in v estig ate this p ro p e rty by co n sid erin g four types o f s ta te m e n t in w hich tru th value (tru e/false ) a n d p o larity (a ffirm ativ e/n eg a tiv e ) w ere b oth v a r­ ied. T h e follow ing ex am p les illu stra te the four sta te m e n ts.

26

Elementary reasoning tasks T ru e False T ru e False

affirm ative affirm ativ e negative negative

(T A ) (FA ) (T N ) (F N )

4 is a n even 6 is a n o d d 4 is n o t a n o dd 6 is not a n even

num ber num ber num ber num ber

W aso n (1961) c arried o u t tw o e x p erim e n ts using m a te ria ls o f the sort illu stra te d . S trictly sp e a k in g su b je cts a re verifying the sen ten ces a g ain st th e ir se m a n tic m em o ry , b u t th e evenness a n d o d d n e ss o f n u m b ers is h ighly o v e rle a rn t a n d th u s im m e d ia tely a v ailab le for all subjects. T h e re su lts d id , in an y event, p ro v e re aso n a b ly c o m p a ra b le w ith la te r se n te n c e -p ic tu re v erificatio n tasks a n d will serve to illus­ tra te the u su a l findings. In one o f the e x p erim e n ts su b je cts w ere given a verification task in w hich o n e o f th e four types o f sen ten ce w ould be p re sen te d a n d th e su b je ct re q u ire d to m ake a tru e /fa lse ju d g m e n t as quickly as possible. T h e o th e r e x p erim e n t, how ever, involved a construction task on w hich th ere has been little su b se q u e n t w ork. In this task th e su b je ct w as given a n in co m p lete sen ten c e w ith o r w ith o u t a neg ativ e, ‘ . . . is (n o t) a n even n u m b e r’, a n d in stru cte d to fill in a n u m b e r e ith e r to m ak e the sen ten ce tru e o r to m ake it false. T h u s, in a ra th e r different sense, we a g a in h a v e th e four categories, T A , FA , T N , FN . T h e c o n stru c tio n task re su lts show ed th a t b oth falsity a n d n e ­ g a tio n slow ed laten cies in a d d itiv e fashion, the o verall o rd e r being T A < F A < T N < F N . O n th e verificatio n task latencies, how ever, there w as no c le ar effect o f falsity, only o f n e g atio n . E rro r scores suggested th a t th e T N w as harder th a n the FN . M a n y su b se q u e n t exp erim en ts have, how ever, c onfirm ed th a t such a n interaction be­ tw een p o larity a n d tru th values o ccu rs reliab ly on the v erification latencies. A la te r e x p e rim e n t by W aso n a n d J o n e s (1963) in clu d ed a re p etitio n o f this c o n d itio n w ith a u to m a tic tim in g (a sto p -w a tch w as used in th e o rig in a l stu d y ). W h ile false affirm atives w ere c o n ­ sid erab ly slow er to p rocess th a n tru e affirm atives, th e false negative w as a c tu a lly slightly quicker th a n the tru e negative. T h is in te ra c tio n has been co n sisten tly found in su b se q u e n t se n te n c e -p ic tu re verifi­ cation tasks p ro v id ed th a t (a) th e sen ten ces a re p re se n te d before the p ictu res a n d (b) the n e g a te d va lu e s a re not c o n v erted by the subject in to a n e q u iv a le n t affirm ativ e form (see T ra b a sso , 1970). S u b seq u e n t stu d ies h a v e u su ally found a significantly fa ster ju d g ­ m ent on th e F N th a n th e T N (e.g. C la rk a n d C h a se , 1972; J u s t a n d C a rp e n te r, 1971, b u t not G o u g h , 1966). T h is m ay be less c le a r on

Sentence verification

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th e W a s o n s tu d ie s b e c a u s e th e n e g a tiv e s are r e c o d a b le (e.g . ‘n o t e v e n ’ = ‘o d d ’). T h e a d d itiv e a n d in te ra c tiv e effects a r e sh o w n s c h e m a tic a lly in F ig u re 3 .1 . N o te t h a t in e ith e r c a s e b o th n e g a tiv e c o n d itio n s a re slo w e r t h a n b o th a ffirm a tiv e c o n d itio n s . W a s o n (1 9 6 1 ) a c c o u n ts for th e d is c re p a n c y b e tw e e n c o n s tr u c tio n a n d e v a lu a tio n ta s k s a s follow s. O n th e c o n s tru c tio n ta s k o n e first o f all th in k s o f a n u m b e r w h ic h w ill m a k e th e s ta te m e n t tr u e , a n d th e n re v e rse s it i f th e in s tr u c tio n is to m a k e th e ru le false. T h u s o n b o th a ffirm a tiv e a n d n e g a tiv e p r o b le m s th e false ta s k ta k e s lo n g e r.

F IG U R E 3.1 S c h e m a tic re p re s e n ta tio n s o f a d d itiv e a n d in te ra c tiv e effects in re sp o n se la te n c ie s, for d ifferen t ty p es o f se q u e n c e

TA

FA

TN

FN

FA

TN

FN

(a) A d d itiv e effect

TA (b) I n te ra c tiv e effect

28

Elementary reasoning tasks

O n th e v erification task , how ever, it is th e T N ra th e r th a n the FN w hich involves a d o u b le negative. T h e four types o f sen ten c e can be defined as follow s (W aso n , 1980). T ru e False T ru e False

affirm ative - a fact affirm ative - a falsehood n egative — a d e n ia l o f a falsehood n egative - d e n ia l o f a fact

T h e F N , e.g. ‘6 is n o t a n even n u m b e r ’ is easily p erceived since it is evid en t th a t 6 is a n even n u m b e r, so th e negative m akes it false. T h e T N , e.g. ‘7 is not a n even n u m b e r ’ is h a rd e r since o n e m ust delete the n egative, decid e the sen ten c e is false, th en b rin g the n egative back to d ecid e th a t is, a fte r all, tru e. T h u s a n e x tra step o f p rocessing is re q u ire d . T h e in te rp re ta tio n o f the p o la r ity /tru th v alu e in te ra c tio n , a n d the conditions u n d e r w hich it occurs, will be explored fu rth e r in the section on in fo rm a tio n -p ro c essin g m odels. T h e p o in t to n o te h ere is th a t th e verification task does n o t p ro v id e a 'p u r e ’ m e a su re o f the difficulty o f c o m p re h e n d in g the n egative. T h e latency d e p e n d s not only on th e p resen ce o f th e neg ativ e, b u t also on th e n a tu re o f the task th a t one is re q u ire d to perfo rm w ith it. I f c o m p re h en sio n processes a re n o t in d e p e n d e n t o f o p e ra tio n a l re q u ire m e n ts on such a sim ple re aso n in g task, it is h a rd ly to be exp ected th a t th ey w ould be so on the m ore com plex tasks to be discu ssed la te r in the book. W a so n ’s orig in al in te n tio n w as to in v estig a te the w ays in w hich positive a n d negative information could best be c o m m u n ic a te d (see W ason, 1980). H e w as not, as is often su p p o sed , co n ce rn ed w ith ‘tran sfo rm a tio n a l co m p le x ity ’, for C h o m sk y ’s theo ries h ad h a d little im p a c t on B ritish psychology a t th is tim e. A n A m e ric an lite ra tu re c oncerned w ith C h o m sk y ’s (1957) th eo ry d id , how ever, d ev elo p in p arallel, a n d should also be c o n sid ere d as p a rt o f the ‘sy n ta c tic ’ ap p ro ac h . T h is line o f w ork w as in itia te d by G eorge M iller. T h e basic idea w as th a t if C h o m sk y ’s th eo ry h a d ‘psychological re a lity ’ th en tr a n s ­ form atio n al com plexity - p resen ce o f negatives, passives etc. should re q u ire a d d itio n a l cognitive sp a c e a n d p rocessing tim e. In the early e x p erim e n ts (M iller, 1962; M iller a n d M c K e a n , 1964) he tried to m ea su re ‘tra n s fo rm a tio n tim e ’ by a su b tra c tio n m eth o d . Subjects w ere show n a sen ten ce in e ith e r kernel (a sen ten c e w ith o u t

Sentence verification

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tran sfo rm a tio n s - sim ple, active, affirm ative, d e c la ra tiv e ), negative, passive, o r passive n eg ativ e form a n d asked to find a ‘m a tc h ’ in a list o f sen ten ces, e ith e r in th e sam e form , o r in one o f th e o th ers. T ra n s fo rm a tio n tim e w as tak e n to be th e difference b etw ee n the tim e tak e n to m a tc h a sen ten ce to itself, a n d to a tran sfo rm a tio n a lly different version. F o r ex am p le, th e difference betw een th e tim e tak en to m atc h a kernel to its n eg ativ e a n d to m a tc h a kernel to itse lf w as taken as th e n eg atio n tim e. I f th e passive a n d passive n egative tim es are co m p u te d sim ilarly , th en the differences betw een those should also e q u al th e sa m e n eg atio n tim e. T h e re su lts u sin g this o dd tec h n iq u e w ere q u ite e n co u ra g in g , b u t the early o p tim ism w as soon to be d isc o u rag e d . S tu d ies by G ough (1965, 1966) a n d Slobin (1966) w ere a m o n g the first to use the se n ten c e-p ic tu re v erification task w h ich su b seq u e n tly b ecam e so p o p u lar. In line w ith M iller, these stu d ies found th a t b o th negatives an d passives slow ed do w n p rocessing tim e, b u t th a t the effect w as m uch stro n g e r for negatives. T h is in itself is a w k w ard for the lin ­ guistic theory since th e p assive involves fa r m o re com plex re ­ a rra n g e m e n t o f th e kernel, a n d hence suggests th a t som e a d d itio n a l semantic difficulty w as also asso ciated w ith the neg ativ e. G ough (1966) also in tro d u c e d a th ree-seco n d d elay betw een th e sentence an d the p ic tu re to allow tra n s fo rm a tio n a l d e co d in g to be com plete. T h e effect o f n eg ativ es a n d passives d id not, how ever, d isa p p e a r from the verificatio n latencies. Som e ev idence for the tra n s fo rm a ­ tional co m p lex ity h y p o th esis w as also claim ed o n the basis o f m em ­ ory tasks (e.g. S avin a n d P erchoneck, 1965; M ehler, 1963), b u t su b se q u e n t re sea rc h suggested th a t e rro rs in recall a re b e tte r ex­ plained in term s o f su b je c ts’ re ta in in g the essential meaning o f w h at is p re sen te d , irresp ectiv e o f its g ra m m a tic a l form (e.g. F ille n b a u m , 1966; J o h n s o n -L a ird a n d S tevenson, 1970). A pow erful c ritiq u e o f all th ese kinds o f e x p erim e n t w as m a d e by G o ld m an -E isler a n d C o h e n (1970), w ho p o in t o u t th a t sentences co n ta in in g n eg ativ es a n d passives o c cu r far m o re in freq u e n tly in everyday lan g u a g e th a n ones w hich a re affirm ativ e a n d active. T h u s a sen ten ce-freq u en cy effect, a n alo g o u s to th e w ell-know n w ordfrequency effect, could be a n a rtifa c tu a l c au se o f th e o b serv ed c o m ­ preh en sio n a n d m em o ry deficits a sso ciated w ith tran sfo rm a tio n a lly com plex sentences. T h is ty p e o f re sea rc h w as, in an y case, set back by C h o m sk y ’s (1965) revision o f his o rig in a l theory, in w hich the

30

Elementary reasoning tasks

th eo retical basis for the tra n s fo rm a tio n a l com plexity h y p o th esis is far less c le ar (see G re en e , 1972). T h e o n e u n d isp u te d re su lt th a t all th ese e x p erim e n ts (a n d sim ila r su b seq u e n t ones) hav e in c o m m o n is th a t negatives a re reliably m ore difficult to process th a n affirm atives. I t seem s to m e th a t one pow erful a rg u m e n t a g a in st a sy n ta c tic e x p la n a tio n o f th is is th a t the difficulty o f n e g atio n seem s to be a c h a ra c te ris tic o f thought ra th e r th a n lan g u ag e. T h e difficulty o f u tilisin g negative information has been d e m o n s tra te d acro ss a w ide v a rie ty o f p a ra d ig m s. F o r exam ple, on c o n ce p t-id e n tifica tio n tasks, su b jects find it h a rd e r to learn from negative as o p p o sed to positive in stan c es (e.g. Sm oke, 1932; H o v la n d a n d W eiss, 1953; B ru n e r, G o o d n o w a n d A u stin , 1956). S u b jects find it h a rd to c o n stru c t o r solve c oding p ro b lem s w here they hav e to m ake use o f n e g ativ e in fo rm a tio n (W hitfield, 1951; D o n a ld so n , 1959, C a m p b e ll, 1965). S ubjects also find it dif­ ficult to refute h y p o th eses on tasks w h ere they need to g e n era te negative in stan c es in o rd e r to do so (see W aso n a n d Jo h n s o n -L a ird , 1972, a n d also M iller, 1967, M y n a tt, D o h e rty a n d T w e n ey , 1977) an d so on. W e will now c o n sid er stu d ies th a t w hile in v estig a tin g n egatives an d passives in a lin g u istic c o n te x t, recognised th a t they m ay serve a sem an tic function.

Semantic factors in sentence verification W ason (1959) suggested a se m a n tic a sp e c t o f negatives, in th a t they m ight evoke u n p le a sa n t em o tio n al c o n n o ta tio n s d u e to a sso ciatio n w ith p ro h ib itio n in ch ild h o o d . T h e ev idence claim ed in su p p o rt for this h ypothesis has, how ever, been m ost ten u o u s a n d u n sa tisfac to ry . F o r exam ple, E ife rm a n n (1961) re p e a te d W a so n ’s (1961) e x p eri­ m ents in H e b rew using one o f tw o negatives ‘lo’ a n d ‘e n y o ’, the la tte r o f w hich is nev er used in a p ro h ib itiv e co n tex t. As p re d ic te d , th ere w as som e evidence th a t ‘e n y o ’ w as p rocessed faster, b u t th ere is no w ay o f d e te rm in in g w h a t a sp e ct o f the linguistic difference betw een the tw o w o rd s is responsible. T h e o th e r type o f ev idence th a t has been offered for the e m o tio n ­ ality hyp o th esis is th a t im p licit negatives a re faster to process th a n explicit n egatives. T h e idea is th a t the im plicit negative c arries the sam e logical fu n c tio n a n d in fo rm a tio n -p ro c essin g re q u ire m e n ts (see

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C a r p e n te r a n d J u s t , 1975) b u t lacks th e e m o tio n a l c o n n o ta tio n s . W a so n a n d J o n e s (1963) sh o w ed th e n e g a tio n difficu lty w as re d u c e d by tra in in g su b je c ts to use a n o n se n se w o rd to serv e as a n e g ativ e (D A X = ‘is n ’t ’). T h e ir c la im th a t th is w as d u e to lac k o f e m o tio n a l c o n n o ta tio n h a s su b s e q u e n tly b e en w ith d ra w n o n th e g ro u n d s th a t th e re su lt c o u ld be a n a rtifa c t o f sp e c ia l s tra te g ie s a d o p te d (see W a so n a n d J o h n s o n - L a ir d , 1972; W a s o n , 1980). F u r th e r e v id e n c e for th e h y p o th e s is w a s c la im e d b y J o n e s (1966a; 1966b; 1968) u sin g n o t a v e rific a tio n ta s k b u t a d ig it-c a n c e llin g task. H e r b a sic fin d in g w a s th a t in s tru c tio n s s u c h a s 'D o n o t m a rk 3, 5, 7, m a rk all the re s t’, took lo n g e r to c a rry o u t th a n in stru c tio n s o f th e fo rm ‘M a rk all n u m b e rs e x ce p t 3, 5, 7’. O n e difficu lty o f in te rp re tin g J o n e s ’s re su lts is th a t o n e c a n n o t tell w h e th e r th e e x tra d ifficulty o f th e e x p lic it n e g a tiv e lies in c o m p re h e n d in g it, o r c o m ­ p ly in g w ith it. A re c e n t e x p e rim e n t r u n by P h ilip B rooks, in m y o w n d e p a r tm e n t, u se d a s e n te n c e -p ic tu re v e rifica tio n task a n d se p ­ a ra te d c o m p re h e n s io n tim e s (C T ) from v e rifica tio n tim e s (V T ) th e fo rm e r m e a s u re d th e tim e th a t su b je c t u se d to re a d a n d u n d e r ­ s ta n d th e in s tru c tio n b efo re th e p ic tu re w a s p re s e n te d . E x p lic it n e g ativ es s u c h a s ‘R e sp o n d tru e to all sh a p e s w fiich a re n o t g re en o n e s’ w ere c o m p a re d w ith im p lic its su c h a s ‘R e sp o n d tru e to all sh a p e s e x ce p t th o se w h ic h a re g re e n ’. T h e re su lts w e re c o m p lic a te d by in te ra c tio n s w ith th e o r d e r o f p re s e n tin g task s. H o w e v e r, w h e re d ifferences b e tw e e n th e tw o ty p es o f n e g a tiv e e m e rg e d , th ey w ere d ifferen t in th e tw o a n a ly se s. O n V T o u r su b je c ts, like J o n e s ’s, te n d e d to be slo w e r in c a rry in g o u t a n e x p lic itly n e g a tiv e in s tr u c ­ tion. H ow 'ever, on C T s u b je c ts a p p e a re d to u n d e rs ta n d th e e x p lic it form m o re q u ick ly . J o n e s ’s d ig it-c a n c e llin g task w o u ld be h eav ily lo ad e d o n V T , o f c o u rse. I t is n o t c le a r w hy th ese d isc re p a n c ie s sh o u ld a ris e , b u t th e re s u lt o f o u r C T a n a ly se s m ig h t in d ic a te a n a d d itio n a l lin g u istic c o m p le x ity o f th e im p lic it form , a n d a n e m o ­ tio n a lity effect c a n n o t be ru le d o u t. In m y view , th e m o st im p o r ta n t s e m a n tic c h a ra c te ris tic o f n e ­ g a tio n lies in th e p r a g m a tic a s p e c t first d isc u sse d by W a s o n (1965). H e p o in ts o u t th a t a s ta te m e n t su c h a s ‘T h e tra in w as n o t la te this m o rn in g ’ im p lie s th a t th e tra in n o rm a lly is late . F u r th e r , it is a n o m ­ alous to sa y th a t ‘A h o rse is n o t a fish ’ b u t se n sib le to sa y t h a t ‘A w h ale is n o t a fish ’. In th e 1965 p a p e r W a so n w as m a in ly c o n c e rn e d w ith th e id e a th a t a n e g a tiv e is n o rm a lly u se d to d e n y so m e th in g

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w hich is ex cep tio n al in its c o n te x t (like w hales a n d fish), a n d p ro ­ duced e x p erim e n tal ev idence on a n a rtificial task to su p p o rt this. S ubjects w ere show n a d isp lay o f n u m b e re d coloured lig h ts in w hich (say) seven w ere red a n d o n e w as blue. W aso n a rg u e d th a t a negative o f the form ‘N o 3 is not re d ’ w as m o re ‘n a tu r a l’ th a n one o f the form ‘N o 5 is n o t b lu e ’. Since the g e n era l c o n te x t is red , th en it is only n a tu ra l to use a n e g ativ e to in d ic a te a n exception. T h e latency a n aly sis su p p o rte d th is ‘e x ce p tio n a lity h y p o th e sis’ b u t not a n a lte rn a tiv e ‘ra tio h y p o th e sis’. H o w ev er, W aso n no lo n g er co n ­ siders the la tte r to be a correctly d eriv ed p re d ic tio n from th e p ra g ­ m atic a rg u m e n t (see W aso n , 1980). A m ore g e n era l form o f this a rg u m e n t discu ssed by W aso n (1972), is th a t the n egative is n o rm ally used to d e n y a p rio r belief. W e do not use a n e g ativ e to a sse rt new in fo rm a tio n , a n d as m en tio n ed earlier, p e rfo rm a n ce o n a v a rie ty o f cognitive tasks is im p e d e d by such ‘u n n a tu r a l’ usage. W e use a n e g ativ e to say so m e th in g a b o u t a p rio r o r presupposed affirm ative, nam ely th a t it is false. G reene (1970a, 1970b) sim ilarly a rg u e d th a t a negative has a se m an tic fu n ctio n o f ‘sig n allin g a c h a n g e in m e a n in g ’. F o r ex am p le, given the sentence: x exceeds y it is ‘n a tu r a l’ to d e n y th is by a n e g ativ e such as: x does n o t exceed y b u t ‘u n n a tu ra l’ to affirm it by a n eg ativ e su c h as y does n o t exceed x In h e r e x p erim e n t she m e a su re d su b je c ts’ latencies to decid e if tw o sen ten ces m ea n the sam e th in g o r not. W ith p assive sentences she a rg u e d th a t the o p p o site effect sh o u ld occur: a passive w hich re ta in s m ea n in g (y is exceeded by x) is m o re ‘n a tu r a l’ th a n one th a t differs (x is exceeded by y). As p re d ic te d , the ‘n a tu r a l’ sen ten ce p airs w ere processed fa ster in e ach case. W h e th e r this is d u e to ‘se m an tic fu n c tio n ’ o f th e sen ten ce form s is, how ever, d e b a ta b le . So far as the n eg ativ es a re c o n ce rn ed , G re en e w as effectively re p lica tin g the gen eral fin d in g th a t a false n eg ativ e is processed fa ster th a n a

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tru e negative: a p o in t to w hich we shall re tu rn in the next section. T h e fin d in g th a t T ru e Passives a re processed fa ster th a n False Passives m ig h t also be a cc o u n ta b le in term s o f in fo rm a tio n -p ro cessing differences. W ith th e benefit o f th e h in d sig h t ach iev ed by c o n sid eratio n o f th e in fo rm a tio n -p ro c essin g m odels dev elo p ed late r, G re en e ’s p a p e rs seem so m e w h a t naive. She a ssu m es, in effect, th a t p erfo rm an ce on a v erificatio n task is a d ire c t fun ctio n o f c o m p re ­ hension processes, w ith o u t reference to re aso n in g o p e ratio n s. N e v er­ theless, no one seem s to d o u b t th a t negatives do n a tu ra lly seem to deny p re su p p o sitio n s, in clu d in g the lea d in g a d v o c a te o f the in fo rm a tio n -p ro c essin g a p p ro a c h , H . C la rk (see C la rk a n d C lark , 1977). Before e x am in in g these m odels, let us c o n sid er briefly th e se m a n ­ tic function o f the passive. I f we a cc ep t G re e n e ’s a rg u m e n t th a t it is not to a lte r m ea n in g , th en w hy sh o u ld the p assive voice exist at all? A m ore re aso n a b le view is th a t w hile th e p assive does not drastically a lte r th e m ea n in g , as th e n eg ativ e does, it m akes a su b tle change. Jo h n s o n -L a ird (1968a; 1968b) suggested th a t th e passive is used to e m p h a sise th e logical ob ject o f the sen ten ce. I f we take a sim ple active sen ten c e as follows: T h e boy h it th e girl ‘B ov’ is b o th th e g ra m m a tic a l (surface stru c tu re ) a n d logical (deep stru c tu re ) su b je ct, w hile ‘g irl’ is th e g ra m m a tic a l a n d logical object. In the p assive form : T h e girl w as h it by the boy the logical o bject is now th e g ra m m a tic a l su b je ct a n d vice versa. J o h n s o n -L a ird ’s a ssu m p tio n th a t the passiv e is used to em p h a sise the logical o bject is su p p o rte d by a r a th e r o dd e x p erim e n tal te c h ­ nique. S u b je cts w ere re q u ire d to d e cid e w hich o f v a rio u s coloured strip s w ere b e tte r d e sc rib e d by sen ten ces such as ‘R ed is follow ed by B lue’, on th e a ssu m p tio n th a t a la rg e r a re a o f c o lo u r w o u ld be m atc h ed to the m ore ‘im p o rta n t’ p a rt o f the sentence. T h is a s ­ su m p tio n , a n d c o n se q u en tly J o h n s o n - L a ird ’s c onclusion, h a s been recently c h allen g e d by C o ste rm a n s a n d H u p e t (1977); an d J o h n s o n -L a ird (1977) h a s replied. In conclusion to th is section, it sho u ld be seen th a t w hile a rg u ­

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m ents for th e se m a n tic fu n ctio n o f negatives a n d passives seem plau sib le a n d have, in fact, g a in e d w ide acc ce p tan c e, th e e x p eri­ m en tal evidence on w h ich they rest is ra th e r w eak. T h e m a in p ro b ­ lem w ith th e stu d ies co n sid ered is a failu re to c o n sid er th e o p e ra tio n s req u ire d for th e so lu tio n o f the e x p erim e n tal tasks. W e now look at a tte m p ts to d eal w ith this la tte r p ro b lem .

The information-processing models In fo rm atio n -p ro c e ssin g m odels o f sen ten c e verificatio n first a p p ea red in conference p a p e rs by T ra b a s s o (1970) a n d C la rk (1970). T h e tw o a u th o rs a p p e a re d in d e p e n d e n tly to have devised logically e q u iv a len t m odes. T ra b a s s o ’s p a p e r is m ore co m p lete in th a t he deals w ith W a s o n ’s c o n stru c tio n -ta sk d a ta as well as the verification task. H e w as also th e first to p o in t o u t th a t the o rd e r o f p re sen tin g th e p ic tu re a n d sen ten ce w as im p o rta n t. C la rk ’s m odel w as m o re precisely fo rm u la ted , how ever, a n d after its su b se q u e n t p u b lic a tio n in a n e x p a n d e d form by C lark a n d C h a se (1972), it becam e the best-know n a n d m ost w idely cited m odel o f this kind. T h e ir p a p e r will be d e sc rib e d in som e d e ta il to illu stra te this type o f a p p ro a c h . C lark a n d C h a se p re se n t tw o m odels: M o d el A to a c c o u n t for ex p erim en ts w here th e sen ten c e is p rocessed before th e p ic tu re , a n d M odel B to a c c o u n t for the reverse situ a tio n . B oth m odels, how ever, in co rp o ra te a g e n era l n o tio n o f a se q u e n tia l stra te g y m oving th ro u g h a series o f fixed stag es, a n d m ake th e stro n g a ssu m p tio n th a t the total resp o n se tim e is th e sim p le a d d itio n o f th e tim e tak e n a t each stage. T h is g e n era l m o d el w hich is also a p p lic a b le to d e d u ctiv e tasks is illu stra te d in F ig u re 3.2. T h e y fu rth e r assu m e th a t re p re ­ sen tatio n o f b oth p ictu res a n d sen ten ces takes place by enco d in g the stim u lu s in to a co m m o n , a b s tra c t p ro p o sitio n a l code. A fter this encoding has been co m p le te d , c o m p a riso n s a re then m ad e on the p ro p o sitio n a l re p re se n ta tio n s. T h u s th e ir p a p e r c o n stitu te s a d irec t a p p lic atio n o f p ro p o sitio n a l theory (discussed in C h a p te r 2) to a reasoning task. T h e a c tu a l fo rm u la tio n o f th e ir m odels is very specific to th eir p a ra d ig m , w hich m u st be ex p la in ed . S u b jects in th e first e x p e rim e n t w ere show n a d isp lay w h ich h a d a se n ten c e on th e left a n d a p ictu re on the rig h t. T h e re w ere tw o types o f p ic tu re sh o w in g e ith e r a s ta r

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FIG U R E 3.2 A general sequential strategy which is implied by various models of sentence verification and reasoning

a b o v e a p lu s o r vice v e rsa . S e n ten c es w e re e ith e r a ffirm a tiv e e.g. ‘s ta r is a b o v e p lu s ’ o r n e g a tiv e e.g. ‘p lu s is n ’t below s t a r ’. S u b je cts w'ere re q u ire d to d e c id e as q u ick ly as p o ssib le w h e th e r o r n o t the d isp la y w'as ‘tr u e ’ (se n te n c e m a tc h e s th e p ic tu re ) o r ‘false’ (se n ten c e d o e s n ’t m a tc h th e p ic tu re ). M o d e l A a s su m e d th a t th e se n te n c e w as p ro c essed first, a n d h a s th e fo llow ing ‘a d d itiv e ’ sta g es.

Stage 1 - Representation o f sentences I t is a ssu m e d th a t a ffirm a tiv e s a re e n c o d e d a s e le m e n ta ry p ro p o s i­ tio n s, a n d n e g a tiv e s a re e n c o d e d a s false a ffirm ativ es. A ssu m in g a p ic tu re sh o w in g A a b o v e B th e fo u r logical p o ssib ilities a re as follow s:

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TA FA TN FN

Sentence A is above B A is below B A isn ’t below B A isn ’t above B

Representation (A above B)* (B below A) (false (A below B) (false (A above B)

T h ese re p re se n ta tio n s consist o f a n in n e r strin g (A above B), etc., plus a n o u te r strin g , w hich c o n ta in s a m a rk e r for falsity in th e case o f negatives, a n d is im p licit in th e case o f affirm atives. C la rk a n d C h ase assu m e th a t e n co d in g a n eg ativ e will take longer th a n e n ­ coding a n affirm ativ e by a c o n sta n t a m o u n t. T h e y also a ssu m e th a t ‘above’ is a m ore n a tu ra l w ay o f en co d in g v e rtica lity th a n ‘below ’ an d c o n se q u en tly a ssu m e th a t a n a d d itio n a l in c re m e n t will be re ­ q u ired for the la tte r stage.

Stage 2 - Representation o f pictures It is assu m e d th a t th e p ic tu re is en co d ed as e ith e r (A above B) or (B below A) a cc o rd in g to the c o m p a ra tiv e used in th e sen ten ce re p re se n tatio n . C la rk a n d C h a se c o m m e n t As for latency p re d ic tio n s one m ig h t a ssu m e a priori th a t the above re p re se n ta tio n sh o u ld be fa ster to c o n stru c t th a n th e below re p re se n ta tio n ju s t as in S tage 1. B u t since th e tw o codes have been found em p irica lly to tak e a p p ro x im a te ly eq u al a m o u n ts o f tim e to c o n stru c t (cf. E x p erim en t II a n d C lark a n d C h a se , in p re p a ra tio n ) M o d el A m akes no provision for the different encoding laten cies o f above a n d below in S tage 2. T h is ra th e r e x tra o rd in a ry re m a rk reveals th e fact th a t w hile the m odels are presented p rio r to the e x p e rim e n t d a ta , they w ere clearly c o n stru cted on a post hoc basis.

Stage 3 - Comparison o f sentence and picture representations C lark a n d C h a se p ro p o se tw o su b sta g e s, involving co m p a riso n o f the in n e r strin g s follow ed by c o m p a riso n o f th e o u te r strin g s. T h e * C lark ’s cu rren t no tation gives A B O V E (A ,B ), etc.

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subject is su p p o sed to have a ‘tru th in d e x ’ set initially to the v alue T ru e . E very tim e a m ism a tch is found the v a lu e o f the ind ex is reversed from T ru e to F alse o r from F alse back to T ru e . T h e o p e ratio n s a t this stag e can be d e scrib ed as follows: Operation I C o m p are in n e r strin g s. I f they m a tc h p roceed to O p e ra tio n 2. I f not proceed to O p e ra tio n la . Operation la R everse tru th index. P roceed to O p e ra tio n 2. Operation 2 C o m p are o u te r strin g s. I f they m a tc h proceed to resp o n se stage. I f not proceed to O p e ra tio n 2a. Operation 2a R everse tr u th index. P roceed to resp o n se stage. T h e o p e ra tio n s d e sc rib e d lea d to p re d ic tio n o f th e in te ra c tio n betw een tr u th v a lu e a n d p o larity n o rm ally o bserved on th e verifi­ c ation task (cf. th e e a rlie r section on sy n ta ctic factors). T h is is illu stra te d in T a b le 3.2. I t can be seen th a t the T A is q u ick e r th an the FA because b o th o p e ra tio n s 1 a n d 2 lead to m atc h es, a n d so n e ith e r reversal o f th e tru th index l a o r 2a is necessary. FA , o n the o th er h a n d , m ism a tch e s a t o p e ra tio n 1 so re q u ire s th e a d d itio n a l tim e for la . T h e F N is q u ick e r th a n th e T N because it m atc h es a t stage 2 w hen the a d d itio n a l ‘false’ in the o u te r strin g o f the sen ten ce re p re se n ta tio n is d e te cte d . T h e c o m p a riso n sta g e th u s p re d ic ts the n o rm ally o bserved in terT A B L E 3.2 Operations required at the comparison stage in Clark and Chase’s (1972) Model A , for the different logical types o f problem S entence rep resentation

P icture representation

O perations

TA FA

(A above B) (A below B)

(A above B) (B below A)

1,2 1,1 a ,2

TN FN

(false (A below B)) (false (A above B))

(B below A) (A above B)

1,1a,2,2a 1,2,2a

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action, a n d processes on e n co d in g a n d c o m p a riso n stages p re d ic t the a d d itio n a l finding th a t n eg ativ es a re slow er th a n affirm atives. It should be noted th a t th e e x p la n a tio n o f w hy th e FN is easier th a n the T N is no m ore th a n a fo rm alisatio n o f the e x p la n a tio n o f W aso n (1961) d escrib ed e a rlie r in this c h a p te r. It does, how ever, m ake a m ore specific p re d ic tio n . All else bein g e q u a l the difference in p ro ­ cessing tim e betw een FA a n d T A sh o u ld be e q u a l to th e difference betw een T N a n d F N (i.e. the tim e tak en to execute o p e ra tio n la ).

Stage 4 - Response production T h e tr u th in d ex is c o n v erted in to a re sp o n se T ru e o r F alse. T h is stage is su p p o sed to a d d a c o n sta n t in c re m e n t to the to ta l response tim e. T h e m odel d e sc rib e d (M o d el A) m akes very specific p re d ic tio n s. T o a g e n era l pro cessin g tim e t0, a n u m b e r o f in cre m e n ts m ay be a d d ed a t e ith e r the R e p re se n ta tio n o r C o m p a riso n stage. C la rk a n d C h ase assign p a ra m e te rs to these tim e c o m p o n e n ts a n d e stim a te them by su b tra c tio n o f to ta l pro cessin g tim e o f v a rio u s sentences. T h e resu lts o f th e ir e x p erim e n ts seem to p ro v id e fairly good evidence for th eir p re d ic tio n s, a n d the p a ra m e te rs d o seem to be a d d itiv e , ra th e r th a n in te rac tiv e . O n e o f the p ro b lem s o f fo rm u la tin g a m odel in su ch p recise term s is th a t it is very p a ra d ig m specific. As soon as slig h t a lte ra tio n s o f the p a ra d ig m a re in tro d u c e d , the m odel h a s to be revised. W7e will consider tw o exam p les. T h e first re la te s to reversing th e o rd e r o f p re sen tin g th e sen ten ce a n d th e p ictu re. A s C la rk a n d C h a se (1972) com m ent ‘M odel A c a n n o t a p p ly to th e p ictu re-first task w ith o u t m o dification, b ecau se it assu m e s th a t th e co d in g o f th e p ic tu re is c o n tin g en t on the co d in g o f th e se n te n c e ’. T h u s they d ev elo p M odel B to cope w ith this o th e r situ a tio n . In M odel B it is assu m e d th a t the p ic tu re is alw ays encoded in term s o f above d u e to linguistic preference (d irec t ev idence for th is a ssu m p tio n is p ro v id ed by C lark an d C h a se , 1974). T h e artificiality o f the m odels is illu stra te d by the fact th a t C lark a n d C h a se a re also forced to m odify the comparison stage. T o d e te rm in e a m a tc h o r m ism a tc h o f the in n e r strin g s in M odel A th ey suggested th a t su b je cts c o m p a re only th e su b je ct o f the in n e r strin g . T h is is b ecau se th e c o m p a ra tiv e above o r below is g u a ra n te e d by the m odel to be id en tica l in e ac h re p re se n ta tio n . In

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M odel B this is not necessarily the case, so a m odified c o m p a riso n rule is in tro d u c e d . E vidence for M odel B is p ro d u c ed b o th in the original p a p e r a n d a la te r stu d y (C lark a n d C h a se , 1974). A second e x am p le o f how p a ra d ig m specific the m odels are is illu stra te d by th e e x p la n a tio n offered for th e finding th a t som etim es the o rd e r o f difficulty o n the v erification task is n o t in te ra c tiv e b u t a d d itiv e (cf. F ig u re 3.1). T h is a d d itiv e re su lt is, for ex am p le, o b ­ tain ed by highly p ra c tise d su b je cts in th e stu d y o f T ra b a sso , R ollins an d S h a u g h n e ssy , (1971). T ra b a s s o a n d C la rk a re b o th in a g ree ­ m ent th a t this is d u e to conversion o f the negative. W h ere a negative refers to a b in a ry d im e n sio n , it m ay be recoded, e.g. not even = odd. W e hav e a lre a d y n o ted th a t th is m ig h t have a cc o u n te d for the w eaker th a n n o rm a l in te ra c tio n o bserved in the W aso n a n d J o n e s (1963) stu d y . I t is q u ite sim p le to see how , for ex am p le, C la rk a n d C h a se ’s M o d el A w ould p re d ic t a n a d d itiv e result if th e n eg ativ e is converted. In ste a d o f re p re se n tin g the sen ten ce 'A isn ’t above B’ as (false (A above B) ), it w ould be re p re se n ted as (A below B) o r (B above A ). T h is m e a n s th a t a t the c o m p a riso n sta g e the su b ject is dealing, in effect, w ith affirm ative re p re se n ta tio n s only, so th a t the false s ta te m e n t will alw ays take longer th a n the true irresp ectiv e o f w h e th er th e o rig in a l sen ten ce w as affirm ativ e o r negative. T h e a d d itio n al pro cessin g tim e o f the negative w ould now be e xplained as the tim e tak en to c o n v ert it in to a n affirm ative form . E v idence th a t d a ta conform to th is m odified M odel A w hen su b jects a re instructed to m ak e conversions w as p ro d u c e d in a stu d y by Y oung an d C h a se (1971), d e sc rib e d by C la rk a n d C h a se (1972). M o re recently, J u s t a n d C a rp e n te r (1976a) hav e show n th a t types o f negatives w hose v erification d a ta a re co n sisten t w ith conversion tend to be su b seq u e n tly recalled in a c o n v erted form . It w as o bserved th a t som e o f the e a rlie r stu d ies o f verification tasks a ssu m e d th a t pro cessin g tim e is a d ire c t fu n c tio n o f c o m p re ­ hension processes. T h e C la rk a n d C h a se m odel a cc o u n ts for the d a ta w ith a m ix tu re o f c o m p re h en sio n a n d v erification p a ra m e te rs. T h e m odel o f C a rp e n te r a n d J u s t (1975) a tte m p ts to a cc o u n t for results in term s o f re aso n in g o p e ra tio n s alone. T h e ir m odel is sim ila r to th a t o f C la rk a n d C h a se in a ssu m in g a re p re se n ta tio n a l stag e w ith a p ro p o sitio n a l fo rm at, follow ed by c o m p a riso n a n d response stages. T h e n o tio n o f tr u th ind ex is also in co rp o ra te d . H ow ever, the m odel a c c o u n ts for differences betw een co n d itio n s w ith resp ect to a single p a ra m e te r, w hich is the n u m b e r o f o p e ra tio n s re q u ire d a t

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the c o m p ariso n stag e. In th is m odel it is assu m e d th a t w h e n ev e r a m ism atch is found in e ith e r the in n e r o r o u te r strin g s, th e tru th index is rev ersed , th e m is m a tc h in g strin g s ‘ta g g e d ’ a n d re co m p are d . In the fu rth e r c o m p a riso n th e c o n stitu e n ts now m a tc h ow ing to the tags. T h is m odel m akes th e very specific p re d ic tio n th a t response latencies will in crease linearly from T A to FA to F N to T N , since each successive case re q u ire s exactly one a d d itio n a l c o m p a riso n o p e ratio n to the one before. T h is re su lt is found in v a rio u s ex p eri­ m en ts w hich C a rp e n te r a n d J u s t them selves h a v e c a rrie d o u t, a n d a n u m b e r o f o th e r stu d ies w hich they cite. D isc re p a n t findings o f som e o th e r stu d ies a re a cc o u n te d for in term s o f p a rtia l conversion o f the neg ativ e a t th e e n co d in g stag e, w h ich leads to a different n u m b e r o f c o m p a riso n o p e ratio n s. C a rp e n te r a n d J u s t ’s (1975) m odel h a s led to a c e rta in a m o u n t o f controversy. T h e re hav e been criticism s p u b lish ed by T a n e n h a u s , C a rro ll a n d B ever (1976) a n d C a tlin a n d J o n e s (1976), w ith replies by C a rp e n te r a n d J u s t (1976) a n d S h o b en (1978). T h e m odel has been c riticised w ith re sp ec t to its a b ility to a cc o u n t for p a rtic u la r e x p erim e n tal re su lts, a n d also on th e g ro u n d s th a t it is p a ra d ig m specific, a n d th u s o f little g e n era l th eo re tic al in te rest. P e rh a p s the stro n g e st ev idence p ro d u c e d in favour o f the C a r­ p e n te r a n d J u s t m odel is th a t o f J u s t a n d C a r p e n te r (1976b). T h e y em ployed the r a th e r ingenious te c h n iq u e o f m ea su rin g the latency o f eye-fixations on the sen ten c e a n d the p ictu re. F o r e x am p le, they take the initial fixation p eriod on the sen ten c e as a m ea su re o f co m p reh en sio n tim e. H e re they found a slight in c re m e n t for n e g a ­ tive sentences, su g g estin g som e e x tra e n co d in g tim e in line w ith C lark a n d C h ase. H ow ever, they also find th a t th e tim e su b se ­ q u e n tly sp e n t gazin g a t th e lo ca tio n m en tio n ed in th e sen ten c e w as linearly re la te d to the n u m b e r o f m e n ta l o p e ra tio n s p o stu la te d to occu r a t th e c o m p a riso n sta g e o f th e ir ow n m odel (in th e o rd e r T A , FA , F N , T N ). H ow ever, th is re su lt w as n o t re p e a te d in e x p erim e n ts w hich in ­ stru c te d su b jects to c o m p re h e n d th e ru le before p re ssin g a key to receive th e in stan c e. T h e e x p e rim e n t ru n by B rooks, d e sc rib e d earlier, found no c le ar p a tte rn in th e V T a n aly sis c o rre sp o n d in g to C a rp e n te r a n d J u s t ’s p re d ic tio n . A lso in a stu d y by G lu sh k o a n d C o o p e r (1978) - w hich is d e sc rib e d in m ore d e ta il in a la te r section - the a u th o rs failed to find an y effect o f lin g u istic com plexity, including n e g atio n , a t th e V T stag e. M o re com plex evidence is

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offered by C a r r a n d B a c h a ra c h (1977) w ho c o m p a red sim u lta n eo u s p re se n ta tio n o f sen ten c e a n d p ictu re, w ith a c o n d itio n w here the p ictu re w as delay ed 4 -5 seconds (subjects co u n te d in the in te rv al to p re v en t re h e a rsa l). A fter a d e ta ile d an aly sis o f th e effect o f re ­ sponse re q u ire m e n ts in the d elay c o n d itio n , the a u th o rs conclude th a t the surface s tru c tu re o f the sen ten ce has no effect on the co m p ariso n sta g e o f the task. T h e valid ity o f the C a rp e n te r a n d J u s t m odel m u st, th en , be seriously q u e stio n e d . T h is a cc o u n t o f th e in fo rm a tio n -p ro c essin g m odels allow s one to form p recise criticism s o f G re e n e ’s (1970a; 1970b) con clusion th a t her resu lts in d ic a te d a n effect a risin g a t a c o m p re h en sio n stage. C o n sid e r one o f h e r sen ten c e p a irs c o n ta in in g a ‘n a tu r a l’ negative: x exceeds y x does not exceed y In term s o f C lark a n d C h a se these w ould be encoded as: (x exceeds y) (false (x exceeds y) ) T h u s th e c o m p a riso n h e re is th a t o f th e F N w ith only one m ism a tch arising. W ith a n ‘u n n a tu r a l’ p a ir such as: x exceeds y y does not exceed x the e ncoding w ould be: (x exceeds y) (false (y exceeds x) ) T h e c o m p a riso n here is as for T N , w ith m ism a tch e s a risin g in b o th in n er a n d o u te r strin g s. In the case o f the passives, p re su m a b ly th e ir d e ep stru c tu re (p ro p ­ ositional) re p re se n ta tio n w ould c o n ta in th e logical re la tio n sh ip plus a tra n sfo rm a tio n a l m ark e r. E.g. ‘x is exceeded by y’ m ig h t be coded as (PA SS (y exceeds x) ). Since the tw o sentences to be c o m p a red w ould be en co d ed se p a ra tely , a n d since b o th h er ‘n a tu r a l’ a n d ‘u n n a tu ra l’ p a irs c o n ta in o n e affirm ativ e a n d one passive, th en the

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encoding tim e w ould be th e sam e. A g ain , the difference can be explained a t the c o m p a riso n stage. Since the passive m a rk e r has no logical effect on tru th value, it can be ig n o red a t th is stage. H e n ce, the ‘n a tu ra l’ p assive p a ir is, in effect, a T A a n d the ‘u n n a tu r a l’ an FA. T h u s G re e n e ’s resu lt could be a sim p le c o n seq u en ce o f the reasoning o p e ra tio n s re q u ire d , a n d h e r n e g ativ ity effect d u e n o t to the se m an tic fu n ctio n o f a negative bein g ‘to signal a c h an g e in m ea n in g ’, b u t in ste a d to the fact th a t a negative tra n sfo rm a tio n reverses tr u th v alues, w h ereas a passive does not. E n co d in g a n d co m p a riso n m odels hav e in fact been a p p lie d to results o b ta in e d w ith p assive sen ten ces (see, for e x am p le, O lso n an d F ilby, 1972; V V annem acher, 1976), b u t sp a c e c o n sid era tio n s p reclu d e th e ir d iscussion here. It is m o re im p o rta n t, for o u r p u r ­ poses, to e x am in e the general a ssu m p tio n s a b o u t lan g u a g e a n d th o u g h t th a t u n d e rlie su c h m odels, th a n to p u rsu e d e ta ils o f the various ex am p les p ro life ratin g in the lite ra tu re . Before d o in g so, a few re m a rk s a re in o rd e r w ith re sp ec t to the c riticism th a t the m odels are p a ra d ig m specific. Som e o f th e e a rlie r stu d ies o f sen ten c e verification w ere criticised for m ak in g inferences a b o u t c o m p re h en sio n in th e ab se n ce o f a theory o f how the tasks a re p erfo rm ed . O n the o th e r h a n d , the m odels w h ic h specify the stra te g ies in d e ta il do seem to be ra th e r artificial a n d task specific. M y o b jectio n to the m odels arises from the fact th a t they a re d evised in too precise a m a n n e r, to p re d ic t d a ta in far too lim ited situ a tio n s. P o p p e r (1959) h as p o in te d o u t th a t th eo ries are m o re falsifiable, a n d h en ce o f m o re scientific value, w hen th e ir a ssu m p tio n s a re very g e n era l a n d th e ir p re d ic tio n s very specific. T h e C a rp e n te r a n d j u s t m odel is su p e rio r to th a t o f C la rk a n d C h a se in this resp ect, since it assu m es less a n d p re d ic ts m ore. H ow ever, b o th m odels w ere c o n stru c te d post hoc to fit a p a rtic u la r set o f resu lts, a n d th u s th e specific n a tu re o f th e ir p re d ic tio n s is n o t over-im pressive, even w hen a p p lie d to new v a ria tio n s w ith in the sam e p a ra d ig m . W h a t the a u th o rs o f su c h m odels d o not seem to do is to fo rm u la te a g en eral th eo re tic al fram ew ork, o f w hich th eir m odel is a p a rtic u la r a p p lic a tio n , a n d assess its v a lid ity acro ss a w ide variety o f e x p erim e n tal p a rad ig m s.

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Wider implications of the information-processing models T w o im p o rta n t g e n era l a ssu m p tio n s seem to u n d e rlie th e use o f the in fo rm a tio n -p ro c essin g m odels. T h e first, illu stra te d by F ig u re 3.2. is the su p p o sitio n o f se q u e n tial stra te g ies. As we shall see, this conception is highly p o p u la r w ith m an y th eo rists w ho a p p ly th e m ­ selves to th e v a rio u s re aso n in g p a ra d ig m s d escrib ed th ro u g h o u t this book. T h e g e n era l n o tio n is th a t re aso n in g tasks hav e tw o m ain stages. T h e first, c o m p re h en sio n (re p re se n ta tio n , e n co d in g ), stage, req u ires a re p re se n ta tio n o f the in fo rm a tio n p re sen te d . T h e second, reasoning (processing, o p e ra tin g ), stag e, involves o p e ra tio n s being carried o u t on th e re p re se n ta tio n a rriv e d a t in th e first stage. T h is fu n d a m e n ta l n o tio n a b o u t the n a tu re o f re aso n in g is intuitively appealin g . As N eisser (1963) p o in ts o u t, th e th in k in g th a t we are conscious o f a p p e a rs to be in trin sic ally se q u e n tial. R e aso n in g m ay not, how ever, be a conscious process, a n d evidence will be p re sen te d la te r in th e book to suggest th a t it is n o t (cf. C h a p te rs 9 a n d 12). A n o th e r re aso n w hy the se q u e n tia l m o d el m ig h t a p p e a l is th a t it conform s to th e g e n era l th eo re tic al conv en tio n s o f cognitive psy­ chology, in w hich th e c y b ern e tic an alo g y o f in fo rm a tio n flow has been g re atly a d o p te d . W h en m em o ry m odels a re so often presen ted in flow -chart form , it w ould be su rp risin g if th e sam e w ere not a tte m p te d by re aso n in g th eo rists. T h e se q u e n tial m odel w ould seem to have its best c h an c e o f fitting d a ta on c o m p a rativ ely sim ple tasks such as w e hav e been con sid erin g here. As long as people get the p ro b lem s right, by a n d large, o n e c an a d d u p th e tim e tak e n a t each p o stu la te d ‘sta g e ’. Such m odels a re m u ch h a rd e r to fo rm u la te w hen p re d ic tio n s o f differences in errors a re re q u ire d , a s we shall see late r. E ven w ith in the verificatio n -task lite ra tu re , how ever, th e n o tio n o f a d d itiv e stages h a s been criticised. S ey m o u r (1975) review s evidence a g ain st the a d d itiv e stage m odel o f lo catio n ju d g m e n t p re se n te d by C h a se an d C la rk (1971). In on e e x p erim e n t, S e y m o u r asked su b je cts in one con d itio n to in v ert th e ir response, say in g ‘yes’ w hen they m ea n t ‘n o ’ a n d vice versa. In the n o rm al c o n d itio n the difference betw een various c o n d itio n s w as as p re d ic te d by the C h a se a n d C la rk m odel. In the in v e rte d re sp o n se c o n d itio n all p ro b lem s w ere e q u ally diffi­ cult. S ey m o u r claim s th a t his m a n ip u la tio n sh o u ld only have affec­ ted the resp o n se sta g e, a n d sh o u ld h av e d o n e so by a c o n sta n t a m o u n t. H e n ce , if th e a d d itiv e stage m odel is c o rrect, th e difference

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betw een c o n d itio n s sho u ld hav e been unaffected. T h is result seem s to cause difficulty for any a d d itiv e sta g e m odel o f th is task, n o t ju s t C hase a n d C la rk ’s. T h e second basic a ssu m p tio n u n d e rly in g th e m odels is th a t reasoning is acco m p lish ed by reference to p ro p o sitio n a l re p re se n ­ tatio n s, w hich a re a b s tra c t codes in to w hich sen ten ces a n d p ictu res alike a re p u t d u rin g co m p re h en sio n . F ro m th e discussion in C h a p te r 2, the re a d e r will be a w are th a t we can c h a ra c te rise twro possible a lte rn a tiv e p o sitio n s to th e p ro p o sitio n a l one: im ag ery a n d d u a l coding. A n im agery th eo ry w ould p o stu la te th a t th e p ro b lem infor­ m atio n w ould be re p re se n te d , a n d c o m p a re d , as visual im ages ra th e r th a n as p ro p o sitio n s. A s C la rk a n d C h a se (1972) p o in t o u t, such a n a p p ro a c h h a s a fu n d a m e n ta l difficulty in th a t one c a n n o t directly encode a neg ativ e. G iven a sen ten c e ‘A isn ’t above B ’, one could only re p re se n t this visually by c o n v ertin g it in to a n affirm ative form , e.g. as ‘A is below B \ T h e late n cy d a ta a re , how ever, gen erally in co m p a tib le w ith th e a ssu m p tio n o f conversion except u n d e r special c o n d itio n s. P eople c an , in a n y case, p erform verificatio n tasks w hen the d im e n sio n s are n o n -b in a ry a n d therefore n o t c o n ­ vertible. N o one seem s to have p u rsu e d a n e x tre m e im a g e ry ex­ p la n a tio n o f th ese tasks, th o u g h this a p p ro a c h has been p o p u la r on the m ore com plex p ro b lem s involving tran sitiv e inference (see C h a p te r 4). A d u a l-c o d in g a p p ro a c h (e.g. N eilsen a n d S m ith , 1973) is far m ore feasible. H e re , one w ould a rg u e th a t sen ten ces n a tu ra lly go into a v e rb a l code a n d p ic tu re s in to a v isu al code. In o rd e r to m ake a c o m p ariso n one m u st e ith e r c onvert the visual re p re se n ta tio n to a verb al form o r vice v ersa. In view o f th e difficulty o f e n co d in g a n egative visually one m ig h t expect th a t p ictu res a re e ncoded v e r­ bally a n d c o m p a riso n s m a d e in the v e rb al code. Before c o n sid erin g this hyp o th esis, how ever, w e will look fu rth e r a t th e claim s for the p ro p o sitio n a l p o in t o f view. C lark , C a rp e n te r a n d J u s t (1973) o bserve ‘in th e p re se n t p a p er, we will c o n tin u e to a ssu m e th a t p e rc e p tu a l events a re cod ed in a n a b stra c t, p ro p o sitio n a l fo rm at a n d will a d d w eight to th is a ssu m p ­ tion w ith new evidence we will p re s e n t’. T h e evidence th a t they p ro d u ce is sim ila r to o th e r e x p erim e n ts o f these a u th o rs a lre a d y referred to. In o th e r w o rd s, b ecau se in fo rm a tio n -p ro c essin g m odels can be m a d e to fit (freq u e n tly post hoc) on the basis o f a ssu m in g p ro p o sitio n al re p re se n ta tio n , th e n th is p ro v id es evidence th a t pic-

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tures a re n o rm ally en co d ed in this w ay. I d o not find this too convincing, a n d n e ith e r does A llp o rt (1975). A llport alleges a w eak­ ness in the use o f su c h tasks to a rg u e for a se m an tic, p ro p o sitio n a l basis for p e rce p tio n ; ‘T h e tro u b le is th a t th e task they em ploy for th eir d e m o n s tra tio n s - m a tc h in g a p ic tu re to a p rio r linguistic d e sc rip tio n - requires th a t th e p ic tu re be re p re se n te d in som e form at co m p atib le w ith the d e sc rip tio n .’ T h e re are really tw o p roblem s here: (1) ju s t because sen ten ces a n d p ictu res can be coded in a com m on form on th ese tasks does not m ea n th a t this w ould alw ays be tru e, a n d (2) the c o m m o n code used need n o t be p ro p o sitio n a l, it could be v e rb al o r visual. It w as a rg u e d in C h a p te r 2 th a t th e difference betw een p ro p o si­ tional a n d d u a l-c o d e th eo ries is no t really to d o w ith th e m ode o f re p re se n ta tio n used, b u t w ith th e ty p e o f p rocessing th a t is p ro ­ posed. I ag ree w ith A n d e rso n th a t e x p la n a tio n s m ay be fo rm u lated in eith er m a n n e r. T a k e , for e x am p le, a stu d y by S ey m o u r (1974). H e used sim p le affirm ative d e sc rip tio n s (D ) such as ‘circle inside sq u a re ’ w hich su b je cts h a d to m atc h a g a in st c o rre sp o n d in g p ictu res (P). T h e re w ere four c o n d itio n s. S u b je cts e ith e r m atc h ed a d e sc rip ­ tion a g ain st a p ic tu re (D P ) o r tw o p ictu res to e ac h o th e r (P P ). P re se n tatio n w as e ith e r sim u lta n e o u s o r successive, w ith a twosecond g a p b etw een the onset o f the in itial D (or P) a n d the s u b ­ se q u e n t P. T h e resu lts show ed th a t on sim u lta n e o u s p re se n ta tio n D P v erifications took longer th an P P v erifications, w hile o n succes­ sive p re se n ta tio n th e re w as no difference. A d u a l-c o d in g e x p la n atio n o f this result w ould p o stu la te th a t in the P P c o n d itio n c o m p a riso n s are m ad e in the visual code irresp ec tiv e o f a delay. In th e D P condition th e d e sc rip tio n c a n be c o n v erted to a p ic tu re to m ake a sim ilar c o m p a riso n , b u t this takes tim e. H e n ce, in the delay co n ­ dition th e d e sc rip tio n is recoded prior to th e p re se n ta tio n o f the p ictu re a n d so th e c o m p a riso n n o lo n g er takes a d d itio n a l tim e. A p ro p o sitio n a l a c c o u n t o f th e sa m e re su lt w ould h a v e to a d m it som e k ind o f d u a lity b etw een visual a n d verb al processes, if only w ith resp ect to the in itial p ro c e d u re o f co n v ertin g in fo rm a tio n from a picto rial o r v e rb al form o f in p u t in to a co m m o n a b s tra c t form . Specifically, to a cc o u n t for S e y m o u r’s resu lt a p ro p o sitio n a l th eo rist w ould have to su p p o se th a t verb al en co d in g takes longer th a n pictorial e ncoding. T h e real a rg u m e n t, th en , is a b o u t th e form o f re p re se n ta tio n in w hich the c o m p a riso n takes place. In a second e x p e rim e n t S e y m o u r (1974) c o m p a red a successive

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PD condition to a successive D P c o n d itio n a n d found th e fo rm er to take m o re tim e. L in g u istic co m p lex ity w as also m a n ip u la te d a n d found to influence PD b u t n o t the D P co n d itio n s. T h e p ro p o sitio n a l theory h a n d le s this result as follows: in this p a ra d ig m processing tim e is d e te rm in e d by w h a t is p re se n te d second. T h u s th e D P con d itio n sh o u ld be fa ster th a n PD b ecau se we hav e a lre a d y a s­ sum ed th a t p ictu res a re encoded faster. L in g u istic com plexity affects only P D , b ecau se its effects on th e d e sc rip tio n o f D P a re lost in the interval. H ow ever, a d u a l-c o d in g m odel could e q u ally a c c o u n t for the sam e d a ta on th e a ssu m p tio n th a t c o m p a riso n s in e ith e r case are m ad e in the p icto rial code, a n d th a t c o n v ertin g the d e sc rip tio n takes longer if it is m ore com plex. D P is faster, a n d th e effects o f com plexity u n m e a su ra b le , b ecau se in th is c o n d itio n the process takes place in th e in terv al. T h is e x am p le show s how p ro p o sitio n a l a n d d u a l-c o d in g e x p la n a ­ tions can b o th be a p p lie d to the sam e effect. C a n they, how ever, be distin g u ish ed ? S e y m o u r (1975), in a d e ta ile d , tech n ical a n d difficult review o f his m an y e x p erim e n ts on su ch m a tte rs , ev en tu ally co n ­ cludes th a t ‘N o co m p ellin g reaso n to d iv id e th e m em o ry system into verb al a n d p icto rial elem en ts w as found . . . I t seem ed co n ­ v enient, th erefo re, to re ta in C la rk a n d C h a s e ’s (1972) n o tio n o f a single a b s tra c t (p ro p o sitio n a l) code . . .’ T h is conclusion is p h ra se d in an in te re stin g m a n n e r w ith re sp ec t to th e d iscussion in C h a p te r 2. T h e re , it w as c o n clu d ed th a t p ro p o sitio n a l a n d im agery theo ries m ay n o t be easy to d istin g u ish in term s o f the fo rm at o f re p re se n ­ tatio n pro p o sed . T h e fact th a t S e y m o u r finds the se m a n tic code a m ore convenient a ssu m p tio n for e x p la in in g this kind o f task, m ig h t tell us so m e th in g m o re a b o u t th e task th a n the stru c tu re o f m em ory. T h e fact th a t S e y m o u r also rejects C la rk a n d C h a s e ’s n o tio n o f a dditive stages u n d e rlin e s th e d istin c tio n betw een th e re p re se n ta ­ tional a n d p rocess a sp e cts o f a theory. T h e G lu sh k o a n d C o o p e r (1978) stu d y also in v estig a te d D P a n d P P tasks b u t im p ro v ed o n th e m eth o d o lo g y o f S eym our. I n E x p e ri­ m en t I, th e su b je ct took as long as he need ed on th e item p re sen te d first so th a t c o m p re h en sio n a n d v erification tim e could be m ea su re d se p a ra tely . T h e a u th o rs call these e n co d in g a n d c o m p a riso n tim es respectively, w hich seem s a bit m isle a d in g to m e. T h e ‘e n co d in g tim e ’ (E T ) m ay be a re aso n a b le m ea su re o f the tim e to encode the d escrip tio n in th e D P c o n d itio n , a n d th e p ic tu re o n th e P P c o n d i­ tion. H ow ever, the ‘c o m p a riso n tim e ’ (C T ) m u st also c o n ta in a

Sentence verification

47

(p resu m ab ly c o n sta n t) tim e to enco d e th e p ic tu re p re sen te d for c o m parison, as well as th e c o m p a riso n tim e itself. O n e in te restin g result is th a t E T for d e sc rip tio n s in creases as a function o f linguistic com plexity, w hile E T for p ictu res is in d e p e n d e n t o f th eir co m p lex ­ ity. T h is q u a lita tiv e difference s u p p o rts a d u a l-c o d in g m odel, a n d is p a rtic u la rly in line w ith a h y p o th esis o f P aivio (1975) th a t w hile the v e rb al system o f cog n itio n is in trin sic ally se q u e n tial in n a tu re , the visual system is c a p a b le o f p a ralle l pro cessin g (cf. C h a p te r 12). I f featu res o f p ictu res a re e ncoded in p a ralle l, th en com plexity need not increase latency. O th e r re su lts o f this e x p erim e n t, w hich w ere re p lica ted in a second m ore com plex e x p erim e n t, w ere also o u t o f line w ith the p ro p o sitio n a l m odels. I t w as m e n tio n ed in th e p revious section th a t G lushko a n d C o o p e r found no effect o f lin g u istic com plexity a t the V T stage, th u s failing to su p p o rt the C a r p e n te r a n d J u s t m odel. T h e C lark a n d C h a se m odel also suffers, how ever, in th a t the effects o f lexical m ark in g d id n o t occur, as p re d ic te d by th eir m odel, a t the C T stage. T h is stu d y is, th en , a lto g e th e r in co n v e n ien t for the p ro p ­ ositional m odels. D espite th e e m p h a sis on p ro p o sitio n a l m odels in recen t stu d ies o f the verification task, th e stu d ies review ed in this section suggest th a t a n e x p la n a tio n in term s o f d u a l c o d in g is very m u ch a n open possibility. C o n c lu sio n s a b o u t the stu d ies discu ssed in this section will be given w ith th e c onclusions for th e c h a p te r as a w hole.

Conclusions W e have seen th a t th e verificatio n task w as devised by W aso n as a w ay o f in v estig a tin g th e p rocessing o f positive a n d negative infor­ m atio n , a n d by e arly psy ch o lin g u ists as a wray o f in v estig a tin g tra n sfo rm a tio n a l com plexity. It w as soon realised th a t the infor­ m atio n p ro cessin g re q u ire m e n ts o f the p a rtic u la r p a ra d ig m w ere im p o rta n t, a n d it w as also suggested by W aso n , in p a rtic u la r, th a t the n e g ativ e h a d se m a n tic effects. R ecen t d e v elo p m en ts have focused p rin cip ally on th e c o n stru c tio n , testin g a n d a p p lic a tio n o f in fo rm atio n -p ro cessin g m odels. T h e se m a n tic a sp e ct seem s to have been ra th e r overlooked in this re ce n t w ork. A lth o u g h G re e n e ’s w ork on se m an tic fu n c tio n m ay be a n a rtifa c t o f p rocessing d e m a n d s, the p ra g m a tic a sp e ct o f n e g atio n , id entified by W aso n , still seem s to be

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im p o rta n t, a n d th ere is a n u nresolved lite ra tu re on th e e m o tio n ality hypothesis. W ason (1972; 1980) claim s th a t v e rifica tio n -ta sk stu d ies o f n e ­ gatio n have low e x te rn al validity. H e p o in ts o u t th a t in real life negatives a re alw ays used to d en y p re su p p o sitio n s, a n d claim s th a t few e x p erim e n ts p ro v id e a n y a p p ro p ria te c o n tex t for th e negative sta te m e n ts they p re sen t. W a s o n ’s c riticism is so u n d in so far as an y e x tra p o la tio n a b o u t the n a tu re o f language is c o n ce rn ed . V erificatio n tasks are still, how ever, sim ple pro b lem -so lv in g e x p erim e n ts in th eir ow n rig h t a n d m ay be expected to tell us so m e th in g a b o u t cognitive processing. T h e in fo rm a tio n -p ro c essin g m odels hav e been based on an a s­ su m p tio n th a t all ‘re a so n in g ’ takes p lac e w ith reference to p ro p o si­ tional re p re se n ta tio n o f sen ten ces a n d p ictu res. W e h av e seen, in the last section, th a t a d u a l-c o d in g a p p ro a c h could also be a p p lie d to the sa m e so rt o f tasks, a n d th a t th ere is som e evidence th a t sentences a n d p ic tu re s a re processed ra th e r differently on these tasks. T h e use o f theories based on im ag ery ra th e r th a n p ro p o si­ tional re p re se n ta tio n will be discu ssed in d e ta il in the follow ing c h a p te r on tran sitiv e reaso n in g . As sta te d e arlie r, th e verification task does not re q u ire d e d u ctiv e reasoning. T h e re is, how ever, no reaso n to su p p o se th a t the s tr a t­ egies a p p lie d to it w ould differ very m u ch from those a p p lic a b le to g enuine d e d u ctiv e tasks. If, for ex am p le, one believes th a t people ap p ly se q u e n tia l stra te g ies based o n p ro p o sitio n a l re p re se n ta tio n s to one so rt o f task, th en it w ould be su rp risin g if one d id n o t expect to find the sam e to be tru e o f the o th e r. O n the o th e r h a n d , if A llp o rt’s (1975) c o n te n tio n th a t su c h m odels a re task specific is correct, th en they m ay n o t g eneralise. I t will, therefore, be o f in te rest to discover w h e th e r the fe atu res o f in fo rm a tio n pro cessin g suggested by the successful m odels o f th e verificatio n task c o rre sp o n d to those a p p a re n t on o th e r re aso n in g tasks to be co n sid ered in this book.

Transitive inference

T h e stu d y o f tra n sitiv e inference involves g en u in e d e d u ctiv e re a so n ­ ing tasks, in w hich su b je cts a re asked to p u t to g eth e r tw o se p a ra te a ssertio n s in o rd e r to d e d u c e a new a sse rtio n as a necessary conse­ q uence. T ra n s itiv ity is a p ro p e rty o f a n y scale o r d im e n sio n on w hich objects can be c o m p a red a n d o rd e re d . S uch scales a re usually defined by the a d je ctiv es d e sc rib in g th eir o p p o site poles, e.g. good - b a d , tall - sh o rt, d a rk - light, etc. In g e n era l, if a re la tio n r is tran sitiv e, th en given th a t A r B a n d B r C it follows th a t A r C. F or exam ple: J o h n is ta lle r th a n Bill. Bill is taller th a n J im . T h ere fo re, J o h n is ta lle r th a n Jim . I t is usually possible to express the tra n sitiv e re la tio n in a negative o r reverse form . F o r ex am p le, in th e above a rg u m e n t, th e second prem ise could be re p la ce d by ‘J i m is sh o rte r th a n B ill’ w ith o u t a lte rin g th e logical necessity o f th e inference. W h e th e r such an a lte ra tio n affects the psychological difficulty is, o f course, a se p a ra te questio n . P roblem s w ith tw o p rem ises a n d a conclusion, as in th e above exam ple, a re know n as linear syllogisms o r three-term series problems. T h e la tte r d e sc rip tio n arises from th e c o n sid era tio n th a t th ree term s are related by the tw o p rem ises (Jo h n , Bill a n d J im ). In o rd e r to define the g e n era l stru c tu re o f these p ro b lem s, let us define a tr a n ­ sitive scale on w h ich A is th e m ost positively p laced item , C the m ost n egatively p laced , a n d B the m id d le term . L et us, in g en eral, call the re la tio n ‘> ’ w hen expressed positively, a n d “< ’ w hen ex49

50

Elementary reasoning tasks

p ressed n e g ativ ely . By d e fin itio n th e n A > B > C , o r to p u t it a n o th e r w ay, C < B < A . T A B L E 4.1

Sixteen possible valid linear syllogisms

P rem ise pairs:

C o n clu sio n

(a) (b)

P rem ise pairs:

C o n clu sio n

(a) (b)

1

2

3

4

A>B B>C

A>B CC B C (p ro b lem 2' is sim ila r). P ro b le m s 4 a n d 1' can be p u t in to n a tu r a l o rd e r by re -o rd e rin g the tw o prem ises. T h e m ost com plex p ro b lem s, a cc o rd in g to H u n te r, a re 3 a n d 3' w hich req u ire b o th conversion o f the second prem ise, and re -o rd e rin g o f the tw o prem ises. H u n te r ’s th eo ry th u s m akes c le ar p re d ic tio n s a b o u t th e relativ e difficulty o f the d ille ren t p ro b lem types show n in T a b le 4.1 a n d its fit to e x p erim e n tal d a ta will be co n sid ered in d u e course. N ext, we c o n sid er th e Im a g e ry th eo ry , a lth o u g h th is term is m isleading for tw o reaso n s. A lth o u g h th e p ro p o n e n ts o f th is view ­ p oint have su p p o sed th a t visual im ag ery is used in solving the p roblem s, th e p re d ic tio n s o f th e th eo ry d o n o t seem to d e p e n d on this a ssu m p tio n . T h e im p o rta n t fe atu re o f th e theory is th a t it p roposes th a t su b jects solve the p ro b lem s by c o n stru c tin g a lin e a r o rd e rin g o f the th ree item s d u rin g c o m p re h en sio n o f the p rem ises, a n d then d ra w the conclusion (or a n sw e r the q u e stio n ) by reference

52

Elementary reasoning tasks

to this lin e a r re p re se n ta tio n . T h e su p p o sitio n th a t this is achieved by c o n stru ctin g a visual im ag e is n o t necessary . I t is also m isle a d in g to talk o f the Im a g e ry th eo ry since th ere a re several v a ria tio n s. T h e o rig in al theory w as p ro p o se d by D e Soto, L o n d o n a n d H a n ­ del (1965). T h e y p ro p o sed th a t the e v alu ativ e d im e n sio n ‘g o o d b a d ’ is im a g in ed as a v e rtica l sp a tia l a rra y , in w h ich ‘g o o d ’ is assigned to th e top a n d ‘b a d ’ to th e b o tto m . T h is h a s su b se q u e n tly been g e n era lise d to o th e r d im e n sio n s w h ich h av e a c le a r positive a n d neg ativ e en d , w ith th e a ssu m p tio n th a t th e positive en d is assigned to the top (e.g. tall, heavy) a n d th e negative en d to the b o tto m (e.g. sh o rt, lig h t). T h e n o tio n o f the sp a tia l a rra y w as derived from in tro sp ec tiv e re p o rts, b u t v a lid a te d by a d ire c t e x p e ri­ m en ta l test to be d e sc rib e d late r. D e Soto et al. p ro p o se d tw o p rin c ip le s w hich affect th e ease o f c o n stru ctin g the m e n ta l re p re se n ta tio n a n d th u s the difficulty o f solving the p ro b lem . T h e first p rin cip le, direction o f working, asse rts th a t th ere is a preferen ce for w orking from to p to b o tto m o f the sp a tia l a rra y . T h e second p rin cip le, end-anchoring, a sse rts th a t it is easier to c o n stru c t a re p re se n ta tio n from a p rem ise w hose first item refers to a n end item (A o r C ). T h u s A > B o r C < B sh o u ld be easier to c o n stru c t th a n B < A o r B > C . L et us e x am in e the p ro b lem s in T a b le 4.1 tak in g ‘> ’ to re p re se n t ‘b e tte r’ a n d ' < ’ to re p re se n t ‘w o rse’. P ro b le m s wrhich use th e sam e re la tio n a l term (b e tte r o r w orse) in b o th p rem ises, i.e. 1, 1 ', 4, 4 ', all c o n ta in one p rem ise w hich is n o t e n d -a n c h o re d (sta rts w ith B). T h e p rin cip le o f d irec tio n o f w orking is a p p lie d b o th b etw een a n d w ithin p rem ises. F o r e x am p le, 1 sh o u ld be easie r th a n 4 ' since the first p re m ise refers to th e to p o f th e a rra y in 1, a n d to the b o tto m in 4 ’. W ith in p rem ises, to p -b o tto m w orking is also p re fe rre d , im ­ plying th a t ‘b e tte r’ sh o u ld be e asie r th a n ‘w orse’. O n th e p ro b lem s w hich m ix th e re la tio n a l term s, i.e. 2 ,2 '; 3 ,3 ', som e a re to be p r e ­ ferred to o th e rs on the basis o f e n d -a n c h o rin g in 2 a n d 2 ' a n d n e ith e r in 3 a n d 3'. D eriv in g p re d ic tio n s from th e tw o p rin cip les to g eth e r is som ew h a t com plex a n d u n c le ar. Jo h n s o n -L a ird (1972), in a tte m p tin g to p re ­ sen t th e th eo ry in a flow -chart form , d e cid ed th a t th e tw o p rin cip les w ere n o t in d e p e n d e n t. H e m odified the th eo ry to o vercom e this p ro b lem , a n d th u s m u st be re g ard e d as th e a u th o r o f an a lte rn a tiv e version. In J o h n s o n -L a ird ’s a cc o u n t th e su b je c t is su p p o sed to in ­ spect e ach p re m ise in tu rn to see w h e th e r o r n o t it is e n d -an c h o red .

Transitive inference

53

I f it is not, the su b je ct is su p p o sed to c o n v ert it. T h e d ire c tio n o f w orking p rin c ip le is th en a p p lie d n o t to th e p re m ise p re se n te d , b u t to the p rem ise th e su b je ct e n d s u p w ith , w hich m ay o r m ay n o t be c onverted. C o n sid e r the follow ing pro b lem : B is w orse th a n A C is w orse th a n B W ho is best? In J o h n s o n -L a ir d ’s version, the su b je c t w ould stu d y th e first prem ise a n d n o te th a t it w as n o t e n d -a n c h o re d . T h e m odel is ra th e r artificial here, in th a t th e su b je ct c a n only a rriv e a t th is conclusion by studying the second premise as well. H e th en know s th a t B is the m iddle term ra th e r th a n A , because it a p p e a rs in b o th prem ises. T h e subject now c o n v erts the first p rem ise in to ‘A is b e tte r th a n B ’, an d p laces A a n d B in the a rra y w orking d o w n w ard s. In this problem th e second p rem ise is e n d -a n c h o re d , so does n o t need conversion. J o h n s o n -L a ird a ssu m es th a t difficulty is a function o f three th in g s, (1) th e need to c o n v ert th e first prem ise, (2) th e need to convert th e second p rem ise, (3) th e d irec tio n o f w orking in placing th e item s referred to in the first premise only. T h e last p re d ­ iction is based o n th e a ssu m p tio n th a t th e first p rem ise ‘se ts’ the d irectio n o f w orking. Since d e S o to ’s theory pro p o sed d irec tio n o f w orking b o th b etw een a n d w ith in e ac h prem ise, a n d based o n the o riginal p rem ises w ith o u t c onversion, J o h n s o n -L a ird ’s m odel a p p e a rs to be su b s ta n tia lly different. T h e best-k n o w n version o f the Im a g e ry theory is th a t o f H u tte n locher (1968) w hich is sim ila r to the o rig in al version o f D e Soto et al. H u tte n lo c h e r’s theory is m u ch influenced by in tro sp ec tio n s o f a d u lt su b jects o n lin e a r syllogism s, a n d a n an alo g y to the p lac em e n t o f a ctu al p h y sical objects in to a rra y s by y o u n g c h ild ren . In e ith e r case she su p p o ses th a t on receiving the first p rem ise (o r in stru c tio n ) the sub ject p laces on e item above th e o th e r in the a rra y (im agined or real). O n receiving the second in stru c tio n the su b je ct m u st now' place the th ird item w ith re sp ec t to th e first tw o. She pro p o ses th a t this is m ore easily acc o m p lish e d if th e th ird ite m is th e g ra m m a tic a l subject o f the second p rem ise. T h is is e q u iv a le n t to p re d ic tin g an e n d -a n c h o rin g effect for th e second p rem ise. T h e th eo ry differs from De Soto’s in no t m ak in g a g e n era l e n d -a n c h o rin g p re d ic tio n for the first p rem ise. F o r d im e n sio n s w ith clearly p referred d irec tio n o f

54

Elementary reasoning tasks

w orking such as g o o d -b a d , th e item p laced first will be th e ‘b e tte r’ one. F o r u n c le a r d im e n sio n s such as ‘lig h t-h a ir -d a rk -h a ir ’ th e item placed first will be th e one m e n tio n e d first in th e prem ise. T h u s it a p p e a rs th a t th ere a re th re e d istin c t versions o f the Im ag e ry theory. C lark (1969) p ro p o sed w h a t has becom e know n as th e L in g u istic theory o f tra n sitiv e inference, w hich in co rp o ra te s the n o tio n th a t reaso n in g o p e ra tio n s a re p erfo rm ed n o t on th e sen ten ces them selves, b u t on th e ir u n d e rly in g p ro p o sitio n a l re p re se n ta tio n . T h is w as as­ serted in the first o f his th ree p rin cip les, w hich he term s prim acy o f functional relationships. A t this tim e his term inology w as influenced by th a t o f C ho m sk y (1965), so th a t he refers to ‘base strin g s’ in the deep stru c tu re . T h e base strin g s can, how ever, be c onsidered e q u iv ­ a le n t to u n d e rly in g p ro p o sitio n s. T h e essential a rg u m e n t is th a t a c o m p a rativ e se n ten ce, su ch as ‘J o h n is b e tte r th a n P e te r’ is encoded as in d ic a tin g th a t b o th J o h n a n d P e te r a re good, b u t J o h n is m ore so. T h u s the u n d e rly in g re p re se n ta tio n is ‘J o h n is g o o d + * , P e te r is g o o d ’. O n the o th e r h a n d ‘P e ter is w orse th a n J o h n ’ w ould be encoded as ‘P e ter is b a d + , J o h n is b a d ’. T h e second p rin cip le, lexical m arking, re la te s to the fact th a t m an y p airs o f b i-p o la r adjectiv es a re a sy m m e tric al. O n e ad jectiv e m ay have a n e u tra l u n m a rk e d sense, w hile th e o th e r h a s only a c o n tra s­ tive m ark ed sense. I f I ask ‘H ow good if J o h n ? ’, I am ask in g only for his p la c e m e n t on the g o o d -b a d scale. I f I ask ‘H ow b a d is J o h n ? ’, I am im p ly in g th a t I th in k he is b ad . T h is u n m a rk e d m arked re la tio n sh ip o ccu rs for m an y , b u t n o t all, b i-p o la r p airs, e.g. ta ll-s h o rt, h e a v y -lig h t. C la rk ’s lexical m ark in g p rin cip le asse rts th a t it sho u ld be e asie r to retriev e in fo rm a tio n from se m an tic m em ­ ory if the u n d e rly in g re p re se n ta tio n is o f u n m a rk e d ra th e r th a n m arked ad jectives. F o r e x am p le, ‘A is b e tte r th a n B ’ sh o u ld be processed fa ster th a n ‘B is w orse th a n A ’. T h e th ird p rin cip le, congruence, a sse rts th a t p ro b lem s m ay be m ore sim ply solved if th e q u e stio n is c o n g ru e n t w ith th e re p re se n ta tio n o f the p rem ises. T h e th ree p rin cip les can be m ost sim ply illu stra te d w ith reference to w h a t C lark calls tw o -term series p ro b lem s (T a b le 4.2). P rem ises in the form ‘A is not as b a d as B’ a re called negative equatives a n d w ere in tro d u c e d by C la rk to d istin g u ish his p re d ic tio n s from Im ag e ry theory - a p o in t w hich will be discu ssed late r. O n * In Clark’s current notation, these would be written ‘Good (John)’, etc.

Transitive inference

55

the p rin cip le o f lexical m ark in g he p re d ic ts th a t p ro b lem I will be m ore ra p id ly solved th a n I I , b u t p ro b lem I ' m ore slowly th a n I I '. T h is is b ecau se ‘g o o d ’ re p re se n ta tio n s are u n m a rk e d . ‘B est?’ is a ssum ed c o n g ru e n t w ith ‘g o o d ’ re p re se n ta tio n s a n d ‘W o rst? ’ w ith ‘b a d ’ re p re se n ta tio n s. H e n ce he p re d ic ts th a t the q u e stio n ‘B est?’ will be a n sw e red m ore ra p id ly on p ro b lem s I a n d I I ', a n d ‘W o rst? ’ m ore ra p id ly on I I a n d I '. C la rk p re sen ts d a ta w hich conform nicely to these p re d ic tio n s.

T A B L E 4.2

Two-term series problems fo r the ‘good-bad’ dimension

Prem ise

A nalysis*

Q uestion

I

A b etter th an B

A is good B is good

(a) Best? (b) W orst?

II

B worse th an A

A is bad B is bad

(a) Best? (b) W orst?

I'

A not as bad as B

A is bad B is bad

(a) Best? (b) W orst?

II'

B not as good as A

A is good B is good

(a) Best? (b) W orst?

* A cco rd in g to th e L in g u istic th e o ry o f C la rk (1969)

T h e a p p lic a tio n to th re e -te rm series is m ore com plex. R efer to T a b le 4.1 a n d take > to re p re se n t ‘b e tte r th a n ’ a n d < to re p re se n t ‘w orse th a n ’. P ro b le m s 1, 1', 4, 4 ' a re h o m ogeneous, i.e. use the sam e adjectiv e. H e w o u ld th u s p re d ic t 1 a n d 1' to be m o re quickly processed since they c o n ta in th e u n m a rk e d ad jectiv e ‘g o o d ’ in th eir u n d e rly in g re p re se n ta tio n . C o n g ru e n c e o f th e q u e stio n ‘best?/ w orst?’ can be a p p lie d to these p ro b lem s in a sim ila r m a n n e r to the tw o term series. T h e h e te ro g en e o u s p ro b lem s 2, 2 ', 3, 3 ' are m ore c o m p licated . N eith er h as ‘in te rn a l c o n g ru e n c e ’, since the tw o p rem ises a re re p ­ resen ted w ith reference to different a djectives. H o w ev er, p ro b lem s 2 an d 2' a re p re d ic te d to be e asie r since they will be c o n g ru e n t w ith the q u e stio n asked. I f the q u e stio n is ‘W h o is best?’ the a n sw e r will be ‘A ’ w hich is c o n g ru e n t w ith the p re m ise in w hich A a p p e a rs (A b e tte r th a n B). I f the q u e stio n is ‘W h o is w o rst?’ th en th e a n sw er ‘C ’ a p p e a rs in th e p re m ise ‘C is w orse th a n B ’ so th a t too is

56

Elementary reasoning tasks

con g ru en t. By c o n tra st on p ro b lem s 3 a n d 3 ' the q u e stio n alw ays tu rn s out to be in co n g ru e n t. T h e re a d e r m ay well have n oticed th a t the p re d ic tio n s o f th e L inguistic th eo ry a re ra th e r sim ila r to th e o riginal Im ag e ry theory. F irstly, if the u n m a rk e d adjective is the one p laced a t the ‘to p ’ o f the a rra y , the lexical m ark in g a n d ‘d irec tio n -o f-w o rk in g ’ m ake the sam e p re d ic tio n s for h o m ogeneous syllogism s. Secondly, it a lso h a p ­ pens th a t th e p re d ic tio n th a t p ro b lem s 2 a n d 2 ' a re e asie r on hetero g en eo u s syllogism s th a n p ro b lem s 3 a n d 3 ' on th e basis o f congruence coincides w ith the p re d ic tio n based o n e n d -a n c h o rin g . C o n se q u e n tly , as we sh all see in th e next section, it is no easy m a tte r to d istin g u ish th e theories in term s o f th eir p re d ic tio n s o f p roblem difficulty. T h e o rig in al aim o f all the tran sitiv e re aso n in g th eo rists w as to p re d ic t the relative difficulty o f the v a rio u s p ro b lem s. W e will e x a m ­ ine evidence o f this so rt, b u t for re aso n s in d ic a te d above it is unlikely to be conclusive. W e will also e x am in e evidence for th e o th e r issues a rising from these theories. F irstly, w h a t direct evidence is th e re th a t p erfo rm an ce is m ed ia te d by m en ta l im ages? S econdly, w h a t evi­ dence is th ere th a t a lin e a r o rd e r is c o n stru c te d a t th e tim e o f c o m prehension? R ecen t w ork on th e d e v elo p m en t o f tran sitiv e reasoning, a n d stu d ies o f m em ory for in ference shed lig h t on the last questio n . F irst, how ever, let us c o n sid er th e q u e stio n o f p ro b lem difficulty.

Predictions about problem difficulty In p re se n tin g th e v a rio u s theo ries it w as p o in te d o u t how they p re d ic te d the relativ e difficulty o f the p ro b lem s show n in T a b le 4.1. W e sh all now look a t som e d a ta . T a b le 4.3 show s d a ta for positive co m p a rativ e p ro b lem s in th ree stu d ies, w here a sy m m e tric al a d je c ­ tive p a irs a re em ployed. N e ith e r H u tte n lo c h e r (1968) n o r D e Soto et al. (1965) re p o rt d a ta se p a ra tely by q u e stio n asked, so th e evi­ dence for co n g ru en c e rests on th e C la rk (1969) d a ta . F irst o f all look a t the p e rc e n ta g e co rre c t d a ta o f D e Soto et al., a n d the m ean latency, a v era g ed o ver q u e stio n type, o f C la rk ’s stu d y . F o r h o m o ­ geneous syllogism s b o th directio n -o f-w o rk in g a n d lexical m ark in g p re d ic t th a t p ro b lem s 1 a n d 1' will be e asie r th a n p ro b lem s 4 a n d 4 '. O n a v era g e this is tru e for b o th d a ta sets. F o r h e te ro g en e o u s

Transitive inference

57

problem s both end-anchoring (De Soto) and congruence predict th at 2 and 2' will be easier th an 3 and 3' - which is again supported in both sets o f data. T A B L E 4.3

Problem

Relative difficulty o f linear syllogisms in three studies

Com parative:

De Soto el al. (1965)

Huttenlocher (1968)

better-worse

taller-shorter

60.5

155

Best? 542

Worst? 610

M 575

52.8

135

498

552

525

61.8

141

535

534

534

57.0

142

484

584

532

41.5

157

500

602

549

38.3

157

612

545

577

50.0

142

593

504

547

42.5

161

627

653

640

I A >B B>C r b > c. A>B 2 A>B CC B q. In th e fo rm er re la tio n , p implies q so th a t one m ay nev er o b serv e p to be tru e w ith o u t also observing q to be tru e . I f p is equivalent to q, how ever, the converse also holds, i.e. o n e m ay n e v er ob serv e q w ith o u t p. p a n d q are e q u iv a len t in th a t they alw ays o c cu r to g eth e r. L ogicians often use the c o n d itio n al se n ten c e, I f p then q, to ex p ress im p lica tio n , w ith the m od ification I f and only i f p then q w h e n it is e x te n d ed to equiv alen ce. In a c tu a l lin g u istic usage, how ever, peo p le a g ain ten d to use the sh o rte r form a n d let se m a n tic factors d e te rm in e the m e a n in g w hich is read. F o r e x am p le, ‘I f it is a d og th en it is a n a n im a l’ obviously does n o t e n ta il th e converse. O n th e o th e r h a n d use o f a c o n d itio n al as a th re a t o r p ro m ise n o rm ally assu m es e q u iv a len c e (see C h a p te r 8). Y ou m ay say to a ch ild ‘I f y ou finish y o u r hom ew ork th e n you m ay go to th e p ic tu re s .’ T h is carries th e p ra g m a tic (ra th e r th a n the logical) inference th a t if h e d o e sn ’t finish it th e n he will n o t be allow ed to go. I f the tw o p ro p o sitio n s a re n o t re g ard e d as e q u iv a len t the sta te m e n t w ould be pointless. T h e re aso n in g p ro b lem s w ith w'hich we a re co n ce rn ed in this book a re set in term s o f sen ten ces a n d w ords, ra th e r th a n a b stra c t relatio n s a n d p ro p o sitio n s. T h e lin g u istic form s th a t h a v e received m ost a tte n tio n a re d isju n ctiv es a n d c o n d itio n als. I t is necessary now' to look in m o re d e ta il a t the logic o f th e re la tio n s th a t these form s m ay be tak e n to convey. O n e w ay to d o this involves looking m o re precisely a t th e tru th -ta b le an aly sis o f these form s. T a b le 7.2 p re ­ sents tw o possible tr u th tab le s for a d isju n ctiv e se n ten c e a n d th ree possible tr u th tab le s for a c o n d itio n a l sentence. T h e tru th -ta b le cases a re form ally defined in term s o f the tru th values o f th e c o n stitu e n t p ro p o sitio n s. F o r e x am p le th e T F case is th a t w'hich o ccu rs w h e n th e first p ro p o sitio n (p) is tru e , a n d the second (q) is false. In th e case o f the form Either p or q it h a s been p ointed o u t th a t this m ig h t be re ad as e ith e r inclusive o r exclusive d isju n ctio n . T h e logical re la tio n s c o rre sp o n d in g to these re ad in g s are defined by th e tru th tab le s given. T h e difference is th a t T T is ‘tru e ’ for a n inclusive a n d ‘false’ for a n exclusive re la tio n . T w o o f the tru th tab le s show n for a c o n d itio n a l ru le c o rre sp o n d to the logical re la tio n s o f im p lica tio n a n d e q u iv alen ce. T h e fo rm er is fal­ sified only by a n o b se rv a tio n o f T F , a n d th e la tte r also by F T . T h e th ird ‘defective’ tru th tab le goes b e yond th e lim its o f s ta n ­ d a rd logic w ith its tw o tru th v alues. A possible th ird tru th v a lu e is ‘in d e te rm in a te ’ o r ‘irre le v a n t’, sym bolised h e re as *?’. W aso n (1966)

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Propositional reasoning

T A B L E 7.2

Possible truth tables fo r disjunctive and conditional sentences

(a) Disjunction S entence

T ru th - ta b le case

pq E ith e r p o r q

(pq) (pq) (pq) (pq)

TT TF FT FF

T r u th valu e o f sentence Inclusive

E xclusive

T T T F

F T T T

(b) Conditional S entence

T ru th - ta b le case

pq I f p th en q

TT TF FT FF

(pq)

T ru th value o f sentence Im p licatio n

Equiv•alence D efective

T

T F F T

(pq) F (pq) T (pq) t

T F p p

h a s p ro p o se d t h a t p e o p le m ay w ell h a v e a d efectiv e tru th ta b le for th e c o n d itio n a l su c h t h a t it is c o n sid e re d irre le v a n t to cases w h e re th e first p a rt o f th e ru le is false. F o r e x a m p le , th e se n te n c e , ‘I f it is a ta b le th e n it h a s fo u r leg s’ is c le a rly tru e o f a fo u r-leg g e d ta b le (T T ) b u t false if a p p lie d to a th re e -le g g e d ta b le (T F ). A c c o rd in g to th e logic o f m a te ria ! im p lic a tio n , th e se n te n c e m u s t be tru e o f a n y th in g w h ic h is not a ta b le . W a s o n su g g e sts th a t p e o p le see su c h in sta n c e s a s irre le v a n t to th e ru le , r a th e r th a n a s verify in g e x a m p le s o f it. T h e ru le sim p ly does not apply to th in g s w h ich a re n o t ta b le s. I t w as s ta te d e a rlie r th a t a r g u m e n ts m a y be m a d e by use o f rules o f inference. S u c h ru le s h a v e b e en a sso c ia te d w ith d isju n c tiv e s a n d c o n d itio n a ls, a n d m a y b e d e riv e d fro m th e tr u th - ta b le a n a ly sis. T h e ru les a re sim p ly s ta te m e n ts o f w h e th e r o r n o t b a sic sy llo g istic in ­ ferences a re v a lid . T h e c la ssic a l A risto te lia n sy llo g ism s d isc u sse d in th e p re v io u s p a r t o f th is b o o k c o n c e rn e d c lass re la tio n s , a n d m a y be m o re p re cise ly d e fin e d a s categorical syllogisms. S im ila r p ro b le m s in v o lv in g c o n d itio n a l se n te n c e s a re so m e tim e s k n o w n a s c o n d itio n a l o r h y p o th e tic a l syllogism s. H o w e v e r, to a v o id c o n fu sio n th ey w ill be d e sig n a te d conditional inferences in th is book. I n e a c h c ase, th e m a jo r p re m ise is th e c o n d itio n a l s e n te n c e c o n ta in in g tw o p ro p o s i­ tions, a n d th e m in o r p re m ise a n a s s e rtio n o r d e n ia l o f o n e o f its

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c o m p o n e n t p ro p o sitio n s. In th e c o n d itio n a l, th e first c o m p o n e n t (p) is know n a s the a n te c e d e n t, a n d the second c o m p o n e n t (q) as the c o n seq u en t. T A B L E 7.3

Conditional Inferences If p then q

M o d u s ponens (M P) T herefore,

P q

T herefore,

If p then q N ot p N ot q

T herefore,

q P

T herefore,

I f p then q N ot q N ot p

D enial o f th e antecedent (DA)

I f p then q

A ffirm ation o f the consequent (AC) M odus tollens (M T )

In the first inference m o d u s p o n e n s (M P ) th e m in o r prem ise asserts the a n te c e d e n t a n d the c onclusion asse rts the co n se q u en t. T h is inference is v a lid regardless o f w hich tr u th tab le show n in T a b le 7.2 app lies. A ll th e tru th tab le s a g ree th a t we m ay n o t hav e a tru e a n te ce d e n t w ith a false c o n se q u e n t (T F ). So if the a n te c e d e n t is tru e, th en th e c o n se q u e n t m u st be tru e as well. F o r sim ila r reaso n s m odus tollens (M T ) is in d is p u ta b ly v alid . In th is syllogism the m in o r p re m ise denies the c o n se q u en t a n d th e c onclusion de n ie s the a n te ce d e n t. Since T F c a n n o t occu r, a false c o n se q u e n t can only be acco m p a n ied by a false a n te c e d e n t. T o use th e e x am p le given above, if we know th a t so m e th in g is a table we can infer th a t it h a s four legs (M P ), a n d if we know th a t so m eth in g does n o t hav e four legs w e can infer th a t it is n o t a tab le (M T ). In a c tu a l fact, o f course, one c a n h a v e three-legged tab les, b u t the inferences follow on the a ssu m p tio n th a t the given ru le 'I f it is a tab le th en it h a s four legs’ is tru e. T h e n ecessity o f b oth inferences follow s from its im p lic a tio n th a t one c a n n o t h av e a tab le w ith an y o th e r n u m b e r o f legs th a n four, so they a re still v alid if the tru th tab le is defective. T h e o th e r inferences D A a n d A C a re v alid only if m a te ria l e q u iv ­ alence is assu m e d . T h is tru th tab le also forbids F T , so a false a n te ce d e n t m u st be a cc o m p a n ie d by a false c o n se q u en t, a n d a tru e

122

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co n seq u en t m u st be a cc o m p a n ie d by a tru e a n te c e d e n t. U n d e r eith er im p licatio n o r defective tru th tab le s, D A a n d A C a re fa lla ­ cious syllogism s a n d c a n n o t be a d o p te d as lin g u istic ru les o f inference. T h ese inferences w ould seem a b s u rd from the rule given above, since one w ould hav e to p o sit th a t only tab les can h a v e four legs. H ow ever, they w'ould seem re a so n a b le for a ru le such as ‘I f a perso n is m ale th e n th a t p e rso n h a s a n X Y c h ro m o so m e .’ S e m an tics d e ­ term in e a n eq u iv a len c e re ad in g , su c h th a t b o th D A (given not m ale, infer no X Y c h rom osom e) a n d A C (given X Y ch ro m o so m e, infer m ale) seem re aso n ab le. S im ilar d isju n ctiv e inferences can be c o n stru c te d . F o r ex am p le, e ith e r c o m p o n e n t m ay be d e n ie d in the m in o r p rem ise a n d the o th e r asserted in conclusion, e.g. E ith e r p o r q N ot p T h erefo re, q A n inference o f this form is valid u n d e r b o th inclusive a n d ex clu ­ sive re ad in g s, since it is n o t p e rm itte d th a t b o th c o m p o n e n ts can be false. A second ty p e is w h en one c o m p o n e n t is a sse rted in th e m ajo r prem ise a n d the o th e r d e n ie d in co n clu sio n , e.g.: E ith e r p o r q

q T h erefo re, N ot p T h is inference is v alid only if exclusive d isju n c tio n is assu m e d , since only this re la tio n excludes th e p o ssibility o f b o th c o m p o n e n ts being tru e a t th e sa m e tim e. W ith reference to th e th e m a tic ex am p les given e arlie r, we c a n see th a t, for th e se m an tica lly exclusive d isju n ctiv e, th e a lte rn a tiv e s o f polling o ver 15 p e r cen t o f the vote, a n d losing o n e ’s d e p o sit are in co m p a tib le. T h e tru th o f e ith e r p ro p o sitio n im plies th e falsity o f the o th er, a n d vice versa. In th e se m an tica lly inclusive e x am p le, it is clear th a t c a n d id a te s for M S c m u st hav e a t least on e o f th e tw o qualificatio n s specified. So if one q u a lifica tio n is n o t m et they m u st have the o th e r, b u t th e converse o bviously does n o t follow. So far we hav e only co n sid ered c o m p o u n d p ro p o sitio n s involving

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one re la tio n . T h e re a re , how ever, no lim its to the c o m b in a tio n s o f relatio n s th a t m ay be used. T h e only c o m b in a tio n th a t will a rise in the w ork to be review ed is th a t o f n e g a tio n w ith o th e r re la tio n s. F o r exam ple, th e re a re four c o n d itio n al ru les th a t can be c o n stru c te d by p e rm u tin g th e p re sen c e o f a n e g a te d p ro p o sitio n in e ith e r co m ­ ponent: (1) I f p then q, (2) I f p then not q, (3) I f not p then q, a n d (4) I f not p then not q. S im ilarly four d isju n ctiv e ru les can be form ed by p e rm u tin g negatives. W e shall see in the follow ing c h a p te rs th a t the m a n ip u la tio n o f the p resen ce o f n eg ativ e c o m p o n e n ts h a s led to in te restin g e m p irica l findings, a n d stim u la te d im p o rta n t th eo re tic al a rg u m e n ts.

Paradigms M ost e x p erim e n tal stu d ies h av e focused on p e o p le ’s a b ility to reason w ith c o n d itio n als a n d d isju n ctiv es. T h e m ost co m m o n m eth o d used is to p re se n t people w ith a co n d itio n al o r d isju n ctiv e inference to e v alu ate . P ro c e d u re s v ary in th a t som etim es the w hole a rg u m e n t is p re se n te d , a n d su b je cts asked to decide w h e th e r th e conclusion necessarily follows. A ltern ativ ely , the su b jects m ay be given th e prem ises plus a list o f p ossible co n ­ clusions to choose from , o r sim ply asked to sta te w h a t, if a n y th in g , follows from the prem ises. E x p erim en ters hav e also been in te re ste d in in v estig a tin g the psychological tru th tab les th a t people ‘p ossess’ for c o n d itio n al an d d isju n ctiv e rules, a lth o u g h th is p re su p p o se s a c e rta in th eo re tic al a ssu m p tio n . In a d d itio n to in ferrin g su ch tr u th tab les from inference tasks, th ere h a v e b een v a rio u s ‘d ire c t’ a tte m p ts to assess these. S ubjects could be asked to construct in stan c es w hich conform to, or c o n tra d ic t th e rules. A ltern a tiv e ly , a n d m o re co m m o n ly , p eople are asked to evaluate the effect o f p re sen te d in stan c es on the tru th v alue o f the rule. T h is is esse n tia lly sim ila r to the se n te n c e -p ic tu re v eri­ fication task (cf. C h a p te r 3), a lth o u g h th e in stan c es e v a lu a te d a re n ot n ecessarily p ictu res. F o r e x am p le, su b je cts m ay be given the ‘ru le ’: ‘If the le tte r is not A th en th e n u m b e r is 3’ T h ey m ay th en be p re sen te d w ith a le tte r-n u m b e r p a ir, A3, a n d

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asked if it conform s to, c o n tra d ic ts, o r is irre le v a n t to th e rule. T h e task differs only in co m p lex ity from th e verification tasks review ed in C h a p te r 3. T h o se involved single a sse rtio n s a n d d e n ia ls, w h ereas the above com b in es th em w ith a c o n d itio n al re la tio n . T h e above exam ple also h a s a th ird tru th v alu e (irrelev a n t) p e rm itte d . T h e p rim a ry m e a su re m e n t used in these tasks h a s been th e fre­ quency o f a lte rn a tiv e an sw e rs given. H o w ev er, som e o f th e w ork, (see e.g. E v an s, 1977a; E v an s a n d N e w ste ad , 1977; 1980) h a s e m ­ ployed response late n cy as a se c o n d ary m ea su re . W h en latencies are m e a su re d on re aso n in g tasks it is not n o rm ally possible to elim in ate those based on e rro rs as is c u sto m a ry w ith sim p le cogni­ tive tasks. T h is is b ecau se th e d efin itio n o f a n ‘e r ro r ’ is d e b a ta b le , a n d also b ecau se th e degree o f v a ria b le re sp o n d in g is too larg e to m ake d a ta d ro p p in g p ra c tic a b le . It is best to look u p o n th e re ­ sponses as reflecting decisions w ith tw o m e a su ra b le c h ara cte ristics: latency a n d outcom e. T w o o th e r tasks a re c onsidered in this p a rt o f the book, b o th o f w hich w ere devised by W aso n . W h ile these tasks re q u ire u n d e r­ sta n d in g o f p ro p o sitio n a l logic for th e ir so lu tio n , they also involve a d d itio n a l devices su ch as h y p o th esis fo rm atio n a n d active seeking o f in fo rm atio n . O n e o f th ese tasks, th e T H O G p ro b lem , is d esigned to in v estig ate p e o p le ’s u n d e rsta n d in g o f th e logic o f exclusive d is­ ju n c tio n a n d is discu ssed in C h a p te r 10. T h e o th e r, k now n a s the ‘selection ta s k ’ o r ‘fo u r-ca rd p ro b le m ’ h a s g e n e ra te d m u c h recen t research, a n d p ro b a b ly o ccasioned m ore in te re stin g psychological w ork th a n a n y o th e r single p a ra d ig m review ed in this book. F o r this reason, it is acc o rd ed a c h a p te r o f its ow n (C h a p te r 9).

Issues T h e issue o f prim ary' in te re st in th e review o f w ork on classical syllogism s (P a rt II ) w as the d e b a te for a n d a g a in st ra tio n alism . T h e H en le view th a t all re aso n in g e rro rs w ere a ttr ib u ta b le to e rro rs o f in te rp re ta tio n ra th e r th a n logic w as e x am in ed in som e d e ta il. I t w as con clu d ed th a t th e h y p o th esis d id n o t fare very well unless one assum es th a t th e in te rp re ta tio n o f a given sen ten ce can v a ry across p a rad ig m s. I t w as also o b serv ed th a t rival e x p la n a tio n s in term s o f non-logical biases a n d in tru sio n s o f p e rso n al beliefs received equ ally good e m p irica l su p p o rt.

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T h e sa m e issue arises in th e stu d y o f p ro p o sitio n a l reaso n in g , in w hich som e a u th o rs have tried to a p p ly H e n le-ty p e e x p la n atio n s. H ow ever, th e issues b ro a d e n h ere in several respects. F o r exam ple, a different a sp e ct o f the n o tion o f ra tio n a lism is ex p lo red w ith respect to w ork o n th e selection task (C h a p te r 9). T h is is th e idea th a t b e h a v io u r is d e te rm in e d by conscious stra te g ies w hich a re a v a il­ able to in tro sp ec tio n . E v idence will be p re sen te d w hich causes dif­ ficulties for this view , a n d stim u la te s a lte rn a tiv e th eo retical proposals. T h e discussion o f p ro p o sitio n a l re aso n in g p e rfo rm a n ce will also be influenced by th e tw o-factor th eo ry o f re aso n in g (cf. E vans, 1972a; 1977a, 1977b) w hich w as m en tio n ed in C h a p te r 5, b u t m ust now be ex p la in ed in m ore d e ta il. T h e theory p o stu la te s th a t the v a ria b ility o b serv ed in resp o n se to re aso n in g tasks is com posed o f tw o o rth o g o n al sta tistic a l c o m p o n e n ts, e ach o f w hich reflects the influence o f a d istin c t type o f factor. W ith su ita b le c o n tro ls - often involving the m a n ip u la tio n o f negatives - it is possible to d istin g u ish a logical a n d non-logical c o m p o n e n t o f p e rfo rm a n ce . T h e ‘logical’ co m p o n en t reflects th e d e g ree to w hich su b je c ts’ resp o n ses a re re ­ lated to th e logical stru c tu re o f th e task - su c h respon ses need not be ‘logical’ in th e sense o f logically c o rre c t. T h e non-logical com ­ p o n en t reflects th e e x te n t to w hich su b je cts resp o n d to logically irrelev a n t fe atu res o f th e p ro b lem s. T h e th eo re tic al a ssu m p tio n s a b o u t th e n a tu re o f the tw o factors u n d e rly in g these c o m p o n e n ts have evolved so m e w h a t o ver succes­ sive p a p e rs, a n d a sy n th esis will be given here. T h e logical com ­ p o n en t is th o u g h t to arise from th e su b je c t’s a tte m p t to solve the task as in stru c te d . T h e fact th a t som e inferences a re m ore read ily perceived th a n o th e rs is a ttrib u te d to linguistic influences - w h at E vans (1972a) calls interpretational facto rs - o r to th e a m o u n t a n d difficulty o f th e cognitive p ro cessin g they re q u ire . T h e non-logical co m p o n en t is th o u g h t to reflect resp o n se biases, a tte n tio n to logi­ cally irre le v a n t featu res o r a p p lic a tio n o f in a p p ro p ria te he u ristic s. Since the tw o c o m p o n e n ts a re sta tistic a lly o rth o g o n al, this im plies th a t the u n d e rly in g processes a re parallel in n a tu re . In o th e r w ords a conflict m odel is a ssu m e d in w hich logical a n d non-logical influ­ ences c o m p ete for co n tro l o f the su b je c ts’ responses. T h is m eans th a t the relativ e weighting given to th e tw o factors m u st be taken into a c c o u n t in e x p la in in g th e d a ta . A form al m odel in c o rp o ra tin g

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these p ro p e rtie s h a s been d eveloped by E v an s (1977b) a n d will be explained in C h a p te r 9. O n e w ay in w hich th e tw o-factor th eo ry is testa b le is in its a ssu m p tio n th a t lin g u istic factors affect o nly th e logical c o m p o n e n t o f p e rfo rm a n ce , w h ereas non-logical biases arise from specific o p ­ e ratio n a l re q u ire m e n ts o f th e task (see E v an s, 1972a). A n exam ple o f the la tte r is a n a p p a re n t preference for en d o rsin g a rg u m e n ts th a t have negative ra th e r th a n affirm ativ e conclu sio n s (see C h a p te r 8). T h is so rt o f ‘re sp o n se b ia s’ sh o u ld be in d e p e n d e n t o f th e lin g u istic o r logical s tru c tu re o f the task. C o n v ersely , v a ria tio n s in the logical co m p o n en t a ttrib u te d to linguistic influences sh o u ld be m anifest on tasks o f different s tru c tu re w hich involve th e sa m e lin g u istic form s. T h e fo rm alisatio n o f th e th eo ry in th e form o f a m a th e m a tic a l m odel (E vans, 1977b) also in cre ases its p re d ic tiv e pow er, a n d we sh all see in C h a p te r 10 how a p p lic a tio n o f the m odel revealed a n e rro r in the a p p lic a tio n o f th e theory w hich m ig h t not oth erw ise h a v e been d etected . F inally a n d m ost re ce n tly E v an s (1980a) has linked the tw o fa cto r th eo ry to th e W aso n a n d E v an s (1975) ‘d u a l-p ro c ess th eo ry ’ in w hich b e h a v io u ra l resp o n ses a n d v e rb a lisa tio n s w ere a ttrib u te d to d istin c t system s o f th o u g h t. T h e c o n se q u en t ‘revised du al p ro c ess’ theory is e x p la in ed a n d assessed in C h a p te r 12 (P a rt IV ). T h e tw o -facto r th eo ry leads to an in te re st in lin g u istic a n d inte rp re ta tio n a l factors, as d o o th e r th eo re tic al a p p ro ac h es. It differs rad ically from re p re se n ta tio n a n d p rocess m odels, how ever, in a s­ su m in g parallel influences on b e h a v io u r ra th e r th a n se q u e n tial stages. A lso, w hile the logical c o m p o n e n t reflects the influence o f in te rp re ta tio n a l factors as assu m e d by th e H en le h y p o th esis, it does not a ttrib u te all re aso n in g e rro rs to su c h influences. In d e e d , m an y erro rs a re su p p o sed to arise from n on-logical biases. Since the H en le a p p ro a c h w ould be p referred on the g ro u n d s o f p a rsim o n y , it is n ecessary to d e m o n s tra te its in a d e q u a c y to a c c o u n t for th e d a ta an d e x p lain th e n eed to p o stu la te a tw o-factor e x p la n a tio n . T h e relative m erits o f these tw o p ositions will be co n sid ered th ro u g h o u t the discussion o f e x p e rim e n ta l re su lts in P a rt I I I . In a d d itio n to th e influence o f task a n d linguistic structure on reaso n in g p e rfo rm a n ce , the effect o f p ro b le m content will be a m a tte r o f m ajo r co n cern . L ogically, a p ro b le m ’s so lu tio n is unaffected by the m ea n in g o f the a c tu a l p ro p o sitio n s su b s titu te d for p a n d q. P sychologically, how ever, c o n te n t v a ria b le s m ay h a v e a p ro fo u n d

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influence as we saw in C h a p te r 6. T h is influence could arise from the presence o f c o n te x tu al cues w hich a lte r th e in te rp re ta tio n o f the pro b lem sentences. S uch effects can be h a n d le d by H e n le ’s theory o r the lo g ic a l/in te rp re ta tio n a l c o m p o n e n t o f th e E v an s tw o facto r theory. T h e la tte r theory, how ever, p e rm its o f a n a lte rn a tiv e effect discussed by E v an s (1977b); it m ay affect the weighting given to logical versus n on-logical processes. T h e g e n era l im p lica tio n s o f the effects o f c o n te n t a n d o th e r v a ria b le s will be tak en u p in P a rt IV .

Conditional reasoning

S tudies o f c o n d itio n a l reaso n in g hav e g en erally focused on sentences o f the linguistic form I f p then q, a lth o u g h a few stu d ies have also u tilised th e form p only i f q, a n d these will be discu ssed la te r in this c h a p te r. Som e o f th e w ork in v estig a tin g c o n d itio n a l re aso n in g has h ad little o r no th eo re tic al c o n te n t. In som e cases th e a im seem s to be sim ply to d isc o v er w h e th e r o r n o t peo p le hav e the co m p eten ce to p e rfo rm c erta in logical inferences, a n d how su ch co m p eten ce develops w ith age. T h e p ro b le m w ith this a p p ro a c h is th a t it a s­ sum es th a t th e a b ility to perform , for ex am p le, a m o d u s tollens inference is situ a tio n in d e p e n d e n t. I f a su b je ct c a n solve a specific e x p erim e n tal p ro b le m w ith th is logical stru c tu re , th e n it is su p p o sed th a t he ‘possesses’ it a s p a r t o f his general logical c o m p eten ce. As we shall see, th is a s su m p tio n is h a rd to ju stify . T h e findings will, how ever, be d iscu ssed w ith reference to the th eo re tic al p ositions a d o p te d by H en le a n d by E v an s (cf. C h a p te r 7).

Studies of conditional reasoning ability Conditional inferences A n u m b e r o f stu d ies hav e assessed p e o p le ’s ten d en cy to m ake the four inferences asso c iated w ith c o n d itio n a l rules - M P , D A , A C , a n d M T (cf. T a b le 7.3). F re q u e n tly , a b s tra c t c o n te n t is used. F or exam ple, the follow ing defines a n M T inference, w hen th e su b je ct is asked to reaso n a b o u t le tte r-n u m b e r pairs:

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Conditional reasoning

129

G IV E N (1) I f the le tte r is A th en th e n u m b e r is 6 (2) T h e n u m b e r is n o t 6 C O N C L U S IO N T h e le tte r is n o t A A su b je ct m ig h t be p re sen te d w ith th e above a rg u m e n t a n d asked to assess its v a lid ity . H e m ay be asked to decid e w h e th e r o r not the conclusion necessarily follow s from th e p rem ises, o r else to ra te the tru th o f th e c onclusion a ssu m in g th e tru th o f the prem ises. I f su b je c ts’ o bserved responses reflect only th e ir in te rp re ta tio n o f the sentence, th en tw o different re aso n in g p a tte rn s m ig h t be ex­ pected, a cc o rd in g to w h e th e r I f p then q is in te rp re te d as im p lica tio n o r equivalence (see last c h a p te r). In th e form er case, su b je cts should endorse M P a n d M T b u t not D A a n d A C . In the la tte r, they should endorse all four inferences. I f g ro u p d a ta reflect a m ix tu re o f su b jects em ploying b o th in te rp re ta tio n s th e n w'e sh o u ld expect th e frequency o f M P a n d M T to e q u al 100 p e r c en t, a n d the freq u en cy o f D A a n d AC to e q u al e ac h o th e r a t som e level in te rm e d ia te b etw een 0 an d 100 p er cent. M ost early e x p erim e n ts looked only a t affirmative c o n d itio n als, I f p then q (see W aso n a n d Jo h n s o n -L a ird , 1972). W e will c o n sid er first som e d a ta for rules o f th is sort. T a b le 8.1 show s the re su lts o f three stu d ies o f a d u lt reaso n in g . T h e d a ta show a fairly c o n sisten t p a tte rn . M P is very freq u e n tly e n d o rsed . M T , th o u g h e n d o rsed m ore often th a n n o t, is co n sisten tly a n d so m etim es c o n sid era b ly , less often e n d o rsed th a n M P . T h is causes p ro b lem s for th e H en le hypothesis, in w hich it is assu m e d th a t re aso n in g e rro rs arise solely d u e to m isin te rp re ta tio n . It is n o t c le a r how th e c o n d itio n a l could be in te rp re te d su ch th a t M T w ould n o t be n ecessary. T h e o th e r p red ictio n , th a t D A a n d A C frequencies will be e q u a l, fits p re tty well w ith in e ac h stu d y o r e x p e rim e n ta l condition. T A B L E 8.1 Percentage o f adult subjects endorsing conditional inferences in several studies, fo r an affirmative rule, I f p then q Study

MP

DA

AC

MT

T a p lin (1971) T a p lin a n d S tau d en m ay er (1973) E vans (1977a)

92 99 100

52 82 69

57 84 75

63 87 75

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A n u m b e r o f stu d ies hav e looked a t c h ild re n ’s a b ility to solve con d itio n al syllogism s. H e re, th e in te re s t h a s focused on P ia g e t’s theory o f form al o p e ratio n s. F o r e x am p le, H ill (1961) (cited by Suppes, 1965) claim ed th a t c h ild ren o f age 6 -8 w ere a b le to p erform re m a rk ab ly well o n c o n d itio n a l re aso n in g p ro b lem s, w hich o u g h t to re q u ire form al o p e ra tio n a l th o u g h t. O ’B rien a n d S h a p iro (1968) confirm ed th is finding, a lth o u g h th ey d id n o t, u n fo rtu n a te ly , re p o rt d a ta on the different kinds o f c o n d itio n al inference. R oberge (1970) an d K o rd o ff a n d R o b erg e (1975) d o re p o rt evidence for d e v elo p ­ m en ta l im p ro v e m en t in c o n d itio n al re aso n in g a b ility , b u t th e g e n ­ eral p a tte rn o f difficulty acro ss inference types is sim ila r to th a t o f adu lts: th a t is, M P is c o rre c tly e n d o rsed m o re often th a n M T a t all ages, w hile th e ‘fa llac io u s’ D A a n d A C also ten d to be en d o rsed (very often in y o u n g c h ild re n ). T h e M P /M T difference is n o t h a rd to e xplain if a sim p le H e n le position is a b a n d o n e d . G iven I f p then q, th e inference p therefore q is so e v id e n t th a t o n e w o u ld h a rd ly w ish to call it reaso n in g . I t is h a rd to see how o n e co u ld u n d e rs ta n d th e m ea n in g o f th e c o n d i­ tional w ith o u t m ak in g M P . M T , how ever, does re q u ire som e reasoning. W ith reference to th e M T p ro b le m p re se n te d e a rlie r, the subject m ig h t a rg u e so m e th in g like: ‘A ’s alw ay s hav e a 6 w ith th em , so any le tte r w hich does not hav e a 6 w ith it c a n n o t be a n A ’. T h e re are tw'o o th e r factors w h ich m ig h t a c c o u n t for th e e x tra difficulty o f M T . O n c e c o n cern s th e directionality o f th e c o n d itio n al: it is a rg u a b le th a t inferences from a n te c e d e n t to c o n se q u e n t a re easie r to m ake th a n those in reverse. T h e second fa cto r is n eg ativity: M T involves a n e g ated second p rem ise a n d a n e g a te d conclusion. T h e d ire c tio n ­ ality o f c o n d itio n als will be c o n sid ere d in a la te r section; th e p ro b lem o f negativ ity will be c o n sid ere d now. I f n e g ativ e c o m p o n e n ts a re in tro d u c e d in to the rules, th en the a d d itio n a l p rem ises a n d c onclusions c o rre sp o n d in g to th e four c o n ­ ditio n al inferences a re as show n in T a b le 8.2. I t will be noticed th a t each inference is now a sso c iated w ith b oth affirm ative a n d negative prem ises a n d conclusions, a cc o rd in g to th e rule. A n u m b e r o f stu d ies hav e show n th a t the p a tte rn o f re sp o n se to the four c o n d itio n a l inferences is sig n ifican tly affected by the in tro ­ d u c tio n o f n e g ativ e c o m p o n e n ts in th e rules (R o b erg e, 1971b; 1974; 1978; E v an s, 1972b; 1977a). T h e R o b erg e p a p e rs d o n o t p re se n t th e d a ta in a w ay w h ich e n ab les one to see the p a tte rn s for e ac h rule a n d inference se p a ra te ly , so T a b le 8.3 p re se n ts d a ta for the E v an s

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131

Conditional inferences fo r rules involving negative components MP DA AC MT c o n c lu d e g iv e n c o n c lu d e g iv en c o n c lu d e g iv en c o n c lu d e

R u le

giv en

(1) I f p then q e g. I f th e l e tte r is A th e n th e n u m b e r is 7

p

q

A

7

(2) I f p then not q e .g . I f th e l e tte r is C th e n th e n u m b e r is n o t 5

p

q

C

not 5

(3) / / not p then q e g I f th e le tte r is n o t R th e n th e n u m b e r is 1

p

q

not R

1

(4) I f not p then not q e.g. I f th e l e tte r is n o t W th e n th e n u m b e r is n o t 4

p

, q

n o t \V n o t 4

P q not A not 7

q

P q not C 5

q

P A

q

P not 5 C

q

q

q

q

not 1

1

P

q

q

W

4

P R

7

P not R

P not 4 not W

P not 7 not A

5

P n o t c:

P not 1 R

q

P

4

w

p = 'not p ’ q = ‘not q ’

(1977a) stu d y . Also in clu d ed a re th e d a ta o f P o llard a n d E vans (1980, E x p e rim e n t 1), w ho used a different p a ra d ig m w hich a p p e a rs to be psychologically e q u iv a len t. T h e y p re sen te d su b je cts w ith one c onditional ru le a n d asked th em w h e th e r a n o th e r c o n d itio n al rule w as e n ta ile d by it. F o r e x am p le, given th a t th e (affirm ative) con­ d itio n a l is true: I f p th en q subjects m ig h t be asked if an y o f the follow ing m u st also be true: I f n o t p th en not q (inverse) I f q th en p (converse) I f n o t q th e n n o t p (c o n tra p o sitiv e ) T h e ir d a ta a re p re se n te d on th e a ssu m p tio n th a t e n d o rsin g the inverse, converse a n d c o n tra p o sitiv e a re psychologically e q u iv a len t to en d o rsin g D A , A C a n d M T . R eference to T a b le 8.2 should in d ic a te th e logical sim ila rity o f th e tw o tasks. E m p irica lly the tw o tasks d o seem to p ro d u c e sim ila r re su lts, w ith a ra n k c o rre latio n o f 0.886 b etw een th e E v an s, a n d P o llard a n d E v an s d a ta across conditions. T h e R oberge, E v an s, a n d P o llard a n d E v an s stu d ies all show certain sy ste m atic effects o f negatives. F o r ex am p le, th e M T infer-

132

Propositional reasoning T A B L E 8.3 Percentage o f subjects endorsing conditional inferences fo r rules which contain negative components MP

DA

AC

MT

I f p then q E v an s (1977a) P o llard a n d E v an s (1980)*

100 -

69 54

75 66

75 59

I f p then not q E v an s (1977a) P o llard a n d E vans (1980)*

100 -

12 30

31 37

56 72

I f not p then q E v an s (1977a) P o llard an d E vans (1980)*

100 -

50 47

81 72

12 34

I f not p then not q E v an s (1977a) P o llard a n d E v an s (1980)*

100 -

19 37

81 64

25 44

Overall E v an s (1977a) P o llard a n d E vans (1980a)*

100 -

38 35

67 60

42 53

* E x p e rim e n t 1.

ence is re lia b ly less o ften m a d e w h e n th e a n te c e d e n t is n e g a tiv e , as in th e follow ing e x am p le: G IV E N (1) I f th e le tte r is n o t D th e n th e n u m b e r is 7 (2) T h e n u m b e r is n o t 7 C O N C L U S IO N T h e le tte r is D T h e c o n c lu sio n is v a lid , b u t m o st su b je c ts r a te it as ‘in d e te rm in a te ’. O n e p o ssib le e x p la n a tio n o f th is w o u ld be t h a t a n e x tra ste p o f in feren ce is re q u ire d to d e a l w ith a d o u b le n e g ativ e. M T lea d s th e su b je c t in th e a b o v e e x a m p le to in fer t h a t th e le tte r c a n n o t be n o t a D; h e m u s t th e n re alise th a t th is im p lies th a t th e le tte r m u s t be a D. I f th e difficu lty is d u e to a n in a b ility to d e n y a n e g a tiv e , th e n the D A in fere n ce sh o u ld a lso be less fre q u e n t w h e n th e c o n se q u e n t is n e g ativ e, as in

Conditional reasoning

133

G IV E N (1) I f the le tte r is B th en the n u m b e r is not 4 (2) T h e le tte r is not B C O N C L U S IO N T h e n u m b e r is 4

DA is in d ee d m a d e significantly less often w hen th e c o n se q u en t is neg ated in b o th th e E v an s, a n d P o llard a n d E v an s stu d ies (cf. T a b le 8.3). H ow ever, th e A C inference is also significantly m ore often en d o rsed in b o th stu d ies on th e rules w ith n egative a n te ­ cedents. W h y sh o u ld su b je cts find it easier to affirm a c o m p o n e n t w hich is negative? W e sh all re tu rn to th is p ro b lem shortly. It w ould be ex trem ely difficult to exp lain the resu lts o f these studies by a rg u in g th a t th e negatives a lte r su b je c ts’ in te rp re ta tio n o f the rules. F o r ex am p le, if A C occurs m o re often on the rules w ith negative a n te c e d e n ts b eca u se such ru les a re in te rp re te d as eq u iv ­ alences, th en a c o rre sp o n d in g in crease in D A inference sh o u ld o c cu r on these rules. It does n o t. S im ilarly, the red u ced D A on rules w ith negative c o n se q u en ts sh o u ld be a cc o m p a n ied by a c o rre sp o n d in g decrease in A C , if th ese rules are m o re often in te rp re te d as im p li­ cation. In fact, in the E v an s (1977a) stu d y , A C significantly increased on these rules. T h e re su lts a re b est d e sc rib e d w ith in th e fram ew ork o f th e E vans tw o-factor theory (see C h a p te r 7). I t is assu m e d th a t th e n egatives do not affect th e in te rp re ta tio n o f rules, a n d hence th e logical co m ­ p o n en t, b u t affect c e rta in non-logical resp o n se biases. In this case, E vans (1977a) p ro p o sed th a t su b je cts are m ore in clined to a cc ep t a conclusion w hich is negative r a th e r th a n affirm ative. T h e effects o f n eg atio n on all th ree inferences (D A , A C , M T ) a cc o rd w ith this bias. T h e lack o f effect o f n eg ativ es on M P is ex p la in ed as in d ic a tin g a w eig h tin g totally in fav o u r o f the logical c o m p o n e n t on these inferences (w hich people a lm o st alw ays e v a lu a te c o rre c tly ). T o p u t it a n o th e r w ay, M P is totally w ith in the su b je c t’s logical co m p eten ce a n d th u s re sista n t to re sp o n se biases. P o llard a n d E v an s (1980) hav e suggested th a t this ‘n eg ativ e con­ clusion b ia s’ m ight be d u e to a c au tio u s a ttitu d e o n th e p a r t o f the subjects. A negative conclusion is less likely to be false. F o r exam ple, the conclusion ‘T h e le tte r is A ’ is only tru e if one p a rtic u la r le tte r is actu ally p re sen t, w h ereas the conclusion ‘T h e le tte r is n o t A ’ can

134

Propositional reasoning

only be falsified in o n e w ay. I f in d o u b t, a n e g ativ e m ig h t seem to be a safer bet. (T h is a rg u m e n t is e la b o ra te d in C h a p te r 11.) W hen the inference ra te is av era g ed across the four rules, then the influence o f resp o n se b ias is co n tro lled for an y given inference, since tw o affirm ative a n d tw o negative conclusions a re involved in th e four p ro b lem s p ooled in e ac h case (see T a b le 8.2). U n fo rtu n a te ly these av erag ed ra te s c a n n o t be tak e n to in d ic a te th e re la tiv e stre n g th o f different inferences in th e ‘logical c o m p o n e n t’. F o r e x am p le, the average ra te o f M P is a p p ro x im a te ly d o u b le th a t o f M T (T a b le 8.3). T h is does n o t, how ever, necessarily m ean th a t th e re is a stro n g e r ten d e n cy to m ak e M P on the basis o f su b je c ts’ u n d e rs ta n d ­ ing o f the rule. T h is is b ecau se the weighting given to the logical co m p o n en t is not th e sa m e on the tw o inferences. As a lre a d y no ted , p a rt o f th e v a ria b ility on M T is a c c o u n te d for by re sp o n se-b ias effects, w h e rea s they hav e negligible effect o n M P . T h e a c tu a l n a tu re o f the logical c o m p o n e n t c a n only be d isco v ered by fittin g a form al m odel. T o d a te , th is h as been a tte m p te d only for d a ta collected on the W 'ason selection task (see C h a p te r 9). P ollard a n d E v an s (1980) h av e, how ever, utilised a n a lte rn a tiv e tec h n iq u e to in v estig a te w h e th e r th e re is a logical basis to an y con d itio n al inferences o th e r th a n th e M P inference. T h e y a n aly se d ind iv id u al differences, to test the h y p o th esis th a t som e su b jects have m ore logical a b ility th a n o th ers. I f th is w ere so, th e n th e a b ility to m ake (say) a n M T inference on one ru le sh o u ld be c o rre la te d w ith the a b ility to m ak e it on a n o th e r. W h en in d iv id u a l differences for base ra te o f offering c onclusions w as c o n tro lled , they found no evidence o f such a c o rre latio n . In a second e x p erim e n t, th ey looked at su b je c ts’ ten d e n cy to reject th e o p p o site o f an in ference. F o r exam ple, if a n M T (c o n tra p o sitiv e ) p ro b lem is th e follow ing: G IV E N I f th e le tte r is B th en th e n u m b e r is 2 C O N C L U D E I f the n u m b e r is not 2 th en th e le tte r is n o t B th en its o p p o site, M T (O ) is G IV E N I f th e le tte r is B th en th e n u m b e r is 2 C O N C L U D E I f th e n u m b e r is n o t 2 th en th e le tte r is B In th is e x p e rim e n t su b je cts could say th a t the c onclusion w as e ith e r necessarily true, necessarily false or neither. T h e a u th o rs a rg u e th a t, if the a b ility to say ‘tru e ’ to th e fo rm er is d u e to a logical a p p re c i­ ation o f M T , th en it sh o u ld c o rre late w ith a ten d en cy to say ‘false’

Conditional reasoning

135

to the la tte r. T h e y fo und only a w eak asso c iatio n for M T a n d D A inferences, a n d they a ttrib u te d th e in d iv id u a l differences they found to differences in su sce p tib ility to n eg ativ e conclusion bias, ra th e r th an to differences in logical ability. T h e d e g ree o f in d e p e n d e n c e o f p e o p le ’s resp o n se to different p roblem s o f re la te d logical stru c tu re in th is stu d y is really q u ite re m a rk ab le , a n d a p p e a rs to defy a n y ra tio n a listic e x p la n atio n . T h e above is on e o f very few stu d ies th a t hav e looked a t in d iv id u a l differences in re aso n in g , a n d this a p p ro a c h sho u ld surely be a d o p te d m ore often.

Inferred truth tables I t is u n fo rtu n a te , in view o f the p rev io u s section, th a t m ost a u th o rs stu d y in g co n d itio n al re aso n in g have looked only a t affirm ative rules. F u rth e rm o re , m a n y h a v e ten d e d to infer u n d e rly in g in te rp re ta tio n s o r tru th tab le s from su b je c ts’ o b serv ed responses to c o n d itio n al syllogism s (e.g. T a p lin , 1971; T a p lin a n d S ta u d e n m a y e r, 1973; S ta u d e n m a y e r, 1975; S ta u d e n m a y e r a n d B ourne, 1978; R ips an d M a rcu s, 1977; M a rc u s a n d R ips, 1979). In this a p p ro a c h , su b jects a re classified as h a v in g a tru th tab le for e ith e r im p lica tio n (or c o n d itio n al) o r eq u iv a len c e (or b ico n d itio n a l). T h e fo rm er involves subjects w ho m ak e M P a n d M T b u t n o t D A a n d A C , w hile the la tte r classification is for su b je cts w ho m ake all four inferences. T h e a u th o rs a d o p tin g th is a p p ro a c h freq u e n tly p re se n t th e ir d a ta only in th is classified form , w ith o u t giving th e a c tu a l frequencies o f p a rtic u la r inferences. H o w ev er, th is classification system rests c rit­ ically on th e ra tio n a list a ssu m p tio n th a t peo p le reaso n logically given th e ir p e rso n al in te rp re ta tio n o f th e rules. I t will be e v id e n t th a t th e th eo re tic al positio n a d o p te d in th e p rev io u s section is q u ite in co m p a tib le w ith this. T h e re it w as p ro p o sed th a t th e a c tu a l fre­ q uency o f re sp o n d in g to c o n d itio n al inference p ro b lem s w as co n ­ sid erab ly d isto rte d by th e non-logical negative conclusion bias. I f this a ssu m p tio n is co rre c t, th en one w ould expect th a t the a tte m p t to infer tru th tab le s from inference tasks w ould be ra th e r unsuccessful. I n p a rtic u la r, o n e w o u ld ex p ect th e d a ta o f m an y subjects not to conform c o n sisten tly to a p a rtic u la r tr u th tab le . L et us look a t th e evidence. T a p lin (1971) found th a t only 45 p e r cent o f his su b je cts re aso n e d in a c o n sisten tly tru th -fu n c tio n a l m a n n e r,

136

Proposilional reasoning

the g re at m ajo rity o f these being classified as ‘e q u iv a le n c e ’. T a p lin an d S ta u d e n m a y e r (1973) found m u ch h ig h e r consistency (a b o u t 80 p er cent) w ith th e m ajo rity a g ain co n fo rm in g to ‘e q u iv a le n c e ’. In a second e x p e rim e n t, how ever, less th a n 50 p e r cen t w ere tru th -fu n c tio n a l, a n d th e m ajo rity o f these classified as ‘implication’. T h is last e x p erim e n t differed from the o th e rs in th a t su b je cts w ere not asked sim ply to ra te the c onclusion as tru e o r false, b u t given an in te rm e d ia te ‘so m etim es tru e (o r false)’ o p tio n . M a n y su b jects sw itched th e ir response on D A a n d A C p ro b lem s from tru e to som etim es true. A p a rt from th e u n im p re ssiv e p ro p o rtio n o f ‘tru th -fu n c tio n a l’ s u b ­ jec ts in these th re e e x p erim e n ts, th e d isc re p a n c y in th e la tte r resu lts casts d o u b t on th e inferred tru th -ta b le a p p ro a c h . S u b je c ts’ in ­ te rp re ta tio n o f the ru les sh o u ld su rely n o t d e p e n d on the m eth o d o f testing th e ir inferences. A ctu ally , som e form o f in d e te rm in a te choice, as in T a p lin a n d S ta u d e n m a y e r’s second e x p erim e n t, is logically necessary. C o n sid e r th e follow ing AC syllogism : G IV E N (1) I f the le tte r is H th en the n u m b e r is 7 (2) T h e n u m b e r is 7 CONCLUDE T h e le tte r is H A su b je ct asked to ra te th e tru th o f this conclusion, given the tru th o f th e p rem ises, can only be logically c o rre c t if he m akes an in d e te rm in a te response. T h e c onclusion m ig h t o r m ig h t n o t be tru e, so a tru e /fa lse forced choice forces the su b je ct to m ake on e o f tw o erroneous inferences. S ta u d e n m a y e r (1975) in clu d e d a ‘so m e tim e s’ categ o ry . H e co n ­ ceded th e existence o f non-logical factors in c o n d itio n al reaso n in g tasks, b u t n e v erth ele ss m a in ta in e d the classification o f responses in to u n d e rly in g tr u th tables. In th ese e x p erim e n ts su b je cts w'ere given different se m a n tic co n tex ts, th e effects o f w hich will be d is­ cussed in a la te r section. O u r co n ce rn h ere is the consistency w ith w hich such classifications a re m ad e . T h e p ro p o rtio n o f c o n sisten t subjects w as 78 p e r cen t w ith a b s tra c t m a te ria l a n d only 55 p e r cent w ith co n cre te m a te ria l. H ow ever, c o n sisten t su b je cts w ere not necessarily tru th -fu n c tio n a l, a n d th e ir classifications o f tru th tables did not re q u ire a b so lu te consistency, so the d a ta a re h a rd to assess.

Conditional reasoning

137

S ta u d e n m a y e r a n d B o u rn e (1978), re q u irin g only 75 p e r cent co n ­ sistency, failed to classify a n a la rm in g 33 p e r c en t o f th e ir su b jects in one e x p erim e n t. A recen t stu d y by M a rc u s a n d R ips (1979) p ro d u ces even w orse figures. O v e r a variety o f se m an tic contexts, responses to c o n d itio n al inferences w ere logically c o n tra d ic to ry for an average o f 53 p e r cen t o f su b jects tested. In assessing these figures tw o p o in ts m u st be b o rn e in m ind. F irstly th e fact th a t som e su b je cts do co n sisten tly conform to a tru th table m ay n o t be b ecau se they a re ‘u sin g ’ it. N on-logical factors w ould conceivably p ro d u c e the sam e resp o n se p a tte rn . S econdly, som e su b je cts m ay a p p e a r c o n sisten t by chance. I f all su b jects behave in a p ro b a b ilistic m a n n e r, c erta in highly p ro b a b le c o m b in a tio n s will a p p e a r co n sisten tly for som e su b je cts b u t not for o th ers. In o th er w'ords, o n e c a n n o t be su re from an y o n e e x p erim e n t th a t som e subjects hav e q u a litativ ely d istin c t in te rp re ta tio n s from oth ers. T h e q u e stio n o f consistency acro ss tasks will be reconsidered later. W e now tu rn to so-called ‘d ire c t’ a tte m p ts to m ea su re tru th tables for c o n d itio n al rules.

‘Direct’ measures o f psychological truth tables In the p rev io u s section tru th tables w ere referred to as re p re se n tin g eith er im p lica tio n o r equiv alen ce. H ow ever, it w as p o in te d o u t in the previous c h a p te r th a t th e tru th tab le s m ay be ‘defectiv e’, i.e. con tain ‘irre le v a n t’ o r in d e te rm in a te tru th v alues (see T a b le 7.2). Even if tr u th tab le s could be inferred from syllogistic p e rfo rm a n ce , this could n o t lea d to th e d e tectio n o f defective v alues. F o r exam ple, M P a n d M T b o th follow from the fact th a t a tru e a n teced en t-false co n seq u en t (T F ) c o m b in a tio n is fo rb id d en , reg ard less o f how F T an d F F a re re p re se n ted . O n e o f th e e arlie st a tte m p ts to achieve d ire c t m e a su re m e n t o f a n u n d e rly in g tru th tab le wras by Jo h n s o n -L a ird a n d T a g a rt (1969). T hey expressed the im p lica tio n re la tio n p u q in four linguistic form s: (1) (2) (3) (4)

I f p th en q N ot p if n o t q N ot p o r q N e v er p w ith o u t q

138

Propositional reasoning

T h e a c tu a l se n ten c es used referred to c o m b in a tio n s o f le tte rs a n d n u m b e rs on c ard s. S u b je cts w ere given a pack o f c ard s w hich included c o m b in a tio n s c o rre sp o n d in g to all four logical p o ssibilities - T T , T F , F T , a n d F F . T h e y w ere asked, for each rule, to so rt them in to th re e piles, c o rre sp o n d in g to th e classifications ‘tr u e ’, ‘false’ an d ‘irre le v a n t’. N ow , the defective tru th tab le for im p lica tio n p ro p o se d b y W ason (1966) classifies T T as tru e , T F as false, a n d F T a n d F F a s irrele ­ v a n t. T h is c a n be a b b re v ia te d as T F ?? T h is w as in d ee d th e m o d al response p a tte rn for th e c o n d itio n al ru le (form (1)). O f the o th ers, only ru le (4) p ro d u c e d a sim ila r p a tte rn . S u b je cts’ responses to rules (2) a n d (3) w ere highly v a ria b le . T h u s , w hile su p p o rtin g W a so n ’s h y p o th esis for th e affirm ativ e c o n d itio n al I f p then q, J o h n s o n -L a ird a n d T a g a r t ’s e x p e rim e n t also show s th a t su b je c ts’ u n d e rsta n d in g o f im p lica tio n is h ighly d e p e n d e n t u p o n its linguistic expression. In the review o f w ork o n c o n d itio n a l inferences, it w as claim ed th a t a s u b s ta n tia l a m o u n t o f re sp o n d in g w as a ttrib u ta b le to n onlogical factors, w hich could o nly be id entified by the m a n ip u la tio n o f n egative co m p o n e n ts. T h e sa m e m a n ip u la tio n occasions sim ila r c onclusions w'hen tru th -ta b le tasks a re used (E v an s, 1972c; 1975; E vans a n d N e w ste ad , 1977). T h e first stu d y alo n g these lines w as th a t o f E v an s (1972c), w hich a tte m p te d to re p lic a te Jo h n s o n -L a ird an d T a g a r t’s fin d in g s w ith a different tec h n iq u e , th e h o p e b e in g to g eneralise th e ir re su lts to rules w ith n eg ativ e co m p o n e n ts. In this e x p erim en t su b jects w ere given a n a rra y o f coloured sh a p e s, alo n g w ith a ru le p re se n te d o n a c a rd , e.g. IF T H E S H A P E O N T H E L E F T IS A R E D C IR C L E , T H E N T H E S H A P E O N T H E R I G H T IS N O T A G R E E N S Q U A R E . F or each rule, su b je cts w ere given b o th a verificatio n a n d a falsification task. In th e v erification task, su b je cts w ere asked to place tw o figures from th e a rra y side by side to m ak e th e ru le tru e. T h ey w ere asked to in d ic a te all possible w ays o f d o in g this, b u t allow ed to g en eralise, e.g. ‘A red circle on th e left, to g e th e r w ith a n y th in g except a green sq u a re on the rig h t m akes it tru e ’. In the falsification task, su b je cts w ere asked to d e m o n s tra te all possible falsifying c o m b in a tio n s. B ecause e ac h p ro c e d u re w as e x h au stiv e, any logical case n o t c o n stru c te d o n e ith e r could be inferred to be

Conditional reasoning ‘irre le v a n t’, w ith o u t explicitly p o in tin g classification.

139

the su b je ct to su ch a

T A B L E 8.4 The combinations o f affirmed (matching) and negated (mismatching) values corresponding to each logical case on each rule, in the truth table task. Logical Case R ule

TT

TF

FT

FF

( 1) I f p then q

pq

pq

pq

pq

A7

A3

G7

H2

pq

pq

If

e.g. the letter is A th en the n u m b er is 7

•CT a.

pq

e.g. the letter is C then the n u m b er is not 5

C8

C5

L9

D5

(3) I f not p then q

pq

pq

pq

■cr a.

e.g. the letter is not R then the n u m b er is 1

Qi

L5

R1

R9

(4) I f not p then not q

pq

pq j4

pq

pq

W5

W4

(2) I f p then not q

If

If

If

e.g. the letter is not W then the n u m b er is not 4 p = not p

A6

q = not q

In o rd e r to u n d e rsta n d th e an aly sis o n e m u st first c o n sid er the co m b in a tio n s o f va lu e s p ro d u c in g th e different logical cases, as negatives v a ry in the rules (T a b le 8.4). A pq c o m b in a tio n occurs w hen a so lu tio n m a tc h e s b o th va lu e s n a m e d in th e rule. T h is co r­ resp o n d s to T T for the affirm ative ru le I f p then q. H ow ever, this m atc h in g c o m b in a tio n c o rre sp o n d s to a different logical case on each o f th e o th e r rules. In th e above e x am p le th e ru le is o f the form I f p then not q. H e n ce the d o u b le m a tc h (red circle - green sq u a re) m akes th e a n te c e d e n t tru e b u t the c o n se q u e n t false (th e T F case). I t can be seen from T a b le 8.4 th a t in e ac h ru le the four logical cases are p ro d u c ed o n e ac h ru le by e ac h o f th e four c o m b in a tio n s - p q , p q , p q , p q . H o w ev er, th e m a p p in g o f ‘m a tc h in g ’ v a lu e s o n to logical cases is different for each.

140

Propositional reasoning T A B L E 8.5 (i) Evans’ (1972c) results pooled over the four rules and classified by (a) logical case and (b) by matching case. Results are percentage frequencies (n = 24)

(a) Logical Case TT TF FT FF

T ru e

C lassification False Irrelev an t

99 3 14 33

0 80 34 23

1 17 52 44

34 41 40 34

52 33 27 25

14 26 33 41

(b) Matching Case pq pq pq pq

T A B L E 8.5 (ii) The frequency o f construction o f each logical case on rules where they constitute a double match, pq, (data from same experiement). % F requency False Irrelevant

Logical C ase

Rule

T ru e

TT

Ifp then q Ifp then not q I f not p then q I f not p then not q

¡00

0

0

0

96

4

8

75

17

29

38

33

TF FT FF

T h e resu lts o f th e E v an s (1972c) stu d y a re show n in T a b le 8.5, pooled o ver the four rules. W h en we look a t th e d a ta by tru th -ta b le case (T a b le 8.5 (i)(a )), we see th a t th e p re d ic tio n o f th e defective tru th ta b le is u p h e ld . T h e m o d al re sp o n se is ‘tru e ’ for T T , ‘false’ for T F a n d ‘irre le v a n t’ (i.e. n o n -c o n stru c te d ) for F T a n d FF . H o w ­ ever, w hen F T a n d F F are c o n stru c te d , the fo rm er is often seen to falsify a n d th e la tte r to verify. T a b le 8.5 (i)(b ) show s th e d a ta a rra n g e d by ‘m a tc h in g c a se ’. Since e ach m a tc h in g case a p p e a rs eq u ally often as e ac h logical case,

Conditional reasoning

141

w hen pooled o v e r the four rules, a n y effect o f th is fa cto r is seen as ‘non -lo g ical’. I f one looks a t the ‘irre le v a n t’ c o lu m n , th en a c le ar tren d can be seen for these (n o n -c o n stru c te d ) choices to in crease as the n u m b e r o f m fim atches increases. In o th e r w ords su b je cts a re m ore likely to c o n stru c t a n in stan c e if its item s m a tc h those n a m e d in the rule. E v an s (1972c) term ed th is effect ‘m a tc h in g b ia s ’. T h e discovery o f this a p p a re n t non-logical resp o n se bias p a ralle ls the finding o f negative conclusion b ias on the c o n d itio n al inference tasks, a n d len d s su p p o rt to the E v an s tw o-factor theory o f reaso n in g (cf. C h a p te r 7). T h e n a tu re o f the ‘logical c o m p o n e n t’ is so m e w h a t e asie r to d ete rm in e th a n on the inference tasks, b ecau se th e re a re th ree responses, o f w hich only on e - ‘irre le v a n t’ - is affected by the non-logical m atc h in g . T h u s th e c o n stru c tio n o f T T as ‘tru e ’ a n d T F as ‘false’ does in d ee d seem to reflect su b je c ts’ u n d e rsta n d in g o f the rule. T h e F T a n d F F cases a re m ore difficult to in te rp re t. I t could be th a t th e h igh ‘irre le v a n t’ ra te is d u e to the possession o f a defective tru th ta b le in the logical c o m p o n e n t. A ltern a tiv e ly , th ere could be less weighting given to the logical c o m p o n e n t o n these cases, w ith the ‘irre le v a n ts’ a risin g from m a tc h in g bias. E v an s a n d N ew stead (1977) h av e, for e x am p le, show n th a t m a tc h in g b ias is m uch stro n g e r on the F T a n d F F cases. I f we a ssu m e th a t the m atc h in g effect is really a su p p re ssio n o f re sp o n d in g on m ism a tc h in g cases, th en we c a n resolve the p ro b lem . Is th ere still a h ig h e r irrelev a n t ra te on false a n te c e d e n t cases if we look only a t ru les w here such cases m atc h ? L et us look a t the freq u en cy o f selecting each logical case in th e E v an s (1972c) d a ta , on th e ru les w hen a d o u b le m atc h is involved (T a b le 8.5 (ii)). A lth o u g h th ere is m ore ‘irre le v a n t’ re sp o n d in g to F T a n d F F , it is relatively low in cases th a t m a tc h . T h u s th e ev idence for the defective tru th tab le m ay be a p a rtia l a rtifa c t o f g re a te r su sce p ti­ bility to resp o n se bias on th ese cases. So far as F T is c o n ce rn ed , the logical c o m p o n e n t a p p e a rs to d e te rm in e p rim a rily a ‘false’ classifi­ cation. R e sp o n d in g to F F is rou g h ly ra n d o m acro ss av ailab le re­ sponses. T h is an aly sis a g a in rests u p o n the a ssu m p tio n th a t the in te rp re ta tio n o f th e c o n d itio n al is n o t affected by th e pre sen c e o f negative co m p o n e n ts. O th e rw ise the high ra te o f classification o f F T as false in th e ru le I f not p then q m ig h t be tak en to in d ic a te th a t this p a rtic u la r ru le is in te rp re te d as equiv alen ce. H ow ever, the effects o f m a tc h in g on ‘irre le v a n t’ classifications c a n n o t, in gen eral,

142

Propositional reasoning

be e xplained as a n illusion crea te d by in te rp re ta tio n a l effects o f negatives. F o r e x am p le, T F sho u ld be ra te d as 'fa lse ’ u n d e r an y in te rp re ta tio n o f the c o n d itio n al, b u t significant in creases in ‘irrelev a n ts’ o c cu r on th is case, as the n u m b e r o f m ism a tch e s increases. T h e m a tc h in g bias effect is not re stric te d to c o n stru ctio n tasks such as th a t o f E v an s (1972c). It h as also been d e m o n s tra te d on e v alu atio n tasks, w h ere all tru th tab le cases a re p re sen te d in tu rn w ith each rule. T h e su b je ct is n o rm ally asked to decid e w h e th e r the in stan ce conform s to th e rule, c o n tra d ic ts the ru le o r is irre le v a n t to it. W h en these responses a re classified as 'tr u e ’, ‘false’ a n d ‘ir­ re le v a n t’, a re m a rk a b ly sim ila r set o f d a ta is o b ta in e d (e.g. E vans, 1975, E v an s a n d N e w ste ad , 1977). T h u s , n o t only a re su b je cts less likely to c o n stru c t a m ism a tch in g case, b u t they a re also less likely to consider it re le v an t (tru e o r false) if it is p re sen te d to th em for ev alu atio n . O u r a n aly sis o f th e logical c o m p o n e n t is also s u b s ta n ­ tia ted by th e d a ta o f these la te r studies. A m ore e x tre m e form o f m atc h in g b ias has been o bserved in young c h ild ren (P a ris, 1973), w ho ten d to classify all m a tc h in g cases as ‘tru e ’, a n d all o th e r cases as ‘false’, irresp ec tiv e o f th e linguistic form o f th e rules p re se n te d . It is possible, as W aso n (1969a) su g ­ gests, th a t in com plex re aso n in g tasks a d u lt su b je cts m ay , to som e extent, regress to ch ild h o o d p a tte rn s o f th o u g h t, a n d this could be w h a t is h a p p e n in g to a d u lt su b je cts e x h ib itin g m a tc h in g b e h av io u r. W h a t o th e r e x p la n a tio n can be offered for th is m a tc h in g (re ­ sponse) bias? T h e o bvious a n sw e r lies in a n a p p e a l to the difficulty o f negativ ity (cf. C h a p te r 3). T h e su b je ct finds it h a rd to th in k in term s o f a ‘not 7’, a n d so is m o re likely to a tte n d to th e values nam ed in the rule (E v an s, 1975; see also Jo h n s o n -L a ird a n d W aso n , 1970). A p ro b lem w ith this e x p la n a tio n , how ever, is th e in te ra c tio n of m a tc h in g case w^ith logical case. W e have n o ted a lre a d y th a t T T c o n stru ctio n s w ere unaffected in th e E v an s (1972c) stu d y , a n d th a t E vans a n d N e w ste ad (1977) also show ed th a t the effects o f m a tc h in g bias w ere largely re stric te d to the F T a n d F F cases, using an ev alu atio n task p ro c e d u re . F u rth e r p ro b lem s arise in in te rp re tin g the effect, from in co n siste n t resu lts o f re aso n in g stu d ies usin g d is­ ju n c tiv e rules (C h a p te r 10). F u rth e r d iscussion o f the m a tc h in g b ias effect will hen ce be deferred for the tim e being.

Conditional reasoning

143

Conclusions I t has been show n th a t it is n o t easy to infer the n a tu re o f the logical c o m p o n e n t o f p e rfo rm a n ce on these tasks. T h e p ro b le m is th a t the stre n g th o f resp o n se bias effects is not in d e p e n d e n t o f the logical cases u n d e r c o n sid era tio n . T h u s we m u st d istin g u ish the n a tu re o f a re sp o n se ten d e n cy re la te d to th e logical stru c tu re , from the e x te n t to w hich th a t ten d en cy c o m p e tes w ith non-logical te n d ­ encies. W e c a n , how ever, say w ith som e confidence th a t su b jects m ake the inference M P , a n d see T T as verifying a n d T F as falsifying in tru th -ta b le tasks. T h e s e ‘lo g ical’ ten d e n cie s a re a d ire c t conse­ quen ce o f u n d e rs ta n d in g a c o n d itio n al rule. T h e y a m o u n t to a recognition by th e su b je ct th a t I f p then q m ea n s th a t a n y o b se rv atio n o f p m u st be a cc o m p a n ie d by a n o b se rv atio n o f q. O n e o th e r p ossible in te rp re ta tio n a l effect suggested in these analyses is a ten d e n cy for som e su b je cts to in te rp re t th e ru le I f p then q as a n e q u iv a len c e. T h is w ould e xplain th e evidence o f a tendency to re g a rd F T as falsifying o n th e tru th -ta b le task (T ab le 8.5) a n d also th e relativ ely h igh ov erall AC ra te on inference tasks (e.g. T a b le 8.3). T h is still leaves th e p ro b lem o f w hy th e M T an d D A rates a re relatively low. O n av era g e, M P is m ad e a b o u t twice as often as M T , a n d A C a b o u t tw ice as often as D A , o v e r all rules (T ab le 8 .3 .). I t w as p o in te d o u t e a rlie r th a t M T re q u ire s m ore reaso n in g to achieve th a n M P a n d is m o re su sce p tib le to c o m p e tin g response biases. T h e A C /D A difference co u ld be e x p la in ed in a sim ilar w ay. I f the su b je cts tre a t th e ru le as a n eq u iv a len c e th en they a re re aso n in g n o t only w ith o rig in a l ru le I f p then q b u t also its converse I f q then p. In effect A C a n d D A a re th e M P a n d M T inferences for this co n v erse rule, a n d p re su m a b ly h a v e th e sam e relative stre n g th as in th e orig in al. T h e re a re som e in te re stin g p a ralle ls h ere to th e w ork on syllogistic reaso n in g discu ssed in C h a p te r 6, w here it w as show n th a t th ere is qu ite a lot o f ev idence to suggest th a t peo p le tre a t u n iv ersal s ta te ­ m en ts (A ll A are B ) as equiv alen ces. A n o th e r p a ra lle l is th e pre fe r­ ence for fo rw a rd p ro c essin g o f syllogism s. O n e fu rth e r possible ex p la n atio n o f th e M P /M T difference is a preference for reaso n in g forw ards. T h e A C /D A difference is likew ise a preference for fo rw ard p rocessing w ith th e converse ru le I f q then p. T h e evidence for d ire c ­ tionality effects is discu ssed in th e n ex t section. T h e d iscussion o f p ossible c o n n ec tio n s b etw een th e ‘lo gical’ com ­

144

Propositional reasoning

po n en ts o f the inference a n d tru th -ta b le tasks show s how h a rd it is to explain m o re th a n a sm all p ro p o rtio n o f th e d a ta in term s o f logical re aso n in g processes. I t is not su rp risin g th a t if ‘in te rp re ta ­ tio n s’ are im p u te d on th e a ssu m p tio n o f w holly logical re aso n in g (a la H e n le), th e co n se q u en c e is very large d isc rep a n cie s betw een tasks. M a rcu s a n d R ips (1979) used a n e v a lu a tio n task in w hich subjects w ere allow ed only tw o responses; ‘c o n siste n t’ a n d ‘inco n ­ siste n t’: the fo rm er c ateg o ry in clu d in g b o th ‘tru e ’ a n d ‘irre le v a n t’ responses. E ven w h en they looked only a t th e 82 p e r cent su b jects w ho could be classified as m ak in g e ith e r im p lica tio n a n d e q u iv a l­ ence in te rp re ta tio n s, th ey found m a n y ‘e rro rs ’ o f re aso n in g o n an inference task relativ e to the ‘in te rp re ta tio n ’ d eriv ed from the tru th -ta b le task. M a rc u s a n d R ips re sp o n d ed to these findings by c o n stru ctin g a m odel o f re aso n in g to a c c o u n t for e rro r o n th e infer­ ence task. T h ey a ssu m e th a t re aso n in g on the tru th -ta b le task is m ore o r less e rro r free. T h is a ssu m p tio n is im possible to ju stify in the light o f th e m a tc h in g bias effects discu ssed here, a p ro b lem o f w hich th e a u th o rs w ere a p p a re n tly u n a w a re , since they failed to cite an y w ork em plo y in g n egative rules. T h is review o f w ork o n c o n d itio n al re aso n in g h a s revealed the presence o f n o n-logical resp o n se biases in b o th c o n d itio n al inference an d tru th -ta b le tasks. T h e re is, how ever, som e evidence o f a co m ­ m on logical c o m p o n e n t o f p e rfo rm a n ce u n d e rly in g the tw o types o f task. T h e re m a in d e r o f this c h a p te r is d ev o ted to c o n sid era tio n o f ling uistic factors w hich m ay influence the logical o r in te rp re ta tio n a l c o m p o n e n t o f c o n d itio n al reasoning.

Linguistic factors in conditional reasoning In this section the term interpretational r a th e r th a n logical c o m p o n e n t will be p referred . I t will be a ssu m e d th a t a n y effects o f sy n ta c tic o r sem an tic lin g u istic facto rs a re o rth o g o n a l to th e non-logical effects d e m o n stra te d by th e m a n ip u la tio n o f negative c o m p o n e n ts (co n clu ­ sion bias, m a tc h in g b ias). T h is m e a n s th a t even if o nly affirm ative rules a re used, a n y shift in, say, th e ra te o f M T inference, occasioned by m a n ip u la tio n o f linguistic c o n te n t, will be assu m e d to be m e­ diated by the in te rp re ta tio n a l c o m p o n e n t.

Conditional reasoning

145

Syntactic factors: directionality and ‘only i f rules Several allu sio n s w ere m a d e in th e p revious p a rt o f th e c h a p te r to the fact th a t the su p e rio rity o f M P o ver M T could be d u e to a ‘d ire c tio n a lity ’ effect. T h e su p p o sitio n is th a t the lin g u istic form I f p then q m u st invite a n te c e d e n t to c o n se q u e n t inferences far m ore strongly th a n in th e reverse d irec tio n . (H ig h A C ra te s w ere a ttr ib u ­ ted to e q u iv a len c e in te rp re ta tio n s ra th e r th a n to b a c k w a rd re a so n ­ ing.) Several a u th o rs hav e in d e p e n d e n tly p o stu la te d th a t such d irec tio n a lity m ig h t be reversed by a n a lte rn a tiv e lin g u istic ex p res­ sion o f im p lica tio n , p only i f q (R ip s a n d M a rc u s, 1977; E vans, 1977a; B rain e, 1978). I t is essen tial h e re to a p p re c ia te th a t p only i f q h a s the sam e tru th table as I f p then q, a n d not th e sam e one as I f q then p. E v an s (1977a) illu stra te s th e p o in t w ith th e follow ing exam ples: E l I f h e is a p o lic e m a n th en he is o ver 5'9" in h eight. E2 H e is a p o lic e m a n only if he is o ver 5'9 " in height. Som e reflection o n th ese ex am p les w'ill in d ic a te th a t they are indeed logically e q u iv a len t. In e ith e r case th e rules can only be falsified if a p o lic e m a n is found w ho is not over 5'9 " in h e ig h t (the T F case). N e ith e r w ould be falsified by fin d in g som eone w ho is not a p olicem an to be o ver 5'9". T h u s , in each case, th e first p ro p o sitio n (he is a po licem an ) im plies th e second p ro p o sitio n (he is o ver 5'9" in h eig h t). T h e tw o se n ten c es d o n o t a p p e a r to be linguistically eq u iv a len t, how ever, a n d it is im p o rta n t to ask w hy twro a lte rn a tiv e linguistic form s sh o u ld have precisely the sam e logical form . E v an s (1977a) p oints o u t th a t th ere are tw o d istin c t logical p ro p e rtie s o f im p lica ­ tion, a n d suggests th a t th e ‘I f . . . th en . . (IT ) lin g u istic form is used to em p h a sise the one, a n d th e ‘. . . only if. . (O I) linguistic form to e m p asise the o th e r. T h e first p ro p e rty is th a t the antecedent is sufficient fo r the consequent, i.e. k now ing th a t som eone is a p o licem an is sufficient to infer th a t th ey a re o ver 5'9". T h is p ro p e rty is th a t the consequent is necessary fo r the antecedent. In o th e r w ords, o n e c a n n o t be a p o licem an unless one is o ver 5'9". T h is second p ro p e rty is expressed by M T . E vans (1977a) p ro p o sed th e in tu itiv e h y p o th esis th a t th e I T form is used in n a tu r a l lan g u a g e to express sufficiency o f th e a n te ce d e n t, a n d th e O I form to ex p ress necessity o f the co n se q u en t. It w as

146

Propositional reasoning

p re d ic te d , th erefo re, th a i m o re M P inferences w ould o c cu r in I T a n d m ore M T inferences in O I . T h is w as tested in a n e x p erim e n t in w hich th e pre sen c e o f n eg ativ e c o m p o n e n ts w as also m a n ip u la te d .

T A B L E 8.6 Percentage frequency o f reasoning responses to I T and O I rules, pooled over rules in which the presence and absence o f negated components is manipulated. (a) Inference Task (E vans, 1977a) I f . . . then (n= I6)

. . . only i f . . . (n= I6)

MP

100

76

DA

38

38

AC

67

84

MT

42

59

I f . . . then (n=24)

TT TF FT FF

only i f .

T ru e

False

Irrelevant

T ru e

False

89 9 19 30

5 81 29 11

6 9 52 57

82 11 13 44

12 58 57 16

s' ¡1

(b) Truth table evaluation (Evans, 1975)

Irrelevant 16 30 30 40

N ote: d ev iatio n s o f som e to ta ls from 100 p e r ce n t are d u e to ro u n d in g erro rs.

T h e re su lts o f this stu d y a re show n in T a b le 8.6 (a ), a v era g ed over rules c o n ta in in g negatives. T h e tw o p re d ic tio n s w ere signifi­ c antly confirm ed: th e re w as m ore M P in th e I T g ro u p th a n in the O I g ro u p {p < 0 .0 0 2 , 1-tailed ) a n d m o re M T in th e O I g ro u p th a n in the I T g ro u p ( p < 0 .0 5 , 1-tailed). T h e re w as also significantly m ore A C in the O I g ro u p th a n in th e I T g ro u p (p < 0 .0 5 , 2-tailed ). T h is last re su lt m ig h t suggest th a t eq u iv a len c e in te rp re ta tio n s a re m ore com m on on O I . T h e re is, how ever, no c o rre sp o n d in g increase in DA ra te . T h e in te rp re ta tio n o f th e E v an s (1977a) d a ta is c o m p lica te d by the a b sen ce o f sig n ifican t c o n clu sio n -b ias effects on th e O I rules. H ow ever, th e tre n d s w ere in the ex pected d ire c tio n , a n d O I rules a re clearly n o t g en era lly ex em p t from re sp o n se bias effects, since

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147

they hav e been show n to suffer from stro n g m a tc h in g effects on tru th tab le tasks (E v an s, 1975; E v an s a n d N ew stead , 1977; M a n k telow, 1979). T h e frequency o f logical classifications on such tasks (averaged o ver negatives) show s m ark e d differences, h ow ever (cf. T a b le 8.6 (b )). C o rre sp o n d in g to th e red u ce d M P resp o n se (a n te ­ cedent to c o n se q u e n t d irec tio n a lity ) we see th a t th ere is a sh a rp increase in ‘irre le v a n t’ responses to cases w here the a n te c e d e n t co ndition is fulfilled ( T T a n d T F ), a n d a d ro p in su c h responses to cases w h ere it is n o t (F T a n d F F ). T h e d irec tio n o f classification, tru e o r false, is co n sisten t betw een I T a n d O I rules on each logical case. Rips a n d M a rc u s (1977) e n co m p ass the d ire c tio n a lity id ea in a suppositional theory o f c o n d itio n al reaso n in g . T h e y p ro p o se th a t people e v a lu a te a c o n d itio n al in th e form I f p then q by su p p o sin g the tru th o f the a n te c e d e n t, a n d a ssessing it a g a in st the c u rre n t d a ta base: By the c u rre n t d a ta base, we m ean th e set o f p ro p o sitio n s p re sen tly held to be tru e , th a t is, o u r p re sen t beliefs. T h e seed p ro p o sitio n c o rre sp o n d s to th e h y p o th esis we w ish to e n te rta in . In th e special case o f the c o n d itio n al sen ten ce, th is seed will be the p ro p o sitio n e xpressed in th e a n te c e d e n t clause. T h ey p o stu la te th a t c o n d itio n als a re e v a lu a te d by first o f all tak in g the a n te c e d e n t a s th e ‘seed p ro p o sitio n ’. ‘T h e c o n d itio n al should th en be c onfirm ed in case th e co n se q u en t is a n elem en t of, o r inferrable from , this su p p o sitio n , a n d oth erw ise d isc o n firm e d .’ T h is theory p re d ic ts b o th th e defective tru th tab le - one does n o t e v alu ate the ru le a t all if th e a n te c e d e n t is n o t su p p o sed - a n d the su p e rio rity o f M P o ver M T inference. O n e n o rm ally p roceeds by a ssu m in g the tru th o f the a n te c e d e n t, n o t by a ssu m in g th e falsity o f th e conse­ q u e n t. P re su m a b ly M T can only be m a d e a cc o rd in g to a su p p o si­ tional view if it is a ch iev ed by a reductio ad absurdum a rg u m e n t, as W ason a n d J o h n s o n -L a ird (1972) suggested. F o r ex am p le, c o n sid er the follow ing M T problem : (1) I f th e le tte r is A th en th e n u m b e r is 7 (2) T h e n u m b e r is 3 T h erefo re, T h e le tte r is not A

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In a n R A A a rg u m e n t o n e s ta rts by a ssu m in g th e opposite o f the in ten d ed conclusion. In this case one m u st sta rt w ith th e a ssu m p tio n th a t th e le tte r is A. I f R ips a n d M a rc u s a re rig h t, this is the n a tu ra l su p p o sitio n in d u ce d by th e first prem ise. T h e c o n seq u en ce o f this a ssu m p tio n is th e d e d u c tio n th a t th e n u m b e r is 7 from th e first prem ise. T h is, how ever, lead s to a c o n tra d ic tio n , since we a re told in the second p rem ise th a t the n u m b e r is, in fact, 3. H en ce, the original su p p o sitio n is false a n d th e co n clu sio n d e m o n s tra te d . S urprisingly, R ips a n d M a rc u s (also M a rc u s a n d R ips, 1979) d o n o t m ake this p o in t, a n d a ttrib u te M T difficulty to p ro b lem s o f n egativity - a n a rg u m e n t d isc o u n te d in th e early p a rt o f th is c h a p ­ ter. B rain e (1978) gets closer to the rig h t line in c la im in g th a t M T involves m o re c o m p u ta tio n th a n M P , b u t u n fo rtu n a te ly co m m its the logical e rro r o f c la im in g th a t it does not follow from a defective tru th table. It w as show n e a rlie r th a t fo rb id d in g the o ccu ren ce o f T F is sufficient to ju stify b o th M P a n d M T inferences. R ips a n d M a rc u s (1977) test this th eo ry , in one e x p erim e n t, by co m p ariso n o f I T a n d O I rules. T h e y su g g est th a t w hile th e a n te ­ cedent will be in te rp re te d before th e c o n se q u e n t in I f p then q the reverse m ay be tru e for p only i f q. T h e y test this h y p o th esis in a m ost ingenious m a n n e r. S u b je cts a re given a d ia m o n d split in to a n u m b e r o f cells, w ith a p a ir o f letters in each. T h e y a re given rules to follow, such as: E3 I f th ere is a B in a sq u a re , th en th ere is a n X . E4 T h e re is a B in a sq u a re only if th ere is a n X . T h e tw o a re logically e q u iv a len t, w ith E3 in th e I T form , a n d E4 in the O I form . S u b jects a re th e n asked to in d ic a te w hich cells are consisten t w ith the given ru le, n u m b e rin g th em in th e o rd e r th a t they check th em . T h e e x p e rim e n te rs can th en see w h e th er, for exam ple, th e su b je ct searc h e s by th e cells h e ad e d w ith the letter m en tio n ed in th e a n te c e d e n t. A s p re d ic te d , th is does o c cu r w ith IT rules. C o n tra ry to th e ir e x p ec ta tio n s, O I rules a re n o t co n sisten tly e v alu ated by se a rc h in g for c o n se q u e n t v alues, no r, for th a t m a tte r, by a n te c e d e n t v alues. R ips a n d M a rc u s suggest th a t ‘su b je cts have difficulty in in te rp re tin g only i f tre a tin g it as a ‘sim ple c o n ju n c tiv e ’. T h is suggestion does n o t a cc o rd w ith o th e r d a ta , ho w ev er (cf. T a b le 8.6). W h a t th e ir resu lts d o show is th a t a preference for testin g IT rules by in sp e ctin g the a n te c e d e n t does n o t g en eralise to the O I

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rules, a fin d in g w hich su p p o rts the a n te c e d e n t to c o n se q u en t d ire c ­ tionality o f th e form er. E vans (1977a) suggested th a t d irec tio n a lity effects in I T a n d O I rules m ig h t be re la te d to tem p o ral o r cau sal factors. S u b jects w ere asked to c o n stru c t th e m a tic exam ples o f the tw o form s o f ru le at the end o f th e e x p erim e n t, a n d in clu d e d th e follow ing exam ples: E5 I f it ra in s on T u e s d a y , th en I shall go sw im m ing. E6 T h e m a tc h will take place only if the w e a th e r im proves. B oth E5 a n d E6 are clearly logical im p licatio n s. E5 w ould only be false if it ra in e d on T u e s d a y a n d I d id n o t go sw im m ing, a n d E6 w ould only be false if the m atc h took place a n d the w e a th e r d id not im prove. N ote, how ever, th a t in th e I T sen ten ce (E5) the a n te c e d e n t event p reced es th e c o n se q u en t event in tim e. I f o n e a tte m p ts to convert the rules in to the a lte rn a tiv e form they becom e se m an tica lly a n o m alo u s. T h u s, E5, in an O I form is: It will ra in on T u e s d a y only if I go sw im m ing, a n d E6 in a n I T form reads: I f the m a tc h takes place th en th e w e a th e r will im prove. It w as suggested th a t the n a tu ra l lin g u istic function o f I T a n d O I rules m ig h t be to express im p lica tio n a cc o rd in g to th e tim e o rd e r of th e a n te c e d e n t a n d c o n se q u en t events. T h is w as tested e x p eri­ m entally by E vans a n d N e w ste ad (1977) using a tru th -ta b le task. Subjects w ere p re sen te d w ith a ru le follow ed by successive p re se n t­ atio n s o f tw o letters (a th ree-field tac h isto sco p e w as used). E x am p les of I T rules used w ere as follows: E7 I f th e first le tte r is B th en the second le tte r is R E8 I f th e second le tte r is Z th en the first le tte r is T E q u iv a le n t exam ples in O I form are: E9 T h e first le tte r is B only if th e second le tte r is R E10 T h e second le tte r is Z only if the first le tte r is T

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T h e tru th -ta b le cases w ere p ro d u c ed by th e succession o f letters. T h u s a B follow ed by a P w ould be a T F case for rules E7 a n d E9. A n X follow ed by a Z , on th e o th e r h a n d , w ould be the T F case for rules E 8 a n d E10, since the second le tte r is a Z, b u t th e first (X ) is not a T . It w as hyp o th esised th a t E7 w ould be m ore lin g u istically ‘n a tu ra l’ w ith ‘fo rw a rd s’ tim e o rd e r as c o m p a red w ith th e b a ck w a rd s o rd e r o f E8. F o r O I rules, how ever, it is the b a ck w a rd s o rd e r th a t sho u ld be m ore n a tu ra l, so E10 sh o u ld be e asie r th a n E9. T h is hyp o th esis w as confirm ed by E v an s a n d N ew stead in the a n aly sis o f resp o n se latencies. T h e ir p ro b le m s also m a n ip u la te d th e p resen ce o f n e g a ­ tives, b u t the n eg ativ es fa cto r did n o t in te ra c t w ith th e tem p o ral o rd e r effects. D irectio n o f tim e o rd e r in te ra c te d significantly w ith ru le form in both co m p re h en sio n a n d verification tim e analyses. T h e m e a n total tim es (C T + V T ) w ere as follows: IT IT OI OI

fo rw ards b a ck w ard s fo rw ard s b a ck w a rd s

12.8 14.7 16.8 15.6

seconds seconds seconds seconds

E v an s a n d N e w ste ad c o n sid er a n a lte rn a tiv e e x p la n a tio n o f this result. It is possible th a t su b je cts m ay , illicitly, c o n v ert th e ru le p only i f q in to I f q then p. (N ote th a t th is is not the sam e as tre a tin g it as a n e q u iv alen ce. In th a t event the converse is a ssu m e d in a d d itio n to, ra th e r th a n in stea d of, the sta te d rule.) I f su b je cts do, in fact, m ake such a co n v ersio n , th en w 'hat has been classified as a forw ards tim e o rd e r for the O I ru le, w o u ld in fact be b a ck w a rd s for the converted I T ru le th a t it h a s becom e to th e su b je ct (a n d vice v ersa). F ollow ing a d e ta ile d an aly sis o f the resp o n se-freq u en cy d a ta , how ever, E v an s a n d N e w ste ad c o n clu d e th a t m ost su b je cts re ta in the o rig in al im p lica tio n o f th e O I rule, ra th e r th a n co n v ert it. C o n se q u e n tly , the h y p o th esis p ro p o se d by E v an s (1977a) is g e n ­ erally w ell su p p o rte d by th e E v an s a n d N e w ste ad (1977) stu d y . T h e su p e rio rity o f su b je c ts’ a b ility to reaso n fo rw ard s ra th e r th a n b a ck w ard s w ith the I T ru le is fu rth e r s u b s ta n tia te d by w ork on the W ason selection task (see C h a p te r 9). T h e w ork review ed in this section suggests th a t th is re su lts from th e n a tu ra l lin g u istic function o f the n o rm a l c o n d itio n al form , a n d th a t it is n o rm ally a p p lie d to

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situ atio n s w here ‘forw 'ard’ th in k in g is a p p ro p ria te . In th e nex t sec­ tion we look a t th e w ay in w hich o th e r types o f c o n te n t a n d co n ­ tex tu a l factors influence su b je c ts’ u n d e rsta n d in g a n d use o f con d itio n al sentences.

Semantic factors: content and context effects in conditional reasoning T h e effect o f c o n te n t on logical re aso n in g w as discussed w ith respect to classical syllogism s in C h a p te r 6. O n e hyp o th esis co n sid ered w as th a t co n cre te m a te ria ls m ig h t fa cilitate ‘c o rre c t’ re aso n in g relative to a b s tra c t m a te ria ls, p ro v id ed th a t p rio r beliefs a b o u t th e con clu ­ sions d o n o t b ias ju d g m e n ts . T h is h y p o th esis h as been in v estig ated extensively w ith re g a rd to c o n d itio n al sentences, b u t n e arly all o f this w ork h a s em ployed the W aso n selection task, a n d will conse­ q u en tly be discu ssed in th e n e x t c h a p te r. T h e re h a s, how 'ever, been som e d iscu ssio n o f th e m a n n e r in w hich the se m an tic c o n te x t o f a c o n d itio n a l will influence th e inferences w hich people m ay d ra w from it. A n im p o rta n t idea h ere is th a t pragmatic inferences m ay a rise from c o n te x t, even th o u g h they are not im p lied logically. Social psychologists hav e becom e in te rested in the d eg ree to w hich p ra g m a tic inferences m ay arise in com ­ m u n ic a tio n s, a n d th e im p lica tio n s th a t th is h a s for codes o f a d v e r­ tising p ra ctic e , rules o f c o u rtro o m p ro c ed u re , etc. (See H a rris an d M onaco, 1978.) A sim ila r idea h a s been p ro p o se d w ith specific reference to c o n d itio n a l reaso n in g . G eiss a n d Z w icky (1971) su g ­ gested th a t use o f a c o n d itio n a l se n ten c e in c e rta in co n tex ts invites the DA o r A C inference, even th o u g h it is n o t p h ra se d as a bico n ­ d itio n a l (in d ic a tin g eq u iv a len c e). T h is is p a rtic u la rly tru e o f p ro m ­ ises o r th re a ts , a n d o th e r situ a tio n s w h e re stro n g c au sal o r tem p o ral co nnections exist b etw een a n te c e d e n t a n d c o n se q u en t, e.g: I f you m ow the law n, I ’ll give you five d o llars, clearly ‘in v ite s’ th e D A inference: I f you d o n ’t m ow th e law n, I w o n ’t give you five d o llars. T h is h y p o th esis h a s been tested e m p irica lly by F ille n b a u m (1975; 1976), w ho a rg u es th a t D A sh o u ld n o t be seen as a ‘fallacy’ b u t

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ra th e r as a p ra g m a tic a lly re aso n a b le inference in som e contexts. In d e ed , he is r a th e r d isp a ra g in g a b o u t th e so rt o f stu d ies d e sc rib e d earlier in this c h a p te r, w hich em ploy a b s tra c t p ro p o sitio n s w ith a rb itra ry conn ectio n s. H is a p p ro a c h em p h a sise s th e fact th a t reallife inference alw ays takes place in a se m a n tic c o n te x t in w hich p re su p p o sitio n s a n d a d d itio n a l know ledge will inevitab ly influence the process o f reaso n in g . In one e x p e rim e n t (F ille n b a u m , 1975) su b je cts w ere given a c o n d itio n al sen ten ce a n d asked w h e th e r its converse w as a ‘re a so n ­ able, n a tu ra l in feren ce’ to m ake from it. T h is a p p e a rs sim ila r to the m ethodology o f P o llard a n d E v an s (1980) d e sc rib e d e a rlie r in this c h ap ter. In th e case o f th e ir stu d y , the inverse inference a p p e a re d psychologically e q u iv a le n t to DA. T A B L E 8.7 Percentage frequency o f acceptance o f inverse (D A) inferences in Fillenbaum’s (1975) study

Rule

Prom ises

T h re a ts

C ontingent universals

(1) (2) (3) (4)

85 84 83 83

83 90 86 81

67 60 54 67

I f p th en q I f p then not q I f not p then q I f not p then not q

F ille n b a u m ’s m a te ria ls in clu d e d pro m ises, th re a ts a n d co n tin g e n t u niversals (e.g. ‘I f the m u sh ro o m is red it is e d ib le ’). T h e d a ta for these categ o ries a re show n in T a b le 8.7. It is im m e d ia tely a p p a re n t th a t the D A ra te for th re a ts a n d pro m ises is very high, a n d is in fact, significantly h ig h e r th a n on c o n tin g e n t universals. C e rta in ly the D A inference w ith a b s tra c t c o n d itio n al ru les (T a b le 8.3, second colum n) is m u ch low er. A n o th e r c o m p a riso n betw een F ille n b a u m ’s d a ta a n d th a t observ ed w ith a b s tra c t rules is possible, since he included ru les w ith n e g ativ e c o m p o n e n ts. H is d a ta show n o evi­ d ence o f a b ias to a cc ep t n e g ativ e conclusions, w hich sh o u ld in crease a cc ep tan ce o f the inference on rules (1) a n d (3) relativ e to (2) a n d (4). T h e m o st p lau sib le e x p la n a tio n o f th ese differences is th a t th e use o f th em a tics in creases D A d u e to th e ‘inv ited in fere n ce ’ effect pos­ tu la te d by G eiss a n d Z w icky. T h e lack o f conclusion b ias c an be a ttrib u te d e ith e r to th e g e n era l in cre ase o v e rrid in g th e bias, o r else

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to a sw itch to m o re ‘r a tio n a l’ re aso n in g in th e a b sen ce o f artificial con ten t. Som e c a u tio n a ry c o m m e n ts m u st be m ad e , how ever. F or one th in g , th e a b s tra c t re aso n in g e x p erim e n ts w ere p re se n te d as logical re aso n in g tasks, w hile F ille n b a u m ’s su b jects w ere clearly asked to m ak e p ra g m a tic inferences. A n o th e r p ro b lem arises from a lack o f a tte n tio n to th e e x act n a tu re o f his sentences. H e gives very few ex am p les o f th e sen ten ces used, so it is no t possible to assess p ossible co n fo u n d in g by b elief b ias effects, etc. F ille n b a u m also in v estig a te d inferences w ith c o n d itio n als o f a te m p o ra l/c a u sa l n a tu re (e.g. ‘I f he goes to P aris he will visit the L o u v re’). H e fo u n d sim ilarly high ra te s o f D A in ference w ith such sentences, w hich a re a g a in in te rp re te d as p ra g m a tic inference. A n a lte rn a tiv e a p p ro a c h , m ore co n sisten t w ith th e H e n le h y p o th ­ esis, is to su p p o se th a t th e c o n te x t in d u ces a b ico n d itio n a l o r eq u iv ­ alence in te rp re ta tio n o f th e rule, from w hich D A (a n d A C ) follow logically. S tp u d e n m a y e r (1975) classified p e o p le ’s in fere n tia l p a t­ terns as in d ic a tin g a n ‘u n d e rly in g ’ in te rp re ta tio n as e ith e r c o n d i­ tional (C O N D ) o r b ico n d itio n a l (B IC ) - a tec h n iq u e o f an aly sis criticised e a rlie r in the c h a p te r. H e found th a t a b s tra c t ru les p h ra se d as p causes q led to m o re B IC classifications th a n those in the con d itio n al form I f p then q. H e also m a n ip u la te d p e o p le ’s linguistic p re su p p o sitio n s a b o u t c au sality by th e use o f th e m a tic c o n te n t. C o n sid e r th e follow ing: E l l I f I tu rn th e sw itch th en the lig h t will go on. E12 I f the sw itch is tu rn e d th en th e lig h t will go on. S ta u d e n m a y e r a rg u es th a t in E l 1 th e a n te c e d e n t will be seen as sufficient b u t n o t necessary for th e c o n se q u e n t - since som eone else m ig h t tu rn th e sw itch. O n the o th e r h a n d p re su p p o sitio n s m ight lead us to expect th a t th e a n te c e d e n t is b o th sufficient a n d necessary in the case o f E l 2. H is re su lts a p p e a re d to confirm th e h y pothesis; sentences o f ty p e E 12 w ere a sso ciated w ith co n sid era b ly m ore B IC in te rp re ta tio n s for su b je cts w ho w ere sta tistica lly c o n sisten t. U n fo r­ tu n ate ly , th e p re se n ta tio n o f d a ta in term s o f these d u b io u s classi­ fications, ra th e r th a n ra w freq u en cies o f inference, m akes a c le ar assessm ent o f his fin d in g s difficult. L egrenzi (1970) a rg u e d th a t su b je cts w ere likely to in te rp re t a con d itio n al as eq u iv a len c e if its a n te c e d e n t a n d c o n se q u e n t referred to situ a tio n s w hich w ere strictly b in ary : th a t is, situ a tio n s in w hich

154

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th ere a re only tw o possible events, w hich a re m u tu a lly exclusive. H e show ed su b je cts a p p a ra tu s in w h ich a ball could roll dow n e ith er a left o r rig h t c h an n e l a fte r w h ich e ith e r a red o r a g re en light lit. S ubjects w ere th en asked to e v a lu a te the tru th tab le o f a rule such as: E l 3 I f the ball rolls to the left th e n th e green la m p is lit. E ach tru th -ta b le case w as e v a lu a te d as co n sisten t, in co n siste n t o r irrelev a n t. T w e n ty -tw o o u t o f th irty su b je cts e v alu ate d as follows: left left rig h t rig h t

green red - g re en - red

(T T ) (T F ) (F T ) (F F )

C o n siste n t In c o n siste n t In c o n siste n t C o n siste n t

T h is is th e tru th ta b le o f m a te ria l e q u iv alen ce. A lth o u g h L egrenzi does not re p o rt a b s tra c t c o n tro ls, we know from prev io u s research th a t w ith a n affirm ativ e rule the ‘defectiv e’ tru th tab le is d o m in a n t (F T a n d F F classed as irre le v a n t). It is re aso n a b le to a ssu m e th a t the se m an tic c o n te x t is resp o n sib le for the d isc rep a n cy . R ips a n d M a rc u s (1977) p o in te d o u t th a t it m ig h t be e ith e r the b in ary n a tu re o f th e situ a tio n or c a u sa lity per se th a t w as resp o n sib le for L eg re n zi’s results. T h e y re p e a te d L eg re n zi’s e x p e rim e n t w ith extensions to se p a ra te these e x p la n a tio n s. T h u s th e ir c o n d itio n als referred to e ith e r tw o (b in a ry ) o r th re e (n o n -b in ary ) possible a lte rn a tiv e s, a n d w ere p lac ed in e ith e r c au sal o r n o n -c au sa l c o n ­ texts. T h e y a tte m p te d to classify su b je c ts’ resp o n ses as M C (m a ­ terial c o n d itio n al) o r M B (m a te ria l b ic o n d itio n a l). H o w ev er, they found a n o th e r resp o n se p a tte rn for the n o n -b in a ry p ro b lem s. Som e subjects im posed a on e-to -o n e m a tc h in g betw een th e th ree a n te ­ cedent a n d th ree c o n se q u e n t v alues. T h is c a n n o t be d istin g u ish e d from M B on b in a ry p ro b lem s, so R ip s a n d M a rc u s in v en t a jo in t category' - ‘M B -m a tc h in g ’. S uch classificatio n s w ere significantly m ore fre q u e n t for cau sal th a n n o n -c au sa l co n te x ts, b u t w ere not affected by the b in a ry /n o n -b in a ry m a n ip u la tio n . T h u s it a p p e a rs th a t it is th e causality w hich is re sp o n sib le for L eg re n zi’s effect - a conclusion c o n sisten t w ith F ille n b a u m ’s a n d S ta u d e n m a y e r’s fin d ­ ings. H ow ever, a su b s e q u e n t e x p e rim e n t su g g ested th a t it w as the perceived correlation b etw een a n te c e d e n t a n d c o n se q u e n t values,

Conditional reasoning

155

ra th e r th a n c au sa tio n per se th a t d e te rm in e d the M B m atc h in g response. W h en R ips a n d M a rc u s (see also M a rc u s a n d R ips, 1979) tu rn ed th eir a tte n tio n to c o n d itio n al inferences ra th e r th a n tru th -ta b le tasks, the situ a tio n b eca m e m ore co m p lica te d . A lth o u g h th e cau sal context w as a sso c iated w ith m o re M B classifications, m ost su b jects are u n classifiable on this task. T h e p ro b lem o f a tte m p tin g to classify syllogistic re sp o n ses in to ‘inferred tru th ta b le s’ w as discu ssed in an earlie r section. O v erall, the stu d ies review ed in th is section su p p o rt th e id ea th at peo p le’s b e h a v io u r is d e p e n d e n t on th e c o n te n t o f the c o n d itio n al sentences. A tte m p ts to classify b e h a v io u r in tru th tab les a la H en le are n o t p ro m isin g , how ever. I f the n otion o f co n v erted o r p ra g m a tic inference is a d o p te d in ste a d , th en this c a n be in c o rp o ra te d in to an interpretational component o f p erfo rm an ce. N o n -tru th fu n ctio n al b e h a v ­ io u r will be o b serv ed , o f course, since o th e r sources o f e rro r in the reasoning process, such as response biases, will also influence b ehaviour.

Conclusions O rig in ally , E v an s (1972a) classified the tw o m a in sources o f v a ri­ ance on re aso n in g tasks as interpretational a n d operational; in su b se ­ q u e n t w ork th e la tte r h a s becom e m o re specifically defined as non-logical re sp o n se bias. M a rc u s a n d R ip s (1977) a sse rted a sim ­ ila r view: [T his d isc rep a n cy ] h elps p u t a t rest the long s ta n d in g d e b a te as to w h e th e r e rro rs in logical tasks a re d u e to m is in te rp re ta tio n s o f the p rem ises o r e rro rs in the re aso n in g p rocess itself. T o the ex ten t th a t th is a rg u m e n t can be se ttle d e x p erim e n tally , o u r d a ta im p lica te b o th sources. T h e fact th a t M a rc u s a n d R ips fo rm u la ted a n e rro r-p ro n e process m odel to e x p la in th e ir non-logical effects, w h ereas E v an s p o stu la te d resp onse-bias effects, is a m a tte r o f th eo re tic al taste: in b o th cases, th ere is a rejectio n o f H e n le ’s a ttrib u tio n o f e rro rs only to m isin te r­ p re ta tio n . In m y view th e e lim in a tio n o f th e sim p listic ra tio n a list a p p ro a c h is e ssen tial if p ro g ress is to be m a d e in th is field, a n d it

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is hoped th a t th e u n c o m m itte d re a d e r will perceive its in ab ility to explain th e d a ta o f th e v a rio u s stu d ies review ed. T h e p ic tu re o f c o n d itio n al re aso n in g th a t h as em erged in this c h a p te r is com plex, b u t no t hopelessly so. S tu d ies o f c o n d itio n a l reaso n in g w ith a b s tra c t m a te ria ls in d ic a te som e d e g ree o f logical com petence, b u t a c o n sid era b le a m o u n t o f sy ste m atic e rro r. W hile the d e sc rip tio n o f these n on-logical p a tte rn s as response biases is preferred here, it is recognised th a t o th e rs m ay w ish to olfer ex­ p lan a tio n s in term s o f m isg u id ed re aso n in g stra te g ies. T h e m ore general th eo re tic al issues involved will be ex p lo red in P a rt IV . W hilst th e in te rp re ta tio n a l c o m p o n e n t o f p e rfo rm a n ce is only a p a rtia l d e te rm in a n t o f re sp o n d in g , it is clearly o f c o n sid era b le in ­ terest. T h e review o f linguistic facto rs (sy n ta ctic a n d a lso se m an tic) has revealed evid en ce o f a n u m b e r o f influences on th e reaso n in g process w h ich can be in te rp re te d w ith in a psych o lin g u istic fram ew ork.

The W ason selection task

I n th e p re v io u s c h a p te r, th e focus w a s o n c o n d itio n a l re a so n in g as m e a su re d by in fere n ce a n d tr u th - ta b le e v a lu a tio n s. In th e p re se n t c h a p te r, p e o p le 's re a s o n in g w'ith a c o n d itio n a l se n te n c e I f p then q is a lso in v e s tig a te d , b u t w ith a meta-inference task . S u b je c ts a re n o t sim p ly re q u ire d to d ra w o r assess im m e d ia te in fere n ce s. R a th e r, they a re in v ite d to e n te r ta in a lte rn a tiv e h y p o th e se s w ith re sp e c t to th e t r u th o r fa lsity o f a ru le , a n d a sk e d to test th ese h y p o th eses. T h e p ro b le m re q u ire s so m e u n d e r s ta n d in g o f th e logic o f c o n d itio n ­ als for its so lu tio n , b u t is n o t sim ply a d e d u c tiv e re a so n in g p ro b le m . I t m ay be re g a rd e d a s a n a n a lo g u e o f scien tific h y p o th e s is testin g , in w h ic h th e su b je c t m u s t a p p re c ia te th e n e ed to seek c o n d itio n s w h ic h c o u ld fa ls ify his h y p o th e s is (cf. P o p p e r, 1959). T h e p ro b le m w a s first d e sc rib e d by W a s o n (1966). So m u c h w ork h a s b e en d o n e o n th e p ro b le m sin c e, h o w e v er, th a t it is p o ssib le to d e sc rib e a s ta n d a r d p a ra d ig m , a n e x a m p le o f w h ic h is th e follow ing: T h e su b je c t is to ld t h a t a se t o f c a rd s h a s b e en c o n s tru c te d each o f w h ic h h a s a le tte r o n o n e sid e a n d a n u m b e r o n th e o th e r. In som e e x p e rim e n ts su b je c ts a re g iv en p a c k s o f su c h c a rd s to ex am in e. T h e y a re th e n sh o w n fo u r c a rd s ly in g o n a ta b le (see F ig u re 9.1). T h e su b je c t is th e n to ld th a t th e fo llow ing ru le a p p lie s to these four c a rd s a n d m a y be tru e o r false:

I f th e re is a n R o n o n e sid e o f th e c a rd , th e n th e re is a 2 o n th e o th e r sid e o f th e c a rd .

T h e su b je c t is th e n a sk e d to in d ic a te th o se c a rd s a n d only those c a rd s th a t he w o u ld n e ed to tu r n o v e r in o rd e r to d e c id e w h e th e r 157

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F IG U R E 9 .!

A set o f lo u r c a rd s th a t m ig h t be used in a selection task

R J 2 8 th e ru le is tru e o r false. A n y re a d e r w h o h a s n o t m et th is p ro b le m before m ay w ish to a tte m p t a so lu tio n before re a d in g on . T h e sim p le s tr u c tu r e o f th is ta sk is d e c e p tiv e - m o st in te llig e n t a d u lts fail to solve it. C o rre c t se lec tio n o f c a rd s re q u ire s th e a p ­ p re c ia tio n o f se v e ra l fa cto rs. F irstly , o n e m u st u n d e r s ta n d th a t in o rd e r for th e ru le to be tru e it m u s t be o b e y ed by e v ery c a rd . T h u s if a n y o n e c a rd wfas tu rn e d o v e r a n d fo u n d c o n siste n t w 'ith th e ru le th is w o u ld n o t, in itself, p ro v e th e ru le tru e . C o n v e rse ly , on ly on e c a rd n e ed to be fo u n d w h ic h d o e s not ob ey th e ru le in o rd e r for th e ru le to be falsified. O n c e th is falsification principle is g ra s p e d , th e p ro b le m re d u c e s to o n e o f s e a rc h in g for a n y c a rd s w h ic h co u ld falsify th e ru le if tu r n e d over. T h e n e x t ste p , th e n , is to d e c id e u n d e r w h a t c o n d itio n s th e ru le w ould be false. I n effect th e su b je c t m u s t c o n su lt a t r u th ta b le for th e rule. I f s u b je c ts re g a rd th e ru le a s e x p re ss in g im p lic a tio n , th e n they w o u ld classify on ly th e T F c ase as falsify in g th e ru le. In o u r e x am p le th is w o u ld m e a n a c a rd w'ith a n R on o n e sid e, th a t does not h a v e a 2 o n th e o th e r. T h is falsifying case c o u ld be d isc o v e re d by tu rn in g o v e r th e R o r th e 8 (n o t a 2). W ith a n e q u iv a le n c e tr u th tab le , th e F T case w o u ld a lso falsify - a 2 w ith o u t a n R w o u ld c o n tra d ic t th e ru le . I n th is case th e 2 a n d th e J (n o t a n R ) w o u ld also n eed to be se lec te d . I t sh o u ld be n o te d t h a t th e e x iste n ce o f d efectiv e t r u th ta b le s does n o t affect th e c o rre c t so lu tio n . I n d e fec tiv e im p lic a tio n F T a n d F F a re seen a s irre le v a n t, a n d in d e fec tiv e e q u iv a le n c e F F is seen as irre le v a n t. T h e s e tr u th ta b le s c o n ta in th e sa m e fa lsifying c ases as th e c o rre sp o n d in g tw o -v a lu e d ta b le s, h o w e v er, so choices a c c o rd in g to th e fa lsifica tio n p rin c ip le a re u n a lte re d . In g e n e ra l term s, for a ru le o f th e fo rm I f p then q th e c o rre c t choices w o u ld be p a n d q (n o t q) for a n im p lic a tio n re a d in g a n d all

The Wason selection task

159

four c a rd s for a n e q u iv a le n c e re a d in g . R e a c h in g o n e o f th ese c o rre c t so lu tio n s, as w e h a v e seen , involves se v e ra l p rin c ip le s. I n s u m m a ry : (i) (ii) (iii)

T h e su b je c t m u st a p p re c ia te th e fa lsifica tio n p rin c ip le . H e m u st h a v e a t r u th ta b le to d e te rm in e p o ssib le falsifying situ a tio n s. H e m u st d e c id e w h e th e r eac h o f th e fo u r c a rd s c o u ld rev eal su c h a s itu a tio n .

In p ra c tic e v e ry few su b je c ts offer e ith e r o f th ese so lu tio n s. Som e ty p ical d a ta a re sh o w n in T a b le 9.1. I t c a n be seen th a t m ost su b je c ts (79 p e r c e n t) c h o o se e ith e r p a n d q o r p a lo n e . A ssu m in g th e logic o f im p lic a tio n , th e re a re tw o c h a ra c te ris tic e rro rs ; (i) fa ilu re to select q (m o st s u b je c ts ), (ii) r e d u n d a n t se lec tio n o f q (a b o u t h a lf th e su b je c ts). U n d e r e q u iv a le n c e , se lec tio n o f q is a p p ro p ria te , b u t th e n th e o m issio n o f p a n d q is e rro n e o u s. R e g a rd le s s o f in te r p r e t­ a tio n , th e o m issio n o f th e q c a rd is a logical e rro r.

T A B L E 9.1 Percentage frequencies o f selections on the Wason selection task pooled across four experiments (from Johnson-Laird and Wason, 1970) Cards

% frequency

p .q p p>q>q p .q o th ers

46 33 7 4 10

W aso n (1966) p ro p o se d th a t su b je c ts p o ssess a tr u th ta b le for d efective im p lic a tio n . T h is w o u ld n o t lea d to e rro r, h o w e v er, if th e falsificatio n p rin c ip le w ere a d o p te d . H e e x p la in s th e o b se rv e d se ­ lectio n s by su p p o s in g th a t su b je c ts o p e ra te a verification principle in ste a d . T h a t is, th ey se a rc h for c a rd s w h ic h c o u ld verify th e ru le w h en tu rn e d o v e r, r a th e r th a n th o se w h ic h c o u ld falsify it. W ith th e defective tr u th ta b le , th e on ly v e rify in g c o m b in a tio n is p a n d q so these a re th e c a rd s th a t su b je c ts sh o u ld te n d to select. T h is e x p la n a ­ tio n is in a c c o rd w ith W a s o n ’s (1960) a sse rtio n th a t he h a d d e m o n ­ stra te d a v e rific a tio n b ia s on a n in d u c tiv e re a so n in g p ro b le m . T h e q u e stio n o f w hy su b je c ts c h o o se a s th ey d o o n th e se lec tio n ta sk h a s

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occasioned c o n sid era b le d e b a te in th e su b se q u e n t lite ra tu re , as we shall see late r. F irst, th o u g h , we sh all e x am in e som e early e x p eri­ m en ts devised to give su b je cts in sig h t into th eir e rro n e o u s p e rfo rm ­ ance on the task.

The ‘therapy’ experiments In line w ith his th eo re tic al a cc o u n t o f su b je c ts’ e rro rs, W aso n (1968) devised p ro c ed u re s to e m p h a sise the falsifying p o ten tial o f th e q card. In on e e x p erim e n t, su b je cts w ere in v ite d to ‘p ro jec t falsity ’, th a t is to say w h a t if a n y th in g on th e back o f each card could m ake the rule false. T h e c u rio u s finding w as th a t w hile the m ajo rity o f subjects d id pro ject a falsifying v alu e {p) on to th e b ack o f th e q c ard , this h a d little effect on th eir su b s e q u e n t ten d en cy to choose it on the selection task. In a second e x p erim e n t, su b je cts w ere asked to identify falsifying c o m b in a tio n s, a n d all picked o u t th e pq c ard as the only case. A gain, th is ‘th e ra p y ’ w as o f no benefit on a su b seq u e n t selection task, as c o m p a re d w ith c o n tro l g ro u p perfo rm an ce. A n u m b e r o f o th e r e x p erim e n ts hav e been ru n in w hich an a tte m p t is m a d e to fa cilitate selections by m ak in g su b je cts a w a re o f the falsifying case, a n d th e fact th e q selection c a n p ro d u c e it (W ason, 1969a; W aso n a n d J o h n s o n -L a ird , 1970; W aso n a n d S h a p ­ iro, 1971, E x p erim en t 1; W aso n a n d G o ld in g , 1974). Som e g e n era l features a rise from these studies: (1) G e n era lly , su b je cts hav e no difficulty in recognising the falsifying case o f th e rule, a n d will see, if led, th a t tu rn in g q will lead to this. (2) T h e a d m in istra tio n o f su c h p ro c e d u re im proves p e rfo rm a n ce o f som e su b je cts b u t it is q u ite ineffective for su b se q u e n t selection task p e rfo rm a n ce for a n u m b e r o f o th e rs, w ho still declin e to select the q c ard . (3) S u b je cts’ in tro sp ec tiv e co m m e n ts, if tak en , often reveal in co n sisten t a n d se lf-co n trad ic to ry th o u g h t processes. T h e fact th a t su b je cts c a n identify th e falsifying case is n o t too su rp risin g , in view o f th e re su lts o f re se a rc h in to psycho logical tru th tables (cf. C h a p te r 8). T h e fact th a t d o in g so p ro d u c es only lim ited

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161

facilitatio n o f se lec tio n -task p e rfo rm a n ce is m ost in te restin g , how ­ ever. L et us re tu rn to the an aly sis o f the th ree p o in ts o f u n d e rs ta n d ­ ing re q u ire d for so lu tio n . C lea rly th e a v ailab ility o f the falsifying case from tru th ta b le (ste p (ii)) is not the p ro b lem . Since th e su b je ct is d irec te d to th in k o f th e c o n seq u en ces o f selecting th e q c ard , p re su m ab ly step (iii) is n o t the p ro b lem . Is it, th en , th e first re­ q u ire m e n t, the possession o f a falsification p rinciple? In o th e r w ords, it m ay be th a t su b je cts, th o u g h a w a re th a t q could falsify, d o not see this as a good reaso n for selecting it. H ow ever, in stru ctio n s specifically ask in g for selections to prove th e ru le false o r u n tru e do not p ro d u c e a high ra te o f c o rre c t selections (cf. W aso n , 1968; W aso n an d G olding, 1974). O n e p ro c e d u re w h ich does seem q u ite effective in fa cilitatin g selection o f q is re d u cin g choices to selection o f c o n se q u e n t card s (q an d q) only (Jo h n s o n -L a ird a n d W aso n , 1970; L u n z e r, H a rris o n an d D avey, 1972; R oth, 1979). It could be th a t this is d u e ind irectly to the a n te c e d e n t-c o n se q u e n t d ire c tio n a lity o f th e c o n d itio n al (see C h a p te r 8). P e rh a p s su b je cts on the full task c o n sid er a n te c e d e n t choices first. T h o se su b je cts w ho select only p o n th e s ta n d a rd task m ay th in k o th e r choices a re u n n e ce ssa ry , since tu rn in g p will decide the issue - a q on th e b ack will prove the rule tru e, a n d a q will prove it false. T h is w o u ld , o f course, reveal a n in d u ctiv e fallacy rules c a n n o t be pro v ed tru e unless all e x a m p la rs a re ex am in ed . T h e snag w ith th is e x p la n a tio n is th a t su b je cts freq u e n tly choose q in the sta n d a rd task, so they obviously d o c o n sid er c o n se q u en t choices. R oth suggests th a t the ab se n ce o f th e p c a rd w eakens th e tendency to base responses on m a tc h in g (see next section). R e tu rn in g to th e p ro b le m o f th e re la tiv e ly ineffective th era p ie s, there is clearly so m e th in g m y sterio u s a b o u t this. M a n y su b je cts are, in effect, sa y in g th a t th e q c a rd could falsify the ru le, b u t th a t they do n o t need to tu rn it o v e r in o rd e r to find o u t w h e th e r th e ru le is tru e o r false. N ot su rp risin g ly , in tro sp ec tiv e re p o rts reveal self-contrad ictio n s in such cases. F o r ex am p le, W aso n a n d Jo h n s o n -L a ird (1970) asked su b je cts to m ake a n in itial selection a n d th en to e v a lu ­ ate the c o n seq u en ces seeing the p a n d q c a rd s tu rn e d o v e r (the la tte r rev ea lin g th e falsifying p on the back ). T h e y w ere th en asked to revise selections. A lth o u g h the th e ra p y w as effective for a n u m b e r o f su b jects, th e in te rest focused on th e su b s ta n tia l m in o rity w ho failed to select q in th e ir second selection. T h e a u th o rs q u o te vario u s verb al c o m m e n ts m a d e by su b jects. Som e su b je cts seem ed a w are o f

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the conflict an d tried to ra tio n alise it; o th e rs saw no conflict a n d kept th e ir selection a n d e v alu atio n processes q u ite se p a ra te . W aso n an d Jo h n s o n -L a ird sug g est th a t the selection process ten d s to d o m ­ in ate these su b jects, w ho becom e fixated on th eir o rig in al choices. T h ey also c o m m e n t on the a p p a re n t in d ep e n d en c e o f selection a n d e v alu atio n processes w hich ‘m ay e ith e r in te ra c t o r pa ss one a n o th e r b y ’, a n d ‘conflict in som e in d iv id u a ls b u t n o t in o th e rs ’. E lsew here, W aso n has claim ed th a t p rotocols give evidence o f irreversible th o u g h t processes (e.g. W aso n a n d G o ld in g , 1974) a n d has suggested th a t su b je cts m ay regress, u n d e r e x p e rim e n ta l stress, to p rim itiv e ch ild ish th o u g h t p a tte rn s (W aso n , 1969a). F u rth e r discussion o f the p ro b lem o f se lf-co n trad ic tio n a n d p u z zlin g p ro to ­ cols will be deferred to a la te r section. M e a n w h ile , we will focus on the questio n o f w hy peo p le ten d to select p a n d q in th e first place.

The effect o f negative components U n d e rsta n d in g the origin o f selections really d e p en d s upon finding c onditions u n d e r w hich selection p e rfo rm a n ce im proves, o r a t least s u b sta n tia lly alters. T h e th e ra p e u tic a tte m p ts classified a b o v e a re essentially ra tio n a listic in n a tu re . T h e y a re based on the n o tio n th a t subjects have not p ro p e rly co n sid ered the logical possibilities, o r u n d e rsto o d the im p o rta n c e o f falsification. A ra th e r different a p ­ p roach consists o f m a n ip u la tio n o f a sp e cts o f the task p re se n ta tio n , inclu d in g th e lin g u istic p ro p e rtie s o f th e rule. In early ex p erim e n ts, as Jo h n s o n -L a ird a n d W aso n (1970) note, th e selection p a tte rn a p p e a re d re m a rk ab ly ro b u st, a n d indifferent to a n u m b e r o f p re s­ e n ta tio n factors. T h e se in clu d ed ex p ressin g th e ru le in q u a n tified form : ‘E very c ard th a t h as a p on one side has a q on th e o th e r’, using strictly binary' situ a tio n s for p ip a n d q /q , a n d p re se n tin g a n te ce d e n t a n d c o n se q u en t values on the sa m e side o f p a rtia lly m asked cards. In th e early 1970s, how ever, tw o factors w ere discov ered to hav e significant effect on selection frequencies - w ith o u t th e necessity for ‘th e ra p y ’. O n e o f th ese factors w as the in tro d u c tio n o f realistic ra th e r th a n a b s tra c t c o n te n t in to the rules (W aso n a n d S h a p iro , 1971). A n u m b e r o f stu d ies hav e ex p lo red th is fa cto r a n d will be discussed in d e ta il la te r in the c h a p te r. F o r th e tim e being we will focus on the q u e stio n o f w hy people b eh av e as they d o in the

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a b stra c t task. A p a rt from red u ce d p re se n ta tio n , referred to e arlier, the only fa cto r o f m ajo r significance has been the pre sen c e a n d a bsence o f n eg ativ es in th e rules. In stu d ies o f c o n d itio n al re aso n in g using o th e r p a ra d ig m s , this m a n ip u la tio n h a s co n sid era b ly influenced o bserved re aso n in g fre­ q uencies, a n d yield ed ev idence o f non-logical re sp o n se biases (cf. C h a p te r 8). O n tru th -ta b le tasks, th ere w as ev idence o f a ‘m a tc h in g b ias’, i.e. a ten d en cy to focus u n d u ly on v alues n a m e d in th e rule. Since all early e x p e rim e n ts on th e selection task used only affirm ­ ative rules, a n d since th e p re d o m in a n t choices a re p a n d q, it could well be a fa cto r h ere as well. E v an s a n d L y n ch (1973) c a rrie d out an e x p erim e n t to d istin g u ish a verification bias e x p la n a tio n o f selection choices (W aso n , 1966) w ith a matching bias e x p la n a tio n (cf. E vans, 1972c). T h e y c h a ra c te ris e d th e logical s ta tu s o f the four c ard s on the sta n d a rd selection task as follows: p p q q

tru e a n te c e d e n t false a n te c e d e n t tru e c o n se q u e n t false c o n se q u en t

(T A ) (FA ) (T C ) (FC )

T h e in te re stin g q u e stio n is w 'hether su b je c ts’ choice o f T A a n d T C are d u e to th e ir logical s ta tu s as p o te n tia l verifiers, o r to th eir m atc h in g s ta tu s as c a rd s n a m e d in th e rule. I f th e selection task is a d m in istere d w ith th e p re sen c e o f negatives v a rie d , th en th e tw o e x p la n atio n s c a n be d istin g u ish e d . E v an s a n d L y n ch p erfo rm ed this e x p erim e n t, a n d th e ir fin d in g s a re sh o w n in T a b le 9.2. T A B L E 9.2 Percentage o f cards selections in the Evans and Lynch (1973) experiment (n=24)

R ule (1) (2) (3) (4)

If If If If

p th en q p th en not q n o t p th en q n o t p th en n o t q

TA

C a rd Selected FA TC

FC

(p) 88 (p) 92 (p) 58 (p) 54 73

(P) 8 (P) 4 (P) 29 (P) 46 22

(q) 33 (q) 58 (q) 42 (q) 75 52

(q) 50 (q) 8 (q) 58 (q) 29 36

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I t h as been a rg u ed th ro u g h o u t P a rt I I I th a t response biases combine w ith in te rp re ta tio n a ! ten d en cies in p ro d u c in g th e observed d a ta . C o n se q u e n tly , ev idence for m a tc h in g bias m u st be assessed by c o m p a rin g the freq u en cy o f selection o f m a tc h in g a n d m is m a tc h ­ ing cases w hile holding the logical case constant. F o r e ach logical case - T A , FA , T C , FC - E v an s a n d L y n ch p re d ic te d th a t th e c ard w ould be selected m ore often on th e tw o rules w here it m atc h ed (p or q) th a n on th e tw o w hich it m ism a tch e d (p o r q). T h u s for T A a n d F A th e co m p a riso n is betw een ru les w ith affirm ative a n d n e ­ gative a n te ce d e n ts, a n d for T C a n d FC betw een rules w ith affirm ­ ative a n d negative co n se q u en ts. In sp e c tio n o f T a b le 9.2 reveals th a t all tren d s w ere as p re d ic te d , a n d in d ee d all w ere highly significant. I f the frequency o f selection o f logical cases is co n sid ered w hen averaged across all four rules, th en e ac h h a s benefited o r suffered equally from m a tc h in g bias. Is th ere , th e n , evidence o f a verification bias, i.e. a preference for T C o ver FC ? (T h is co m p a riso n is re a so n ­ able, since the e x te n t o f the m a tc h in g effect is sim ila r in e ach case.) In sp ectio n o f T a b le 9.1 reveals the opposite to be the case, a n d the ex tra FC selection is in fact significant. T h is last finding sh o u ld not, how ever, be tak en too seriously. M a n k telo w a n d E v an s (1979) re ­ p eated the E v an s a n d L y n ch stu d y in tw o e x p erim e n ts. W h ile the m atc h in g b ias effects w ere re p lica ted , th e T C /F C difference w as not. A cross the four rules, th e selection freq u en cies for 48 su b je cts on a c o m p a ra b le a b s tra c t task w ere as follows: T A , 86 p e r cent; FA, 19 p er cent; T C , 53 p e r cent; FC , 52 p e r cen t. T a k e n to g eth e r, the three e x p erim e n ts sug g est th e follow ing conclusions: (1) M a tc h in g b ias significantly influences the selection o f card s, irrespective o f th e ir logical sta tu s. (2) T h e re is also ev idence o f a ‘lo g ical’ o r in te rp re ta tio n a l bias to prefer T A to FA , b u t no reliab le evidence o f a preference betw een T C a n d F C . T h ese resu lts a p p e a r to refute th e verificatio n th eo ry o f W ason. H ow ever, they only d o so if th e n eg ativ es a re assu m e d n o t to affect the interpretation o f th e rules. C o u ld one a rg u e, in H en le fashion, th a t the n egatives effect in te rp re ta tio n a l c h an g e s w hich a lte r the a c tu a l logical sta tu s o f th e card s? I t is n o t easy to see how th is could c rea te the m a tc h in g effect. In tro d u c in g a negative c o n se q u e n t ‘im p ro v e s’ logical p e rfo rm a n ce in th a t T C is less often a n d FC m o re often

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selected. H o w ev er, the in tro d u c tio n o f a negative a n te c e d e n t w orsens p e rfo rm a n ce since selections o f T A red u ce a n d FA increase in frequency. N o gen eral in te rp re ta tio n a l shift (e.g. from im p licatio n to equivalence) could a cc o u n t for such changes. T h e m a tc h in g in te rp re ta tio n does seem co m pelling, b u t th ere a re p ro b lem s. F irstly , w hy d o intellig en t a d u lts m ak e such a p rim itiv e m atc h in g resp o n se in the first place? V a n D u y n e (1973; 1974) criticised the use o f the c o n ce p t o f m a tc h in g bias on the g ro u n d s th a t the origin o f the bias w as not ex p la in ed , a lth o u g h th a t m akes it none the less real. In rep ly , E v an s (1975) suggested th a t su b je c ts’ a tte n tio n w as d irec te d to n a m e d v alues. W h e th e r a ru le re ad s 'I f A th en not 3 ’ o r ‘I f n o t A th en 3 ’, it seem s to be m ak in g sta te m e n ts about the A a n d the 3. T h is e x p la n a tio n ties in w ith linguistic c o n sid era tio n s, since negatives are used to d e n y affirm ative p re s u p ­ positions a n d hen ce d ra w a tte n tio n to th em (cf. C h a p te r 3). M ore im p o rta n tly , V a n D u y n e claim ed th a t th e m atc h in g bias effect did not g en eralise to d isju n ctiv e rules. T h is claim is ex am in ed in C h a p ­ ter 10, w here fu rth e r c o n sid era tio n o f the e x p la n a tio n o f m atc h in g bias will be m ad e . F o r the tim e being, the term ‘m a tc h in g b ia s’ will be used to d e n o te a n e x p erim e n tal o b se rv atio n th a t a n y e x p la n atio n o f selection-task p e rfo rm a n ce m u st take in to a cc o u n t. U n fo rtu ­ nately, m ost p u b lish ed theo ries hav e a voided the e x p la n atio n o f the p h e n o m e n o n by focusing en tirely on the selection p a tte rn s for affirm ative rules.

Insight models P rior to the d e m o n s tra tio n o f th e m a tc h in g effect, J o h n s o n -L a ird an d W aso n (1970) h a d p re sen te d a n insight m odel to a cc o u n t for the resu lts o f early selection task e x p erim e n ts. T h e y w ere co n cern ed w ith e x p la in in g not only th e in itial selection p a tte rn s , b u t also the m odifications a risin g from ‘th e ra p ie s’, in clu d in g a tend en cy for som e subjects to choose p, q a n d q (T A , T C , F C ). J o h n s o n -L a ird a n d W aso n (1970) p re sen t tw o m odels p o stu la tin g vary in g degrees o f insig h ts. W'e will c o n sid er only the second (re ­ vised) m odel here. T h e y p o stu la te th ree states: No insight T h e su b je ct selects c a rd s w hich could verify th e rule.

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Partial insight T h e su b je c t does a p p re c ia te the need to select p o ten tial falsifiers, b u t also chooses c a rd s th a t could only verify. Complete insight T h e su b je c t sees th a t only c ard s w h ich could falsify need be selected. T h e a u th o rs also p o stu la te th a t ‘th e su b je ct w ith o u t in sig h t will focus on c ard s m en tio n ed in the ru le ’. T h is so u n d s like m a tc h in g bias, b u t w ith tw o im p o rta n t differences: (i) they m ak e n o sugges­ tion th a t th is w ould g e n era lise to ru les w ith n e g ativ e c o m p o n e n ts, a n d (ii) they suggest th a t q is chosen as well as p only if the su b je ct assum es th a t the ru le im plies its co n v erse (eq u iv alen ce). U n d e r p a rtia l o r c o m p lete in sig h t, all c a rd s a re c onsidered. Jo h n s o n -L a ird a n d W aso n claim th a t su b je cts w ith no in sig h t will choose p o r p a n d q. U n d e r p a rtia l in sig h t they initially c o n sid er all card s. H ow ever, 'p will be co n sid ered irre le v a n t b e ca u se it could n e ith e r verify n o r falsify.’ All o th e r c a rd s w ill be chosen - p, q a n d q because they co u ld e ith e r verify o r falsify o r bo th . U n d e r c o m p lete insight q is e lim in a ted b ecau se it co u ld n o t falsify, a n d th e su b ject chooses p a n d q. T h e re a p p e a rs to be a n inco n sisten cy h ere (cf. Bree, 1973). I f ro u g h ly h a lf the su b je cts choose q u n d e r no in sig h t because they th in k th e ru le is a n e q u iv a len c e, they sh o u ld hav e pq as well as pq in th e ir tr u th ta b le as a falsifying case. C o n se q u e n tly , u n d e r e ith e r p a rtia l o r c o m p le te in sig h t, su ch su b je cts sh o u ld choose all four cards. In fact, w hile th e ra p ie s often p ro d u c e p,q o r p,q,q c o m b in atio n s, they rarely p ro d u c e p,p,q,q selections. C a n th e J o h n s o n -L a ird a n d W aso n revised m odel a c c o u n t for the m atc h in g -b ias effect o b serv ed by E v an s a n d L ynch, w h en negative co m p o n en ts are in tro d u c ed ? T h is d e p e n d s on how w e in te rp re t th eir d e scrip tio n s o f b e h a v io u r u n d e r no in sig h t - th e sta te in w hich m ost u n tra in e d su b je cts a re p re su m e d to be. I f su b je cts focus on the T A an d T C , reg ard less o f the pre sen c e o f negatives, th en th e m odel m akes th e sam e p re d ic tio n s for n e g ativ e rules as for affirm atives. In this case it could n o t a c c o u n t for the E v an s a n d L y n ch results. Suppose, th o u g h , th a t we assu m e th a t su b je cts focus on p a n d q irresp ectiv e o f th eir logical sta tu s . W7o u ld this lead to th e p re d ic tio n o f m a tc h in g bias? So far as the a n te c e d e n t is co n ce rn ed , th e a n sw e r is definitely no. G iv en th e ru le I f not p then q, th e su b je ct w ould consider p a s well as q b u t he w ould n o t select it, since its logical sta tu s, FA , is ‘irre le v a n t’ in th e defective tru th tab le . T h u s the increase in F A selections on rules w here they m atc h could not be

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ex plained. T h e d ro p in T A selections w hen they d o n o t m atc h (on rules w ith negative a n te c e d e n ts) sh o u ld be m u ch more m ark e d th a n it a ctually is (cf. T a b le 9.2) on I f not p then q; th e T A case (p) should n o t be c o n sid ere d , a n d h en ce selected, by a n y su b je ct in a sta te o f n o insight. T h e p re d ic tio n s o f the effect o f n e g ativ e c o n se q u en ts a re a m b ig u ­ ous. C o n sid e r the rule I f p then not q. Is the significant increase in FC [q) selection, c o m p a red w ith th e affirm ativ e rule, p re d ic te d by the m odel? C e rta in ly a n o in sig h t su b je ct will now c o n sid er th e FC case, since it is n a m e d in the rule. A cco rd in g to the text o f their p a p e r he will not, how ever, select it since it could only falsify a n d not verify th e rule. A cco rd in g to th e flow-chart p u b lish ed by J o h n s o n -L a ird a n d W aso n how ever, he w ould select it. T h e d is­ crep an cy betw een flow -chart a n d text is n o t a p p a re n t w hen only affirm ative rules a re c o n sid ere d , since m a tc h in g a n d verifying are th en alw ays con fo u n d ed . F inally, th e d ra stic d ro p in T C selections on rules w ith negative c o n se q u en ts is p re d ic te d by the m odel (text a n d flow -chart) since these u n n a m e d values w ould n o t be co n ­ sidered. O v e rall, th o u g h , it a p p e a rs th a t the Jo h n s o n -L a ird an d W ason m odel c a n n o t be in te rp re te d in such a w ay as to give a satisfactory e x p la n atio n o f th e E v an s a n d L ynch d a ta . T h u s the J o h n s o n -L a ird a n d W aso n m odel is n o t only slightly inconsistent in its e x p la n a tio n o f affirm ativ e ru le p e rfo rm a n ce , b u t also c a n n o t a cc o u n t for selections on n eg ativ e rules. N evertheless, som e evidence for the m o d el h a s been claim ed by G o o dw in a n d W ason (1972). T h e re is a n in h e re n t c irc u la rity in the m odel w hich they a tte m p t to overcom e. H ow does o n e know th a t a su b je c t has, say, p a rtia l in sig h t, o th e r th a n by ob serv in g his resp o n se to be p,q,q? G o o dw in a n d W aso n trie d to o vercom e this by asking su b ­ je c ts to give w ritte n re aso n s for selecting o r rejectin g e ac h c ard . T h ey reasoned th a t th is w ould show w h e th e r o r n o t su b jects were choosing in o rd e r to verify o r falsify. T h e e x p erim e n t em ployed only the affirm ative form o f rule. G oodw in a n d W aso n claim th a t th e ir resu lts c o rro b o ra te e m p irically th e existence o f th e th ree levels o f insight p o stu la te d by th e in fo rm a tio n -p ro c essin g m odel devised to e x p la in p e rfo rm a n ce on tasks o f this type (Jo h n so n -L a ird and W aso n , 1970). T h e re is a close re la tio n betw een the

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d e g ree s o f in sig h t in d ic a te d by th e p ro to c o ls a n d th e c o rre sp o n d in g se lec tio n o f c a rd s. T h is c o n clu sio n is b a se d larg e ly u p o n th e in sp e c tio n o f s u b je c ts ’ p ro to co ls. T h e a c tu a l ru le u se d w as ‘E v ery c a rd w 'hich h a s a tria n g le on o n e h a lf h a s re d o n th e o th e r h a l f a n d th e stim u li w ere: tria n g le (p ), s q u a r e (p ), red (q) a n d b lu e {q). A su b je c t c h o o sin g p a n d q gave th e follow ing ju stific a tio n s: p p q q

‘T ria n g le : on ly in te re s te d if it h a s re d o n .’ ‘I t is irre le v a n t if th e s q u a re h a s re d o r b lu e o n it.’ ‘R ed: w a n t to k now if it h a s tria n g le o n it.’ ‘I t is irre le v a n t if b lu e h a s tria n g le o n it.’

T h is su b je c t s h o u ld , o f c o u rse , be in a s ta te o f n o in sig h t. T h e a u th o rs c la im th a t th is p ro to c o l sh o w s ‘a s tro n g se t for v e rifica tio n w h ich le a d s to th e se lec tio n o f on ly th o se stim u li m e n tio n e d in th e ru le ’. In a c tu a l fa ct th e su b je c t m a k e s n o re fe re n ce to p ro v in g th e ru le tru e - a n a lte rn a tiv e in te rp re ta tio n is t h a t he is o n ly in te re s te d in see k in g th e m a tc h in g v alu es. T h e e x a m p le s o f p a r tia l in sig h t a n d c o m p le te in sig h t p ro to c o ls cited a re m o re c o n v in c in g , h o w e v er. F o r e x a m p le , a su b je c t c h o o s­ ing p , q a n d q g a v e th e fo llow ing ju s tific a tio n s : p,q ‘T h e e x p e rim e n t m e n tio n s tria n g le a n d re d , th e re fo re w e m u st look a t b o th c a rd s w 'hich sh o w one o f th ese fe a tu re s to see if its o th e r h a lf h a s th e se c o n d fe a tu re re q u ire d if th e s ta te m e n t is t r u e .’ p ‘T h e e x p e rim e n t d o c s n o t m e n tio n a s q u a re , so th e c a rd w ith a s q u a re o n it n eed n o t be loo k ed a t . ’ q ‘W e m u s t look a t th e b lu e c a rd in c ase it h a s a tria n g le on th e o th e r h alf, in w h ich case th e s ta te m e n t w o u ld be u n t r u e .’ T h e s e c o m m e n ts seem in sig h t. T h e first re v ea ls ‘irre le v a n t’ a ttr ib u tio n to sificatio n te n d e n c y . S u b je c ts c h o o sin g p a n d

to c o n ta in all th e in g re d ie n ts o f p a rtia l a v e rific a tio n te n d e n c y ; th e se c o n d a n th e false a n te c e d e n t, a n d th e th ird a fal­ q, a c c o rd in g to th e m o d el, h a v e c o m p le te

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insight a n d sh o u ld choose only in o rd e r to falsify. T h e follow ing protocol a p p e a rs to c onfirm this: p p q q

‘I chose th e tria n g le b eca u se if it h a s blu e on th e o th e r half, it will d isp ro v e th e c la im .’ ‘I ig n o red th e sq u a re b ecau se it h a s n o th in g to d o w ith the c la im .’ ‘I ignored th e red c ard b ecau se it m ay have a tria n g le o r a s q u a re o n th e o th e r h a lf.’ ‘I chose th e b lu e c a rd b ecau se if it h a s a tria n g le on the o th e r half, it w ill d isp ro v e the c la im .’

O n e p o in t to b e a r in m in d is th a t th e G oo d w in a n d W aso n protocols d o n o t c o n stitu te strictly in d e p e n d e n t evidence o f the m odel. Jo h n s o n -L a ird a n d W aso n h a d been in flu en ced by the th e r­ apy e x p erim e n ts in dev isin g the m odel, a featu re o f w hich w as the collection o f v e rb a l pro to co ls. H e n ce re m a rk s su c h as those cited could hav e influ en ced c o n stru c tio n o f th e m odel. A second p ro b lem is th a t one needs to be su re th a t th e v e rb al ju stific a tio n s a re wrh a t they p u rp o rt to be: an a cc o u n t o f th e a c tu a l a priori causes o f selection. T h is issue w ill be discu ssed in d e ta il in th e next section. O th e r in sig h t m odels h av e b een p ro p o se d to e x p la in selection task p erfo rm an ce. O n e o f these, B ree a n d C o p p e n s (1976), h a s been criticised by M o sh m a n (1978), w ho identifies in ac cu ra c ie s in the d eriv a tio n o f p re d ic tio n s a n d th e p re se n ta tio n o f d a ta , as B ree a n d C o p p en s (1978) largely concede. T h e o th e r m ain effort, by Sm alley (1974), takes m ost c o m p re h en siv e a c c o u n t o f early selectio n -task studies. H e suggested th re e m ain so u rces o f v a ria tio n betw een subjects: (1) (2) (3)

In te rp re ta tio n o f sentence. In te rp re ta tio n o f cards. A p p lica tio n o f d ecision rules.

A t stag e (1) su b je cts m ay e ith e r in te rp re t th e ru le as im p lica tio n o r eq u iv alen ce (w ith 'd e fec tiv e ’ tru th tab le s). A t sta g e (2) th e s u b ­ je c t m ay o r m ay n o t a p p re c ia te th e rev ersib ility o f th e c ard s. A t stage (3) they m ay choose only to verify (no in sig h t), to verify an d falsify (p a rtia l in sig h t) o r only to falsify (com plete in sig h t). W ith reference to sta g e (2) o f th e m odel, W aso n (p e rso n al c o m m u n ica ­

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tion) m a in ta in s th a t irrev e rsib ility is n o t a p ro p e rty o f th e c ard s as such, b u t is conferred on them by selection. T h e p o in t is th a t e v alu atio n o f su c h c ard s in a tru th -ta b le task does n o t reveal such asym m etries. S m alley’s m odel m akes m o re specific p re d ic tio n s th a n th a t of Jo h n s o n -L a ird a n d W aso n . F o r ex am p le, in his m odel p a rtia l in sig h t only leads to selections o f p, q a n d q if th e su b je ct has a n im p lica tio n in te rp re ta tio n , a n d p erceives c ard s as reversible. T h e p ro b lem w ith S m alley’s m odel, o f course, lies in its testa b ility - one needs to specify th ree p a ra m e te rs in o rd e r to p re d ic t the b e h a v io u r o f each subject. In p ro v id in g evidence for his m odel, Sm alley, like G oo d w in an d W aso n , relied heavily o n su b je c ts’ v e rb al p rotocols in clu d in g sta te d ju stific a tio n s for choices.

Interpretation of protocols N one o f th e in sig h t m odels h as been a p p lie d to selection tasks using negative rules. T h e d e m o n s tra tio n o f ‘m a tc h in g b ia s’ by E v an s a n d L ynch (1973) a p p e a rs to e m b a rra s s th ese m odels. O n th e o th e r h a n d , su b je c ts’ v e rb al ju stific a tio n s a p p e a r to give som e s u p p o rt to the a u th o rs ’ claim s o f u n d e rly in g in sig h ts o r strategies. W ason a n d E v an s (1975) devised a n e x p erim e n t to resolve this parad o x . E ach su b je ct w as re q u ire d to solve a selection task w ith a n affirm ative ru le - I f p then q - a n d a negative ru le I f p then not q. I f subjects ‘m a tc h ’ on b o th rules, i.e. select p a n d q, they sho u ld choose ‘verify in g ’ cases on the affirm ative rule - T A a n d T C - b u t ‘falsifying’ cases on the negative ru le - T A a n d F C . O n e ac h rule, subjects w ere asked to ju stify the decision to select o r reject each c ard , in the m a n n e r o f the G oodw in a n d W aso n (1972) stu d y . T h e q u a n tita tiv e d a ta w ere in line w ith the m a tc h in g bias effect. N one o f th e 24 su b je cts gave the co rre c t selection (T A - F C ) on the affirm ative rule, a n d 12 o f them chose p a n d q (T A - T C ). O n the negative ru le 15 o u t o f 24 gave the c o rre c t selection w hich is also the m atc h in g c o m b in a tio n o f p a n d q. P rotocols w ere th en ra te d for evidence o f falsification, on the basis o f sta te m e n ts such as ‘I f th ere is a 6 on the o th e r side th en the s ta te m e n t is false’. F alsification protocols w ere o bserved m o re often on the negative p ro b lem , p a r ­ ticularly for those su b je cts w ho received it p rio r to th e affirm ative problem .

The IVason selection task

171

In essence, su b je cts ten d e d to give logically a p p ro p ria te ju s tifi­ cations o f the c a rd s they h a d selected. P a rtic u la rly in te re stin g w ere the protocols o f su b je cts w'ho d id the negative p ro b lem first, a n d m atc h ed on b o th rules. W aso n a n d E v an s re p o rt th ree such p ro ­ tocols w hich a re re p ro d u c e d in T a b le 9.3. T o ease co m p re h en sio n the lexical c o n te n t - le tte r a n d n u m b e r referred to - h a s been sta n d a rd ise d . L ooking first a t the ju stific a tio n s o f the negative task, we see th a t S3 a n d S6 w ould hav e to be classified as d e m o n s tra tin g com plete insight by the G o o dw in a n d W aso n tec h n iq u e. N o t only d o they choose the T A a n d F C c ard s, b u t they ju stify selections w ith ref­ erence to the p ossibility o f falsification. By c o n tra st, th e ir protocols on the su b se q u e n t affirm ativ e rule w'ould be classified as show ing no insight. S u b jects choose T A a n d T C , in the case o f S6, at least, suggesting a v erification m otive for choice. T h ese a re essentially tw o in te rp re ta tio n s o f these resu lts. O n e is to su ppose th a t th e n e g ativ e c o m p o n e n t in d u ces a g en u in e insight for som e reaso n . B u t if th is w ere so, w hy does it d is a p p e a r on p re se n ta tio n o f the affirm ative rule? A lso, we know from the E vans an d L y n ch (1973) stu d y th a t the effect o f in tro d u c in g a n egative antecedent is to m ake choices less logical (few er T A ’s, m o re F A ’s). T h e a lte rn a tiv e e x p la n a tio n , p referred by W 'ason a n d E v an s, is to suppose th a t selections a re highly influenced by m atc h in g , a n d th a t the verbal ju stific a tio n s a re rationalisations. A ccording to th is view, the sub ject asked to ju stify his selection is solving a new problem. T h e p ro b lem is this: given (1) th e in stru c tio n s, (2) th e selections, w h a t is a good reaso n for h a v in g chosen as he did? Since the in stru ctio n s asked su b je cts to ‘estab lish w h e th e r the ru le is tru e o r false’, he evaluates h is selections in these term s. T h e se v e rb a lisa tio n s d e m o n ­ stra te a n a b ility to recognise T T as verifying a n d T F as falsifying a c o n d itio n al rule, a c o m p eten ce o b serv ed in tru th -ta b le tasks (C h a p te r 8). A n in te re stin g fe atu re o f the p ro to co ls cited is th a t ‘m atc h in g b ia s’ n o t only influences the o rig in al selections, b u t a p p e a rs to affect the process o f ju stific a tio n as well. T h is is clearly illu stra te d by S6, w ho ju stifie s th e selection o f B (T A ) on e ac h rule by c o n sid erin g the effect u p o n the rule, if th e m a tc h in g 3 is on the o th e r side o f the card . T h is lead s him to a verifying ju stific a tio n o f T A on the affirm ­ ative rule, a n d a falsifying ju stific a tio n o f T A on th e n e g ativ e rule. T h is o b se rv atio n gives su p p o rt to E v a n s’s (1975) e x p la n a tio n o f the

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T A B L E 9 .3

Three protocols fro m the study o f W ason and E vans (1975)

C a rd s an d responses

N egative task If there is a B. will not be a 3

A ffirm ative task then there

If there is a B. will be a 3

then there

Reasons

Reasons

‘I f the rule w as false, there w'ould be a 3 on the o th er side. If tru e there w ould not be a 3. B a n d 3 should be taken as p a rt o f the sam e a ssu m p tio n .'

‘T h e rule says th a t B is related to 3. It does not say a n y th in g a b o u t there being a logical sequence o f letters to num bers, so no assum ptions about letters a n d nu m b ers o th er th an B an d 3 can be m ad e .’ ‘As above’

S3

U

yes ‘I f the rule w as false, there w ould be a B on the o th er sid e / no ‘T h e rule only states th at there is no relation betw een 3 an d B. It does not state w h eth er there is a relation betw een o th er nu m b ers an d letters’ no ‘As a b o v e.1 yes ‘T o see th a t it is not a 3.’ yes ‘T o ensure th a t it is not a B.' no

‘It need not prove a n y th in g /

no

‘It need not prove anything.*

yes

T f there is a 3 on the o th e r side, then the sta te m en t is false.’ ‘I f there is a B on the o th er side, then the sta te m en t is false.’

‘Logical extension of a rg u m e n t abo v e.’

‘As abo v e.’ ‘T o ensure th a t the reverse is 3.’ ‘T o ensure th a t the reverse is B .’ ‘T h e result m ight be inconclusive.’ ‘T h e result m ight be inconclusive.’

S6

yes

U

no

no

‘W h atev e r n u m b er is on the o th er side will not show' if sta te m en t is tru e or false.5 ‘A ny letter m ay be on the o th er side, therefore no way o f know ing if sta te m en t is tru e .’

‘I f there is a 3 on the o ther side, then the sta te m en t is tru e .’ ‘I f there is a B on the o th er side, then the sta te m en t is true: othew ise it is false.’ ‘A ny n um bers m ay be on the o th er side.’ T f n u m b ers are fairly ra n d o m , then there m ay be an y letter on the o th e r side, thereby giving no indication unless the letter is B .’

The Wason selection task

173

origin o f the m a tc h in g effect. S ubjects do in d ee d seem to th in k th a t the rule is m ak in g a sta te m e n t a b o u t th e n a m e d v alues, reg ard less o f the presence o f negatives. T h e y e v id en tly find it easier to c o n sid er a n affirm ative p o ssibility, su c h as ‘3’, th a n a negative, su c h as ‘n o t 3 ’. E vans a n d W aso n (1976) re p o rt fu rth e r evidence for the ra tio n ­ alisatio n hyp o th esis. S ubjects w ere given the selection task, to g eth e r w ith its ‘so lu tio n ’. T h e y w ere assigned ra n d o m ly to four g roups acco rd in g to how the solu tio n w as defined. T h e y w ere told th a t eith er p\ p a n d q\ p, q a n d q\ o r p a n d q w as the co rre c t answ er. Subjects w ere th en asked to ju stify the selection o r rejection o f each c ard , as specified in th e ‘so lu tio n ’ p rovided. V ery few su b je cts d isp u te d the corre c tn e ss o f the alleged solution, a lth o u g h in m an y cases it w ould obviously differ from the selection they w ould h av e m a d e if asked to solve it in th e n o rm a l w ay. A n in spection .of ju stific a tio n offered for q a n d q revealed th a t the m ajo rity n o t only gave a ju stific a tio n ag reein g w ith th e set so lu tio n (selection o r rejectio n ) b u t gave a h igh confidence ra tin g o f the c orrectness o f this selection. T h is stu d y show s th a t su b je cts can c o n stru ct ju stific a tio n s for a rb itra rily selected solutions, b u t does not prove th a t they a re ra tio n a lisin g w hen ju stify in g th e ir ow n solutions in o th e r e x p erim e n ts. T h e d e m a n d c h ara c te ristic s o f the E vans a n d W aso n ex p erim e n t obviously e x ert a stro n g ‘c o m p lian c e ’ effect. It is w o rth reflecting, th o u g h , th a t if su b jects d o n o t have in tro sp ectiv e access to th e th o u g h t processes u n d e rly in g selections, th en a sim ila r c o m p lian c e effect m ay be o p e rativ e w hen they are asked to ju stify th e ir ow n responses. T h e y m ay devise su itab le ‘re a so n s’ sim ply because th e e x p e rim e n te r h as asked th em to d o so. W aso n a n d E vans w ent on to p ro p o se a d u a l process th eo ry o f reaso n in g , in w hich selections a n d ju stific a tio n s w ere a ttrib u te d to d istin c t th o u g h t processes. T h e d u a l p rocess theory' h a s im p lica tio n s c o n cern in g the n a tu re o f th o u g h t, w hich go well bey ond the ex­ p la n a tio n o f selection task d a ta . Since these im p lica tio n s will be explained fully in th e final c h a p te r o f this book, it is u n n e ce ssa ry to div ert a tte n tio n to th e d u a l process th eo ry a t this p o in t. F o r p u r ­ poses o f the p re se n t c h a p te r it is sufficient to note th a t th is w ork casts serious d o u b t on the s ta tu s o f ev idence for ‘in sig h t’ o r ‘s tra te g y ’ m odels, w hich is b ased u p o n su b je c ts’ v e rb al ju stific atio n s.

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Evans’s stochastic model T h e criticism o f in sig h t m odels is, o f course, in k eeping w ith the general o p p o sitio n to ra tio n a list a p p ro a c h e s th ro u g h o u t this book. T h e sto c h astic re aso n in g m odel (E v an s, 1977b) c an be seen as a fu rth e r a tte m p t to offer an a lte rn a tiv e to th e ra tio n a list a c c o u n t o f reaso n in g . R e ad e rs m ay find its a ssu m p tio n s a b su rd ly c o u n te r-in tuitive. In this case, they m ig h t ask them selves w h e th e r th is o b jec­ tion arises from in tro sp e c tio n c o n sid era tio n s. I f so, c o n sid er the view th a t psychologists c a n n o t reject p u rp o rte d e x p la n a tio n s o f b e h a v io u r sim ply on th e g ro u n d s th a t people d o n o t feel th a t they do th in g s in su ch a m a n n e r. T h e w ork re p o rte d in the last section suggests th a t in tro sp ec tiv e re p o rts m ay n o t be w h a t th ey seem , a poin t w h ich is e la b o ra te d in C h a p te r 12. T h e E v an s (1977b) p a p e r sta rts w ith th e q u e stio n o f w h ere in­ d iv id u a l differences in re aso n in g p e rfo rm a n ce arise. T h e p re d o m i­ n a n t a ssu m p tio n h a s been th a t if tw o su b je cts m ake a different response to th e sa m e p ro b lem th en they a re in different sta te s o f insight, o r a re e m p lo y in g different stra te g ies. An a lte rn a tiv e possi­ bility is th a t b e h a v io u r is in trin sic ally p ro b a b ilistic , o r sto c h astic . I f a g ro u p o f su b je cts all hav e a p ro b a b ility o f 0.6 o f m ak in g a given response, a b o u t 60 p e r cen t o f them w ould be observ ed to m ak e it in a given e x p erim e n t. T h e o bject o f the E v an s (1977b) p a p e r w as to devise a sto c h astic m odel to a c c o u n t for re aso n in g p e rfo rm a n ce in g e n era l, a n d the W aso n selection task in p a rtic u la r. In sig h t m odels o f the selection task place e m p h a sis o n th e combinations o f c a rd s selected, e.g. p,q in d icates no insight; p,q,q p a rtia l in sig h t, a n d p,q co m p lete insight. E vans (1977b), how ever, wras in te rested in p re d ic tin g th e response p ro b a b ility o f e ac h c a rd in d iv id u a lly , a n d th e first ste p w as to check w h e th er o r n o t c a rd selections w ere statistically independent. F o r ex­ am ple, if we know th a t a su b je ct h a s selected q, a re we ab le to p re d ic t th a t he is m o re o r less likely to select q? T h e a n aly sis w as restricted to q a n d q selection for tw o reasons:

(1) F re q u e n cy o f p is too high, a n d p too low, to p e rm it useful sta tistica l analysis. (2) It is th e pre sen c e a n d ab se n ce o f q a n d q selectio ns th a t d istin g u ish es different sta te s in th e in sig h t a n d stra te g y m odels.

The Wason selection task

175

T h e E v an s (1977b) p a p e r p re sen ts a re-an aly sis o f 17 selectiontask e x p erim en ts. In n o n e o f these w as th ere a significant a sso ciatio n b etw een q a n d q selections. T h is sta tistic a l in d ep e n d en c e u n d e r­ m ines th e psychological significance o f c o m b in a tio n s o f c ard selec­ tions e m p h a sise d by the in sig h t m odels. In d e e d , it suggests th a t d a ta sho u ld be re p o rte d in term s o f the raw frequencies o f selecting each card - w hich m an y a u th o rs have o m itte d to do. T h e finding o f in d ep e n d en c e also h a s a n in te re stin g im p lica tio n for th e selection p a tte rn s found a fte r ‘th e ra p y ’, as will be explain ed . U n tra in e d su b je cts n o rm ally choose e ith e r/) o r p,q. T h e sto ch astic in te rp re ta tio n o f this is as follows: (1) (2) (3)

S u b jects hav e a high p ro b a b ility for selecting p. T h e y h av e low p ro b a b ilitie s for selectin g p a n d q. T h e y h av e a n in te rm e d ia te selection p ro b a b ility for q.

N ow su p p o sin g th e ra p ie s a re in tro d u c e d w ith the specific a im o f in creasin g q selections. T h is w as a tte m p te d by W aso n (1969a) using a p rogressive series o f th e ra p ie s w ith a selection task after each stage. A cross the five tests, the selection p ro b a b ility o f q rose from 0.06 to 0.88 - as m ea su re d by the p ro p o rtio n o f subjects choosing it. H o w ev er, th e E v an s (1977b) an aly sis show ed th a t its selection re m a in e d in d e p e n d e n t o f q selections on all five tests. Suppose, th en , th a t the p ro c e d u re h as succeeded in raisin g the selection p ro b a b ility o f q w ith o u t affecting the p ro b a b ility o f selec­ ting an y o th e r c ard . W h a t effect w ould this have on the observed co m b in a tio n s o f card s? T h e a n sw e r is q u ite sim ple. T h e m o d al choices w ould sw itch from p a n d p,q to p,q a n d p,q,q, w hich is exactly w h a t h a p p e n s w hen th e ra p ie s are successful. T h u s ‘com plete in sig h t’ a n d ‘p a rtia l in sig h t responses could sim ply be the sta tistica l consequence o f revising one o f four in d e p e n d e n t c ard selection frequencies. P ollard (1979a) a n aly se d sta tistica l a sso ciatio n s b etw een all four card s in sev eral e x p erim e n ts. H e re p lica ted the in d ep e n d en c e o f q an d q selection, b u t found evidence o f a c o rre latio n betw een p a n d q selections. H e in te rp re ts this as a risin g from in d iv id u a l differences in su scep tib ility to m a tc h in g bias. Som e su b je cts ten d strongly to ignore b o th m ism a tc h in g c ard s. T h e s e findings p a ralle l those o f Pollard a n d E v a n s’s (1980) inference task stu d y (cf. C h a p te r 8) in w hich little c o rre la tio n w as found betw een p e rfo rm a n ce on infer­

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ences o f sim ila r logical type, b u t som e o n th e a p p a re n t basis o f su scep tib ility to re sp o n se biases. If b e h a v io u r is sto c h astic a t the level o f in d iv id u a l su b je cts, th en we m ight also ex p ect in d ep e n d en c e in successive responses from the sam e subjects. T h is is not a necessary c o n seq u en ce o f the sto c h astic a ssu m p tio n , how ever, since it is p ossible th a t th e su b je c t’s resp o n se on the first p re se n ta tio n o f th e selection, w hile ra n d o m ly g e n e ra te d , m ay affect his p e rfo rm a n ce on a second test. N ev erth eless E v an s (1977a) does re p o rt a n a n aly sis o f som e new d a ta p ro v id ed by B ree, w hich p rovides som e evidence o f tria l to tria l in d ep e n d en c e . T h e sto c h astic m odel o f E v an s (1977b) is b ased on the tw o-factor theory o f E v an s (1972a, 1977a). T h e idea is th a t in te rp re ta tio n a l (logical) ten d en cies co m b in e w ith re sp o n se -b ia s (non-logical) te n d ­ encies in p ro v id in g th e o b se rv ed d a ta . T h e m odel form alises the notion o f weighted c o m b in a tio n d iscu ssed previously. T h e re a re th ree p a ra m e te rs, all o f w hich fall in the ra n g e 0 to 1: I T e n d e n c y to resp o n d o n th e basis o f th e in te rp re ta tio n a l co m ponent. R T en d e n cy to re sp o n d on the basis o f response bias, a W eig h tin g factor. T h e m odel is re p re se n te d sc h e m a tic ally in F ig u re 9.2. I t is w ritten in a gen eral form , b u t for c o n sid e ra tio n o f the selection task the ‘re sp o n se ’ w ould be selection o f a c ard . T h e m odel su p p o ses th a t subjects either re sp o n d on th e basis o f in te rp re ta tio n (w ith p ro b a ­ bility a ) o r on th e basis o f resp o n se b ias (w ith p ro b a b ility 1 - a ) . T h e o th e r p a ra m e te rs c a n be seen as c o n d itio n al p ro b a b ilitie s. I is the c h an c e o f selecting a c a rd given th a t re sp o n d in g is b ased on in te rp re ta tio n ; R is th e p ro b a b ility given th a t a resp o n se bias is being used. By elem entary' p ro b a b ility th eo ry th e p ro b a b ility o f a p a r tic u ­ la r response (c ard selection) r is given by P(r) = ct.I + (1 - a ) . R In th e p a p e r, th e m o d el w as teste d a g a in st th e d a ta o f E v an s a n d L ynch (1973). In o rd e r to test th e m odel it w as necessary to assu m e th a t all su b je cts h a d th e sa m e p a ra m e te r v alues, a n d to use the observed p ro p o rtio n o f su b je cts m ak in g a given re sp o n se as a n

The Wason selection task

177

Pr(r) = a. I + ( 1 - a ) . R.

F IG U R E 9.2 S ch em atic rep re se n ta tio n o f th e E vans (1977b) sto ch astic reaso n in g m odel

e stim a te o f th e p rio r p ro b a b ility for e a c h su b je c t. I t w as a lso n e ce ss­ a ry to m ak e se v e ra l a priori a s s u m p tio n s a b o u t p a r a m e te r v alu es. T h e s e w ere as follow s: a v a lu e s T w o v a lu e s:

a a for a n te c e d e n t choices a c for c o n s e q u e n t choices

T h is w a s b a se d u p o n th e o b s e rv a tio n o f E v a n s a n d L y n c h (1973) th a t m o re w e ig h tin g is a p p a re n tly g iv en to logic, a n d less to m a tc h ­ ing, on th e a n te c e d e n t se lec tio n s. T h u s w e w o u ld e x p e c t a a > a c. I values I ta

=

1

I fa

=

0

I tc

=

0

I fc

=

1

178

Propositional reasoning

W h ere

Ita

=

‘in te rp re ta tio n a l p a ra m e te r for T A selectio n s’, etc.

T h is w as b ased on E v a n s a n d L y n c h ’s o b se rv atio n th a t w hen m atc h in g is b a la n ce d by p ooling acro ss th e rules, su b je cts ten d e d to be logically co rrect on th is task. R values It w as assu m e d th a t only tw o v alues w ere needed: R m for responses w h ich m atc h . Rw for responses w hich m ism a tch . O n these a ssu m p tio n s it w as p ossible to devise sim plified e x p re s­ sions o f th e p ro b a b ility o f selecting e ach c a rd in th e E v an s a n d L ynch e x p erim e n t. F o r ex am p le, c o n sid er selection o f F A o n the rule I f not p then q. I t is a n a n te c e d e n t choice, so th e w eighting p a ra m e te r is a a. FA m atc h es on this rule, so the resp o n se bias p a ra m e te r is R m. F in ally , I k a is a ssu m e d 0, so the expression is: P ( F A / I f not p then q) = a a.O + (1 - a a). R m = (1 - O l a ) . Rm F itte d in th is w ay, tw o in d e p e n d e n t m ea su re s w ere found for each expression. T h e y w ere c o n sisten tly very close. It w as also possible to p re d ic t e q u alities betw een p a irs o f differences o r ra tio s o f tw o observed p ro b a b ilitie s (p ro p o rtio n s) w hich a g a in w ere im pressively close. So it a p p e a re d th a t th e m odel fitted well. H ow ever, P o llard (1979a; 1979b) h as show n th a t th e a priori p a ra m e te r a ssu m p tio n s used a re in co rrect. In a tte m p tin g to fit the m odel to his ow n d a ta , he found th a t e stim a te s o f a c w ere freq u en tly negative, w h ereas this p a ra m e te r m u st lie in the ra n g e 0 to 1. T h is m eans th a t in his e x p erim e n ts, T C selections w ere m ore freq u e n t th a n FC selections. T h is could n o t o c c u r if th e assu m e d values o f I p a ra m e te rs w ere g e n era lisa b le. O n closer in sp e ctio n , how ever, P ollard found th a t the assu m e d I va lu e s w ere n o t even c o n sisten t w ith the E v a n s a n d L y n ch d a ta . By m a n ip u la tio n o f the e q u a tio n s o f E vans (1977b), P o llard e stim a te d the v alu e o f the follow ing expressions:

The H’ason selection task

179

(1 - a a) (R m - R m ) (1 - a c) (R m - R m ) T h e e stim a te d v alues from the E vans a n d L ynch d a ta w ere ident­ ical, an o b se rv atio n w hich in d ic a te s th a t a a = oic. H ow ever, on the E vans (1977b) p a ra m e te r a ssu m p tio n s they h a d been e stim a te d to have q u ite different v alu es ( a 3 = 0.511, a c = 0.156). T h is c o n tra ­ dictio n a g ain arises from th e a priori values w hich h a d been assum ed for the I p a ra m e te rs, an d these a re clearly w rong. Pollard does, how ever, find the m odel to fit well w hen these p a ra m e te r a ssu m p tio n s a re d isc ard e d . T h e psychological v a lu e o f the m odel is, in fact, d e m o n s tra te d by his c riticism o f the o riginal p a ra m e te r a ssu m p tio n s. In o rd e r to fit the d a ta he is forced to refo rm u late the psychological an aly sis o f the influence o f in te rp re t­ atio n al tendencies. In sim p le E nglish, th e original p a ra m e te r values were b ased on th e follow ing psychological theory: It w as a ssu m ed th a t su b jects have co m p lete logical co m p eten ce to solve the task c o n ta in ed in th e in te rp re ta tio n a l c o m p o n e n t. H ow ever, w hile they could a p p ly this co m p e ten c e m o re often th a n n o t on the a n te c e d e n t choices, they could a p p ly it m u ch less often on c o n se q u en t choices. T h e re m a in d e r o f re sp o n d in g w as b iased by m atc h in g . P o lla rd ’s c ritiq u e a lte rs th e th eo ry as follows: su b jects give eq u al w eighting to in te rp re ta tio n a l a n d resp o n se bias ten d en cies on all cards. H ow ever, th e c o m p eten ce rev ealed by th e I p a ra m e te rs is not uniform across c ard s, b u t m ore m ark e d for a n te c e d e n t c ard s. T h u s the v alu e o f I t a is high a n d I f a low in a c c o rd an c e w ith logic, b u t the values o f I t c a n d I f c a re in te rm e d ia te a n d little different from one a n o th e r. T h u s the su p e rio r logical p e rfo rm a n ce on a n te c e d e n t selections is a ttrib u te d to su p e rio r logical tendencies a n d not to a d d itio n a l w eig h tin g o f su c h tendencies. T h is d istin c tio n is o f co n ­ sid erab le im p o rta n c e to P o llard (1979a), w ho arg u es from a variety o f sources o f evidence th a t people h a v e little o r no logical co m ­ petence re g a rd in g th e ir tre a tm e n t o f th e c o n se q u en t o f c o n d itio n al rules. T h u s P o lla rd ’s c ritiq u e does n o t a m o u n t to a re fu ta tio n o f the E vans (1977b) a tte m p t to fo rm u la te a sto c h astic m odel o f the tw o-factor re aso n in g theory. R a th e r it is a co rrectio n in its m eans o f a p p lic atio n . W e will now proceed to c o n sid era tio n o f th e effects o f th e m a tic c o n te n t on se lec tio n -task p erfo rm an ce.

180

Propositional reasoning

Facilitation by realism All the se lec tio n -task e x p e rim e n ts d iscu ssed so far hav e em ployed so-called ‘a b s tr a c t’ m ate ria ls. T h e rules refer to re la tio n sh ip s be­ tw een the p re sen c e a n d a b se n ce o f a rb itra rily chosen sym bols (let­ ters, n u m b e rs , co lo u red sh a p e s, etc.) on e ith e r side o f a c ard . N ow , it can be a rg u e d th a t the h igh logical e rro r ra te , a n d th e p rim itiv e m atc h in g bias, give a d isto rte d im p re ssio n o f p e o p le ’s c o m p e ten c e to u n d e rs ta n d logical re la tio n sh ip s in real life. It will be recalled th a t W ilkins (1928) p ro d u c ed evid en ce th a t realistic c o n te n t can facilitate p e rfo rm a n ce on tasks em p lo y in g classical syllogism s (see C h a p te r 6). A n u m b e r o f e x p erim e n ts h a v e been p e rform ed to find ou t w h e th e r a sim ila r fa cilitatio n o f selectio n -task p e rfo rm a n ce could be effected by th e in tro d u c tio n o f th e m a tic c o n te n t. T h e resu lts o f several o f th ese a re su m m a rise d in T a b le 9.4.

T A B L E 9.4 The results o f some experiments manipulating thematic and abstract content.' (% correct (p,q))

W ason an d S hapiro (1971) Jo h n so n -L a ird et al. (1972) V an D uyne (1974) Bracew ell an d H idi (1974)2 G ilhooly an d F alconer (1974)2 M anktelow an d E vans (1979)3

A b stract

T h em atic

6 15 33 8 6 7

63 8! 54 75 22 7

N otes: ' O n ly affirm ativ e ru le s o f th e form I f p then q o r Every p has a q are in c lu d ed . 2 O n ly th e co n d itio n s w h ich re p e a t those o f W a so n a n d S h a p iro are sh o w n here. 3 D a ta pooled o v er five e x p e rim e n ts. T h e freq u en cy o f p.q is tak en from th e raw' d a ta ; th is m e a su re w as n o t re p o rte d in th e p a p e r.

T w o e x p erim e n ts p u b lish e d in the early 1970s yield ev idence o f such faciliation. In th e first (W aso n a n d S h a p iro , 1971, E x p erim en t II ) subjects w ere asked to in v estig a te a claim m a d e by th e e x p eri­ m en ter, su ch as: ‘E very tim e I go to M a n c h e ste r I trav e l by c a r.’

The Wason selection task

181

T h e four c a rd s w ere used to re p re se n t jo u rn e y s , w ith the m eans o f tra n s p o rt w ritte n on one side, a n d th e d e stin a tio n o n th e o th er. W ith th e above rule, th e su b ject m ig h t be show n th e c a rd s show n in F ig u re 9.3.

Manchester

Leeds

Car

F IG U R E 9.3 F o u r cards used in the them atic selection tack o f W ason an d S h ap iro (1971)

Su b jects w ere th e n asked w h ic h c a rd s w ould need to be tu rn e d over in o rd e r to d ecid e w h e th e r th e e x p e rim e n te r’s claim w as tru e or false. T h e co rre c t a n sw e r is ‘M a n c h e ste r’ a n d ‘t ra in ’. T h e a b s tra c t co n tro l c o n d itio n em ployed rules su c h as ‘E very c a rd w hich has a D o n one side h a s a 7 on the o th e r ’. 10 o f th e 16 su b jects tested in th e th e m a tic g ro u p gav e th e co rre c t (p,q) a n sw er, as c o m p a red w ith only 2 o f th e 16 in the a b s tra c t gro u p . T h is re su lt is especially in te re s tin g w h en on e co n sid ers th a t, in a sense, th e a b s tra c t m a te ria l is m o re concrete th a n th e th e m a tic . T h e a b stra c t ru le refers to th e a c tu a l c a rd s them selves, w h ereas the th em a tic ru le refers to h y p o th e tic a l situ a tio n s, o f w h ich th e c ard s a re sym bolic re p re se n ta tio n s. I n th e second e arly e x p erim e n t (Jo h n so n -L a ird , L eg ren zi a n d L eg ren zi, 1972), b o th th e a b s tra c t a n d the th e m a tic ru les referred to the a c tu a l m a te ria ls th a t the sub ject h a d to co n sid er. In the th e m a tic co n d itio n , su b je cts w ere asked to im agine th a t they w ere p o st office w orkers so rtin g letters. A n e x am p le o f the th e m a tic ru le w as: ‘I f a le tte r is sealed th e n it has a 50 lire sta m p on i t ’ Su b jects a re th en sh o w n n o t four c a rd s, b u t four envelopes. T w o h a d the fro n t exposed, o n e b e a rin g a 50 lire sta m p (q) a n d one a 40 lire sta m p (q ). T h e o th e r tw o h a d th e ir reverse sides facing, one sealed (p) a n d th e o th e r u n se a le d (p ). T h e a b s tra c t c o n tro l e m ­ ployed th e u su a l le tte r-n u m b e r re la tio n s on c ard s. All su b je cts p e r­ form ed b o th tasks in c o u n te rb a la n c e d o rd e r. T w o asp e cts o f the

182

Propositional reasoning

results a re strik in g : (i) th ere w as a m assive facilitatio n eifect, w ith 22/24 su b jects show ing su p e rio r logical p e rfo rm a n ce in the th e m a tic condition a n d (ii) those su b je cts wrho p erfo rm e d th e a b s tra c t task after th e th e m a tic task gave the u su a l p o o r p erfo rm an ce. A ny ‘in ­ sig h t’ e n g en d e red by realism e v id en tly does n o t transfer. I f the fa cilitatio n elfect o b serv ed in these stu d ies is g e n u in e a n d reliable, th en it clearly affects o n e ’s a ttitu d e s to th e larg e n u m b e r o f studies e m p lo y in g only a b s tra c t c o n te n t. O n e m ig h t re g a rd the la tte r as h a v in g low ecological v a lid ity for assessing real life re a so n ­ ing. M o re positively, one m ig h t ask w hy the re aso n in g a b ilitie s o f intelligent a d u lts a re so d e p e n d e n t on c o n te n t, a n d p o in t to the d isc rep a n cy betw een these re su lts a n d P ia g e t’s theory' o f form al o p e ratio n s (see W aso n , 1977, a n d C h a p te r 12 o f this book). T h e reliability o f the effect seem ed to be e stab lish e d by a n u m b e r o f su b se q u e n t stu d ies (L u n ze r, H a rris o n a n d D avey, 1972; Bracewrell an d H id i, 1974; G ilhooly a n d F a lco n e r, 1974; V a n D u y n e , 1974). H ow ever, a recen t stu d y by M a n k telo w a n d E v an s (1979) h a s failed to find a n y fa cilitatio n in five se p a ra te e x p erim e n ts. I t is conse­ q u e n tly necessary to look closely a t th e d e ta il o f the in d iv id u a l studies. T h e stu d y re p o rtin g the h ig h est ra te o f so lu tio n w ith th em a tic c o n te n t is th a t o f Jo h n s o n -L a ird et al. d e sc rib e d above. T h is ex p eri­ m en t can be c riticised on th e g ro u n d s th a t it is too realistic. T h e B ritish un iv ersity s tu d e n ts tested a t th a t tim e w ould c e rta in ly have experienced a sim ila r ru le in th e ir ow n real-life ex perience. T h e y w ould th u s b rin g to th e e x p e rim e n t the know ledge th a t one m ay not seal a le tte r w ith a lower valued sta m p on it. T h e y w ould also know th a t if a le tte r h a s a h ig h -v alu ed sta m p it does no t m a tte r w h e th e r o r n o t it is sealed, a n d th a t if it is u n se a le d it does not m a tte r w hich o f the tw o values o f s ta m p is used. T h e p o in t is th a t the sub ject can solve this p ro b le m w ith o u t reasoning at all; he can tran sfer d irec tly his le a rn e d re sp o n se to a n a n alo g o u s real-life s itu ­ ation. I t w ould be in te re stin g to re p e a t the e x p erim e n t w ith a high er-v alu ed sta m p (e.g. 60 lire) re p re se n tin g the q conclusion. T h e lesson h ere is th a t a re aso n in g task is not a re aso n in g task unless it is h y p o th etica l to a d egree; th e m a tic m a te ria ls m u st n o t be used w hich m ak e the c o rre c t a n sw e r d irec tly a v ailab le from m em ory. T h e tow ns a n d tra n s p o rt m a te ria l o f W aso n a n d S h a p iro (1971) have been em ployed by o th e r w orkers. I t w as a rg u e d th a t the

The Wason selection task

183

facilitatio n m ig h t re su lt from th e m a tic terms o r else from a re alistic relation betw een the term s. T w o stu d ies w hich in v estig a te d this p ro d u c ed co nflicting results. G ilhooly a n d F a lco n e r (1974) found the term s ra th e r th a n th e re la tio n to be im p o rta n t, w h ereas B racewell a n d H id i (1974) m a d e th e reverse o b se rv atio n . H ow ever, both found significant fa cilitatio n in th e situ a tio n sim ila r to W aso n a n d S h ap iro - th e m a tic term s and realistic re la tio n s - a lth o u g h in the G ilhooly a n d F a lco n e r stu d y the level o f p e rfo rm a n ce in this co n ­ dition w as still relativ ely low. T h e in te rp re ta tio n o f B racew ell a n d H id i’s resu lt is c o m p lica te d by a n in te ra c tio n w ith th e o rd e r o f reference to a n te c e d e n t a n d c o n se q u e n t in the sen ten ce they used. M an k telo w a n d E v an s (1979) h a v e claim ed th a t the evid en ce for facilitation h a s been o v e rsta te d , a n d p o in t to the fact th a t som e studies (e.g. V a n D u y n e , 1974; L u n z e r et al., 1972) hav e only found the effect w hen o th e r p ro c e d u ra l c h an g e s a re in tro d u c e d such as in stru ctio n s e m p h a sisin g falsification, o r th e use o f ‘re d u c e d ’ a rra y s o f cards. H ow ever, it is the M a n k telo w a n d E v an s stu d y th a t is o u t o f line w ith the rest o f the lite ra tu re , a n d it is necessary to look closely a t their p ro c ed u re s. In four o f the e x p erim e n ts ‘food a n d d rin k ’ c o n te n t w as used so as to p e rm it the in tro d u c tio n o f n egative c o m p o n en ts (in the first tw o e x p erim e n ts only). E x am p les are: If If If If

I I I I

eat m a c a ro n i, th en I d o n o t d rin k c h am p ag n e . d o n o t e at p ork, th en I d rin k red wine. d o n o t e at c hips, th en I d o n o t d rin k b row n ale. e at h a d d o ck , th en I d rin k gin.

S u b jects w ere told th a t each c a rd referred to ‘w h a t I a te a n d d ra n k a t a p a rtic u la r m e a l’. In th e first e x p e rim e n t, a g ro u p test, no difference w as o bserved b etw een p e rfo rm a n ce on su ch se n ten c es a n d a b s tra c t co n tro ls. B oth g roups show ed th e u su a l low logical p e rfo rm a n ce a n d co m p a riso n betw een rules yielded e vidence o f m a tc h in g b ias w ith th e m a tic as well as a b s tra c t c o n te n t. T h is non-effect w as re p lica ted in th ree fu rth e r e x p erim e n ts u sin g in d iv id u a l p re se n ta tio n , in clu d in g tw o e x p erim en ts e m p lo y in g affirm ativ e rules only. T h e final e x p erim e n t re p ea te d W aso n a n d S h a p iro ’s e x p e rim e n t w ith th eir m a te ria ls an d also p ro d u c e d n o facilitatio n . P o llard (1981) a rg u e s th a t the food a n d d rin k m a te ria ls a re not really realistic. H e p o in ts to W 'ason a n d J o h n s o n - L a ird ’s (1972)

184

Propositional reasoning

e m phasis on the im p o rta n c e o f a believ ab le story, a n d claim s th a t the food a n d d rin k s m a te ria ls lack p lau sib ility . O n b a la n ce , the re sea rc h to d a te su g g ests th a t the use o f m a te ria ls w ith realistic reference m ay hav e som e fa cilitatin g effect on p e rfo rm ­ ance. T h e effect is n o t so stro n g o r reliab le as th e early p a p e rs suggest, a n d th ere is clearly a need for fu rth e r resea rc h to d e te rm in e exactly how task c o n te n t is affecting the m a n n e r in w hich su b jects thin k a b o u t th e p ro b lem .

Truth status effects M u c h o f the resea rc h in to th e effect o f re alistic m a te ria ls on syllo­ gistic re aso n in g (C h a p te r 6) w as co n ce rn ed w ith b elief bias. T h e se studies use th e m a tic m a te ria ls to w a rd s w h ich th e su b je ct is likely to have a ttitu d e s. In p a rtic u la r, th e evid en ce suggests th a t su b je cts m ay e v a lu a te th e tru th o f th e syllogism ’s conclusion on th e b asis o f a priori beliefs, ra th e r th a n assessing the logical valid ity o f the a rg u m e n t as in stru c te d . P eople a re m o re likely to assess a n a rg u ­ m en t as ‘v a lid ’ if th ey believe its c onclusion to be true. V a n D u y n e (1976) dev elo p ed a th eo ry o f belief-bias effects in the th em a tic selection task. H e p ro p o sed th a t su b je cts a re m o tiv a te d by ‘cognitive self-rein fo rcem en t’. E ssen tially , his a rg u m e n t is th a t s u b ­ jec ts will seek verifying ev idence for a ru le they believe to be true, an d are m ore likely to seek falsifying evid en ce if they th in k th e rule could be false. In o rd e r to test this h y p o th esis he asked su b je cts to m ake u p c o n d itio n al se n ten c es w h ich th ey th o u g h t e ith e r (1) necess­ arily tru e o r (2) c o n tin g e n tly tru e (so m etim es tru e , so m etim es false). Subjects w ro te do w n five e x am p les o f e ac h from w hich the e x p eri­ m en te r selected one in e ac h category' for th e selection task. A lth o u g h V a n D u y n e ’s task is logically e q u iv a le n t to W a s o n ’s, it is u n u su a l in h av in g not card s. S u p p o se the su b je ct gives the follow ing sen ten ce as necessarily true: I f it is a c a m e ra th en it h a s a lens. T h e e x p e rim e n te r w ould ask the su b je c t to su p p o se th a t he could know only one fact c o n ce rn in g e ith e r th e first o r second p a rt o f the sentence. H e w ould be asked to consider:

The Wason selection task (i) (ii) (iii) (iv)

an an an an

o b ject o b ject o bject o bject

th a t th a t th a t th a t

185

w as a c a m e ra (T A ) w as n o t a c a m e ra (FA ) h a d a lens (T C ) d id n o t hav e a lens (FC )

In e ac h case, he w ould be asked ‘W o u ld it be necessary in this case to look for a d d itio n a l in fo rm a tio n in o rd e r to find o u t w h e th e r the sta te m e n t is tru e o r false?’ S u b je cts w ere also asked to give reasons. V an D u y n e claim ed th a t th e re w ere significantly m o re co rrect answ ers in the c o n tin g e n cy c o n d itio n th a n in th e necessity c o n d i­ tion, in line w ith his p re d ic tio n . H o w ev er, he only scored a co rrect selection, e.g. F C , as ‘c o rre c t’ if th e su b je ct gave the right reason fo r selecting it. P o llard a n d E v an s (1981) re -a n a ly sed his d a ta in term s o f the rawr selection freq u en cies a n d found no differences a t all betw een the c o n d itio n s. T h u s V a n D u y n e ’s p ro c e d u re has affected not the selection o f c ard s, b u t the v e rb al ju stific a tio n s th a t people offer for th em . O n clo ser in sp ectio n , his re su lts arise a lm o st en tirely from people g iving falsifying ra th e r th a n verifying e x p la n a tio n s for the choice o f T A . V a n D u y n e ’s re su lts a re best e x p la in ed in term s o f th e d u a l process th eo ry (cf. W aso n a n d E v an s, 1975 a n d C h a p te r 12 o f this book). I t is q u ite re a so n a b le to su p p o se th a t a p ro c e d u re m ig h t affect th e v e rb al ju stific a tio n process, ra th e r th a n th e selection p ro ­ cess. I t is a lso n o t su rp risin g th a t su b je cts ra re ly envisage a falsifying consequence o f selecting T A w hen they believe the ru le alw ay s to be true. I t w ould be m o re in te re stin g if th e tru th s ta tu s o f th e rule affected the a c tu a l selections them selves. P o llard a n d E v an s (1981) d ecided to give th is a stro n g e r test by re p e a tin g V a n D u y n e ’s ex p erim en t w ith som e a d d itio n a l co n d itio n s. S u b jects w ere asked to c o n stru ct sen ten ces th a t were: (1) (2) (3) o r (4)

A lw ays tru e. S om etim es true. S om etim es false. A lw ays false.

T h e cru cial v a ria b le p ro v e d to be tru th s ta tu s (tru e v. false) ra th e r th a n c o n tin g e n cy (som etim es v. a lw ay s). T h e c a rd selection frequencies, pooled o v e r the c o n tin g e n cy v a ria b le , a re show n in

186

Propositional reasoning

T a b le 9.5. A lth o u g h a n te c e d e n t se le c tio n s a re u n a ffe c te d , c o n se ­ q u e n t c h o ices sh o w c o n sid e ra b le logical im p ro v e m e n t for se n te n c e s c o n stru c te d to b e false. T h e in c re a se in F C se lec tio n s w as h ig h ly sig n ific a n t, a lth o u g h th e d ro p in T C se lec tio n s fell j u s t s h o rt o f significance. T A B L E 9.5 Percentage frequency o f card selections in the Pollard and Evans (1980) experiment. C a rd

TA

FA

TC

FC

T R U E SENTENCES FALSE SE N T E N C E S

94 92

46 42

92 79

61 87

V a n D u y n e ’s c o g n itiv e se lf-re in fo rc e m e n t m ig h t be u se d to ex­ p lain th is effect, b u t P o lla rd a n d E v a n s p u t fo rw a rd a n a lte rn a tiv e a sso c ia tio n a l e x p la n a tio n . I f th e su b je c t believes I f p then q to be tru e , th e n he w ill h a v e le a rn e d a p o sitiv e a sso c ia tio n b e tw e e n p a n d q, as in ‘I f it is a c a t th e n it h a s w h isk e rs’. W h e n he believ es a se n ten c e to be false, h e k n o w s t h a t if p is th e case th e n q will not be, so p a n d q a re n e g a tiv e ly a sso c ia te d , a s in T f it is a c a t th e n it c an ta lk ’. T h u s , P o lla rd a n d E v a n s su g g e st t h a t se lec tio n s a re m e d ia te d by s tro n g T A -T C b u t w eak T A -F C a sso c ia tio n s on tru e se n ten c es. O n false se n te n c e s th e T A - T C a sso c ia tio n is w e a k e r a n d th e T A FC a sso c ia tio n s tro n g e r. T h e a sso c ia tio n a l th e o ry h a s th e a d v a n ­ tage o f offering a n e x p la n a tio n o f th e m a tc h in g b ias n o rm a lly o b ­ served in th e a b s tr a c t task . W h e n th e re is n o se m a n tic c o n te x t to b rin g a sso c ia tio n s fro m real-life e x p e rie n c e to b e a r, it m a y b e th a t th e stro n g e st a sso c ia tio n a l b ia s a rises from th e j o in t m e n tio n o f tw o p a r tic u la r c a rd s in th e ru le. T h u s a p-q a sso c ia tio n m ig h t form re g a rd le ss o f th e p re se n c e o f n e g ativ es a n d th e logical s ta tu s o f th ese selections. P o lla rd (1979a) c a rrie d o u t se v e ra l e x p e rim e n ts w h ic h a tte m p t to m a n ip u la te th e n a tu r e o f th e a sso c ia tio n s fo rm ed in th e a b s tra c t se lec tio n task , by p rio r tra in in g . S u b je c ts w ere g iven a k in d o f p ro b a b ility le a rn in g ta sk in w h ic h th e lik elih o o d o f le tte r- n u m b e r c o m b in a tio n s w as v a rie d . F o r e x a m p le , a su b je c t m ig h t le a rn from re p e a te d e x p o su re to a p a c k o f c a rd s th a t a n A u su a lly o r alw ay s has a 2 on th e b a ck . I f he is s u b s e q u e n tly g iv en th e ru le ‘I f th e re is a n A on one sid e o f th e c a rd th e n th e re is a 2 on th e o th e r ’, a n d

The Wason selection task

187

told th a t th e four c ard s h a v e been selected from the p ack th a t he w as tra in e d on, th is can be re g ard e d as a ‘tru e ’ rule. In this w ay it is possible to give people rules w hich a re alw ays o r u su ally tru e o r false, o n th e basis o f th e ir e x p e rim e n ta l experience. T h is p e rm its a stro n g test o f th e a sso c iatio n al th eo ry , since the tru e ru les a re p ro d u ced by tra in in g a T A -T C a sso c iatio n , a n d th e false ones by tra in in g a T A -F C asso ciatio n . W h en affirm ative-only rules w ere tra in e d a n d tested th e results w ere ra th e r u n c le a r, possibly d u e to c o m p e tin g m a tc h in g associ­ atio n s w hich a re th o u g h t to be stro n g on a b s tra c t rules. H ow ever, in one e x p erim e n t P o llard also used ru les w ith negative c o m p o n en ts. W h en m a tc h in g w as b a la n c e d by po o lin g acro ss rules the associ­ a tio n a l p re d ic tio n s w ere c onfirm ed. S u b jects tested on false sen­ tences selected sign ifican tly m o re F C a n d significantly less T C c ard s th a n those tested on tru e sentences. T h e re w as also a ten d e n cy to select less T A a n d m ore FA in th e ‘false’ c o n d itio n , a lth o u g h only the form er w as significant. T h e s e tre n d s o n a n te c e d e n t selection, w hich P o llard claim ed to be co n sisten t w ith th e a sso c iatio n al theory, seem to p re c lu d e a ra tio n a list e x p la n a tio n o f the c o n se q u e n t effect. O n e c a n n o t sim ply e x p la in th e la tte r as in cre ased logical p e rfo rm ­ ance u n d e r falsity - th e a n te c e d e n t selections a re becom ing less logical. C learly on th e selection task , as o n syllogism s, the tru th s ta tu s o f the sentences used affects p e o p le ’s p e rfo rm a n ce . V ery little w ork has so far been c o n d u c te d , b u t a lre a d y a th eo re tic al div id e has a p p e a re d b etw een th e relativ ely ra tio n a list th eo ry o f V a n D u y n e, a n d th e n o n -ra tio n a l le a rn in g th eo ry a p p ro a c h o f P o llard . T h e a s­ sociational th eo ry will be e x am in ed fu rth e r in C h a p te rs 10 a n d 11.

Conclusions It is a rg u a b le th a t re sea rc h b ased on th e W aso n selection task h as been m ore p ro d u c tiv e o f psychologically in te re stin g findings a n d theories th a n w ork w ith a n y o th e r re aso n in g p a ra d ig m . T h e ex­ p e rim en ts hav e show n a n e x tra o rd in a ry c ap a b ility for illogical reaso n in g in in te llig e n t a d u lts. S u b jects hav e been show n to m a in ­ ta in b la ta n t se lf-co n trad itio n s a n d to tre a t sim ple stim u lu s c a rd s as tho u g h th e ir logical significance d e p e n d e d u p o n w hich w ay u p they h a p p e n to be lying. E v id en ce h a s also been p ro d u c e d to suggest

188

Propositional reasoning

th a t th e processes by w hich su b je cts select c a rd s a re q u ite se p a ra te from those w hich u n d e rlie v e rb al e v alu atio n s a n d ju stific atio n s. T h e selection task h as stim u la te d c o n stru ctio n o f rival m odels p o stu latin g sta te s o f in sig h t on th e one h a n d a n d sto c h astic p ro ­ cesses on the o th e r. M o re g e n era lly , it has p ro v id ed scope for th e o ­ ries based on ra tio n a listic a n d n o n -ra tio n a listic prin cip les. T h e task has been the focus o f re ce n t a tte m p ts to look a t th e role o f c o n te n t in reaso n in g , w ith re g a rd to b oth th e m a tic fa cilitatio n a n d tru th sta tu s effects. It h as pro v ed re m a rk a b ly well su ited to th e m a n ip u ­ lation o f e x p erim e n tal v a ria b le s to test a w hole ra n g e o f th eo re tic al ideas a b o u t th in k in g a n d reasoning. T h e secret o f th e success o f the selection task h a s been in w h a t W ason (1969b) term s its stru c tu ra l sim p licity a n d psychological com plexity. T h e p sychological com plexity o f th e processes it evokes is e x tra o rd in a ry , b u t its stru c tu ra l sim p licity facilitates th e design o f e x p erim en ts to in v estig a te th e ir n a tu re , a n d a id s th e c le a r co n ­ stru c tio n o f th eo re tic al e x p la n a tio n s. T h e b ro a d e r ra m ifica tio n s o f th eo retical ideas in sp ired by p e o p le ’s b e h a v io u r on the selection task a re c o n sid era b le . T h e s e will c o n trib u te strongly to th e d isc u s­ sion o f g e n era l th eo re tic al p ersp ectiv es in th e psychology o f re a so n ­ ing, w hich form s the last p a rt o f th is book.

Disjunctive reasoning

D isjunctives h a v e received far less a tte n tio n th a n c o n d itio n als in ex p erim e n tal stu d ies o f reaso n in g . T h e stu d ies th a t hav e been c a r­ ried o u t n e v erth ele ss p ro v id e som e in te re stin g d a ta o f relevance to the th eo re tic al issues w hich h av e a risen in the w ork on con d itio n al inference. O n e a sp e ct re la te s to the in te rp re ta tio n a l c o m p o n e n t o f reasoning. All d isju n ctiv es can be expressed as logically e q u iv a len t cond itio n als. E xclusive d isju n ctiv es tra n s la te as equiv alen ces, an d inclusive d isju n ctiv es as im p lica tio n s. T h u s , Either p or q but not both h as th e sam e tr u th ta b le as I f and only i f not p then q, w h ereas Either p or q or both h a s th e sa m e tru th tab le as I f not p then q, a ssu m in g a tw o-valued logic (see T a b le 10.1). It w as a rg u e d in C h a p te r 8 th a t w here tw o linguistic form s exist to d e n o te th e sam e logical re la tio n sh ip , they p ro b a b ly re la te to different co n tex ts in n a tu ra l lan g u a g e usage. E vidence w as p re ­ sented to su p p o rt th is h y p o th esis in th e case o f ‘I f . . . th en . . .’ and ‘. . . only if. . .’ sentences. W h a t, th e n , m ig h t the d istin c t linguistic usage o f c o n d itio n als a n d d isju n ctiv es be? O n e w'ay o f a p p ro a c h in g this q u e stio n is to e x am in e som e ex am p les o f ‘n a tu ra l’ disju n ctiv es an d c o n d itio n als, a n d th en c o n stru c t th em in th e ir a lte rn a tiv e form . T h is is d o n e in T a b le 10.1. T w o n a tu ra l exam ples o f a n affirm ative d isju n ctiv e a re given w ith e q u iv a len t c o n d itio n al fo rm u la tio n s, a n d vice versa. In th e first tw o cases d isju n ctiv es o f the form Either p or q are rep laced by c o n d itio n als o f th e form I f not p then q. I t a p p e a rs th a t the negative c o n d itio n al is a perfectly re aso n a b le a lte rn a tiv e th a t could be used in n a tu ra l lan g u a g e. A lso, the a d d itio n o f ‘a n d only i f does n o t seem necessary to clarify m ean in g . T h e se m a n tic cues th a t d istin g u ish exclusive from inclusive re ad in g s o f the disju n ctiv e 189

190

Propositional reasoning T A B L E 10.1

Formal equivalence o f disjunctives and conditionals

Either p or q (or both) *— > I f .not p then q Eg. E ith er D or 7 or both I f n o t D then 7 Truth table

D7 D3 G7 H6

D isjunctive

C onditional

T ru th V alue

TT TF FT FF

FT FF TT TF

T T T F

Either p or q (but not both) *— > I f and only i f not p then q E .g. E ith er T or 2 b ut not both I f an d only if not T then 2 Truth table

T2 T6 B2 J7

D isjunctive

C onditional

T ru th V alue

TT TF FT FF

FT FF TT FF

F T T F

seem also to d istin g u ish e q u iv a len c e from im p lica tio n re ad in g s o f the c o n d itio n al. In the last tw o e x am p les, c o n d itio n als o f th e form I f p then q are re p la ce d by d isju n ctiv es o f th e form Either not p or q. In this case th e n e g ativ e d isju n ctiv e does not a p p e a r to be a cc e p ta b le as an a lte rn a tiv e fo rm u la tio n o f th e affirm ativ e c o n d itio n al. W h ilst it is p ossible to in te rp re t a sen ten ce such as ‘E ith e r it is n o t a d og o r it is a n a n im a l’, it h a rd ly strikes on e as a likely s ta te m e n t to occu r in n a tu ra l lan g u a g e. E vans (1972a) claim ed th a t d isju n ctiv es, unlike c o n d itio n als, are rarely fo rm u la ted in n a tu ra l lan g u a g e w ith negative co m p o n e n ts. T h is lead s to a p re d ic tio n o f in te rp re ta tio n a l difficulty w ith such sentences, a h y p o th esis th a t will be b o rn e in m in d in th e follow ing review o f e x p erim e n tal w ork. L et us, how ever, re tu rn to the a c c e p t­ able a lte rn a tiv e s o f affirm ativ e d isju n c tio n /n e g a tiv e c o n d itio n al. A re th ere su b tle c o n te x tu al cues th a t m ig h t d e te rm in e preference o f usage in n a tu ra l lan g u ag e? W e saw in C h a p te r 2 th a t su b je cts

Disjunctive reasoning T A B L E 10.2

191

Natural uses o f conditionals and disjunctives and their logical

equivalents N a tu r a l form

L ogical e q u iv a le n t

Exclusive disjunctive A c a n d id a te fo r electio n to p a rlia m e n t m u s t e ith e r poll m o re th a n 15 p e r c e n t o f th e vote o r lose his d ep o sit.

I f (a n d o n ly if) a c a n d id a te for e lectio n to p a rlia m e n t d o es n ot poll m o re th a n 15 p e r c e n t o f th e v o te th e n he m u st lose his d e p o sit.

Inclusive disjunction S tu d e n ts o n th e M S c p ro g ra m m e m u st e ith e r h o ld a g o od h o n o u rs d eg ree o r a n e q u iv a le n t p ro fessio n al q u a lific a tio n .

I f s tu d e n ts o n th e M S c p ro g ra m m e d o n ot h o ld a good h o n o u rs d eg ree th e n th ey m u st h av e a n e q u iv a le n t p ro fessio n al q u a lific a tio n .

Conditional equivalence I f a p e rso n h a s a Y ch ro m o so m e th e n th a t p erso n is m ale

E ith e r a p erso n d o es n ot h av e a Y ch ro m o so m e o r th a t p erso n is m ale (b u t n o t b o th ).

Conditional implication I f it is a d o g th e n it is a n a n im a l.

E ith e r it is n o t a d o g o r it is an a n im a l.

re g a rd th e c o n d itio n a l a s directional. G iv e n I f p then q th e y te n d to re a so n fro m th e s u p p o s itio n o f p to th e c o n c lu s io n o f q, a n d to re g a rd th e ru le a s ‘ir r e l e v a n t ’ to s itu a tio n s in w h ic h th e a n te c e d e n t c o n d itio n is n o t fu lfilled . I n th e d is ju n c tiv e fo r m u la tio n E ither p or q th e r e m a y b e so m e e x tr a e m p h a s is o n th e ite m m e n tio n e d first, b u t th e ru le a p p e a r s fa r m o re s y m m e tric a l t h a n th e c o n d itio n a l. P e rh a p s , th e n , th e d is ju n c tiv e fo rm u la tio n is p re fe rre d w h e n th e re is n o w ish to e m p h a s is e a d ire c tio n o f in fe re n c e . L o o k in g a g a in a t th e first e x a m p le in T a b l e 10.2. w e m a y feel t h a t th e c o n d itio n a l fo r m u la tio n is a c tu a lly more n a tu r a l h e re , sin c e a te m p o ra l c o n n e c tio n is e n v is a g e d . F ir s t a c a n d id a te fails to poll 15 p e r c e n t a n d then h e loses h is d e p o s it. T h e c o n d itio n a l e q u iv a le n t re fe rrin g to th e e v e n ts in re v e rs e o r d e r w o u ld n o t be a c c e p ta b le . ‘I f a c a n d id a te fo r e le c tio n to p a r lia m e n t d o e s n o t lo se h is d e p o s it th e n h e d o e s n o t p o ll m o re th a n 15 p e r c e n t o f th e v o te ’. T h e d is ju n c tiv e h e re w o u ld a ls o re a d o d d ly if re v e rs e d . P e r h a p s th e ‘E ith e r . . . o r. . fo rm w o u ld b e c h o se n in a s itu a tio n w h e re th e re la tio n b e tw e e n th e e v e n ts r e p re s e n te d b y p a n d q is q u ite s y m m e tric a l.

192

Propositional reasoning

C o n sid e r ‘P eople a re eligible to vote if they are e ith e r re sid en ts o f the city o r ra te -p a v in g b u sin e ssm e n .’ A n e q u iv a len t c o n d itio n al fo rm u latio n w ould be ‘I f p e o p le w ho a re eligible to vo te a re no t resid en ts o f the city th en th ey a re ra te -p a y in g b u sin e ssm e n .’ A lthough this fo rm u la tio n m ig h t be m ea n in g fu l in som e contexts, it seem s a n o d d w ay to define eligibility o f voters. J u s t a s people rarely use ‘I f a n d only i f to d istin g u ish eq u iv alen ce read in g s o f c o n d itio n als in n a tu r a l lan g u a g e, so it is unlikely th a t they will say ‘o r b o th ’ o r ‘b u t n o t b o th ’ to qu alify a d isju n ctiv e, unless th e c o n te x t is u n c le ar. T h u s a d isju n ctiv e Either p or q p re ­ sented in a n a b s tra c t re aso n in g task, w ith o u t c o n te x t, will be a m b ig u o u s in ju s t th e sa m e w ay as th e c o n d itio n al I f p then q is (cf. C h a p te r 8). T h ese p re lim in a ry lin g u istic c o n sid era tio n s lead to several h y ­ potheses a b o u t d isju n ctiv e reaso n in g p e rfo rm a n ce on a rtificial tasks: (1) S u b jects will h a v e difficulty in te rp re tin g negative d isju n ctiv e rules, w ith a c o n se q u e n t in cre ase in logical errors. (2) In feren ces a sso ciated w ith e ith e r c o m p o n e n t o f a d isju n ctiv e will be relatively sy m m etrica l c o m p a red w ith c o n d itio n al inferences. (3) In the ab se n ce o f c o n tex t the sen ten c e from Either p or q will be am b ig u o u s w'ith resp ect to in clu sio n /ex c lu sio n . T h e c o m p a riso n o f d isju n ctiv e w ith c o n d itio n al re aso n in g is also im p o rta n t w ith re sp ec t to the tw o-factor theory o f re aso n in g (E v an s, 1972a; 1977a) w hich h a s been used to in te rp re t th e c o n d itio n al reaso n in g w ork review ed in th e last tw o c h a p te rs. In th e o rig in al fo rm u latio n (E v an s, 1972a), it w as claim ed th a t th e o p e ra tio n a l c o m p o n e n t (n on-logical resp o n se biases) w as in d e p e n d e n t o f the linguistic fo rm u la tio n o f th e rule. T h is w ould seem to p re d ic t th a t effects su c h as n eg ativ e c onclusion bias, a n d m a tc h in g bias, sho u ld be observed on d isju n ctiv es as well as c o n d itio n als; how ever, th ere is a c o m p lica tio n . T h e s e ‘response b ia s e s’ hav e been d e m o n s tra te d on c o n d itio n als by m a n ip u la tin g the p resen ce o f n eg ativ e c o m p o ­ nents. If, as p re d ic te d by h y p o th esis (1) ab o v e, th is m a n ip u la tio n also d isru p ts th e in te rp re ta tio n a l c o m p o n e n t w here d isju n ctiv es are concerned, the effects o f resp o n se b ias will be co n fo u n d ed w ith in te rp re ta tio n a l shifts. B e arin g this p ro b lem in m in d , we will now look a t the e x p erim e n tal w ork.

Disjunctive reasoning

193

D is ju n c tiv e in fe r e n c e T h e q u e stio n o f in te rp re ta tio n a l difficulties o f the single n egative disju n ctiv e - Either p or not q o r Either not p or q - w as co n sid ered by E vans (1972d; see also W aso n , 1977a). In one o f the e x p erim e n ts o f E vans (1972d) p rem ises o f this form w ere in clu d e d as p a rt o f a test o f reductio ad absurdum reasoning. T h e su b jects re p o rte d g re at difficulty in m ak in g sense o f such sentences. S im ila r o b se rv atio n s w ere m a d e by th e su b je cts o f Jo h n s o n -L a ird a n d T rid g e ll (1972), w hose su b je cts h a d p ro b lem s o f th e form : (1) (2)

Either p or else q, not q, therefore? Either p or else not q, q, therefore?

In e ith e r case the conclusion p is valid. S u b jects m ake it signifi­ can tly m o re often w'hen th e p ro b le m is e xpressed in form (1). J o h n s o n -L a ird a n d T rid g e ll suggest th a t this is d u e to th e fact th a t a c o n tra d ic tio n o f a n affirm ativ e by a negative is e asie r to perceive th a n vice versa. E v an s (1972a) a rg u e d th a t it could a lte rn a tiv e ly be d u e to th e in te rp re ta tio n a l difficulty o f th e negative d isju n ctiv e used in the second form . T h is is s u b s ta n tia te d by th e o b se rv atio n th a t the c o n tra d ic tio n effect is n o t o b serv ed in stu d ies o f c o n d itio n al inference, for e x am p le on the m o d u s tollens inference. T h ese so rts o f d istin c tio n can only be so rte d o u t by e x am in atio n o f a full ra n g e o f inferences on ru les w ith sy ste m atic p e rm u ta tio n o f negatives. T h e possible inferences, e q u iv a le n t to M P , D A , A C , M T on the c o n d itio n al, a re show n in T a b le 10.3. T h e re a re tw o types o f inference; T -F in w hich th e tr u th o f one c o m p o n e n t im plies the falsity o f th e o th er, a n d F -T in w h ich th e falsity o f one c o m p o n e n t im plies the tr u th o f th e o th e r. T h e d irec tio n o f inference is d is tin ­ guished in th e tab le , e.g. T 1 -F 2 d e n o te s a n inference from th e tru th o f the first c o m p o n e n t to th e falsity o f th e second. N ow , regardless o f d irec tio n , F -T inferences a re v alid for all disju n ctiv es, b u t T -F inferences a re v alid only if exclusive d isju n ctio n is a ssu m ed . S u b je cts’ ten d e n cie s to m ake th ese inferences w ith a b s tra c t m a ­ terials h a s been in v estig a te d in a series o f e x p erim e n ts by R oberge (1974; 1976a; 1976b; 1978). W e can assess the evidence for the h ypotheses p re se n te d in the in tro d u c tio n to this c h a p te r w ith respect to his d a ta . F irst o f all, we c o n sid er th e effect o f n eg ativ e rule c o m p o n en ts on p e rfo rm a n ce . R o b e rg e ’s d a ta a re show n in T a b le

194

Propositional reasoning

T A B L E 10.3

Possible inferences from disjunctive rules In fe re n c e

T1 -F 2 * R u le E ith e r E ith e r E ith e r E ith e r

p or q p o r not q not p or q not p or not q

F 1 -T 2

T 2 -F I *

F2-T1

G iv en

C o n c lu d e G iv e n

C o n c lu d e G iv e n

C o n c lu d e G iv e n i C o n c lu d e

P P

not q

q not q

not p not p

not p not p

q

not q

q

not q

q

not p not p

not q

q

P

not q

q

not q

p

P P

q not q

q

P P not p not p

* V a lid o n ly i f e x c lu siv e d is ju n c tio n is a s s u m e d .

10.4. a cc o rd in g to w h e th e r su b jects a re in stru c te d to a d o p t exclusive or inclusive in te rp re ta tio n o f th e rules. I t is cle ar th a t in e ith e r case the affirm ative ru le is easiest. H ow ever, th e inclusive a n d exclusive p roblem s reveal different p a tte rn s . O n exclusive p ro b lem s the d o u b le-n e g ativ e rule, Either not p or q, is easier th a n th e rules w hich have ju s t one n eg ativ e c o m p o n e n t. O n inclusive p ro b lem s the dif­ ficulty o f th e d o u b le-n e g ativ e rules is sim ila r to th a t o f single­ negative rules. T A B L E 10.4 Percentage errors on different disjunctive rules on the Roberge studies Rule

E ith er E ith er E ith er E ith er Key

p or q p o r n ot q p or not q not p or not q

Exclusive

Inclusive

2 16 50 63 24

1 39 56 59 51

3 4 13 7 56 63 55 52 31 36

2 31 48 57 51

4 16 49 53 59

1 Roberge (1974) 2 Roberge (1976a) 3 Roberge (1976b) 4 Roberge (1978)

T h e sim p le st in te rp re ta tio n o f th ese re su lts is as follows: (1) a disju n ctiv e w ith o n e negative is lin g u istically u n n a tu ra l, a n d c o n ­ seq u en tly leads to in te rp re ta tio n a l confusion a n d h igh e rro r rates, a n d (ii) the d o u b le-n e g ativ e d isju n ctiv e ten d s to be c o n v erted into an affirm ative form . T h a t is, th e su b je ct given Either not p or not q dro p s the negativ es, a n d tre a ts it as th o u g h it w ere Either p or q. T h e ev idence for c onversion o f a d o u b le negative lies in its dif­ ferential difficulty w ith inclusive a n d exclusive d isju n ctiv e in stru c ­ tions. U n d e r exclusive d isju n c tio n th e d o u b le negative is logically equivalent to th e affirm ativ e. I f th e ru le is exclusive, all the inferences

Disjunctive reasoning

195

show n in T a b le 10.3 a re valid. I t will be seen th a t an y inference m ad e on th e affirm ative rule m u st also be m ad e o n the d o u b le ­ negative ru le (e.g. G iven p, C o n c lu d e not q). I f in stru ctio n s a re given to in te rp re t th e rules inclusively, how ever, d ro p p in g th e negatives w ould lead th e su b je ct in to e rro r. H e n ce, the su b je ct c an avoid the difficulty o f the d o u b le negative by conversion, b u t only w ith exclu­ sive in stru ctio n s. T h e re is no easy m ea n s o f a v o id in g th e difficulty of single negativ es, in e ith e r condition. R o b erg e’s re su lts a re c o n sisten t w ith o n e o f th e h y p o th eses co n ­ cerning th e in te rp re ta tio n a l c o m p o n e n t o f d isju n ctiv e reaso n in g . A second h y p o th esis w as o f sy m m etry . T h e frequency o f T -F o r F -T inferences sho u ld n o t be affected by th e d irec tio n o f inference be­ tw een first a n d second co m p o n e n ts. R oberge (1976b) p rovides som e relev an t d a ta for exclusive d isju n ctio n p ro b lem s, on w hich b o th T -F a n d F -T inferences a re valid. T h e d irec tio n o f re aso n in g did, in fact, in te ra c t significantly w ith type o f inference m ad e . O v e r all rules the p e rc e n ta g e o f e rro rs w as: T 1 -F 2 38 p e r cent; T 2 -F 1 , 44 per cent; F 1 -T 2 , 36 p e r cent; F 2 -T 1 , 40 p e r cent. T h u s it seem s th a t th ere is som e a d v a n ta g e in re aso n in g fo rw ards - from first to second com p o n en t - p a rtic u la rly on T -F inferences. T h e difference is q u ite sm all, how ever, c o m p a re d w ith the M P /M T difference o n c o n d i­ tionals. T h e th ird in te rp re ta tio n a l h y p o th esis - a m b ig u ity o f in clu ­ sive/exclusive in te rp re ta tio n - c a n n o t be assessed in R o b e rg e ’s studies, since in te rp re ta tio n w as in stru c te d . L et us now c o n sid er th e ev idence for resp o n se -b ia s effects in these tasks. R ecall th a t on th e e q u iv a len t c o n d itio n a l-re a so n in g tasks there is evidence for a b ias to e n d o rse inferences w ith n egative conclusions (see C h a p te r 8). In sp e c tio n o f T a b le 10.3 reveals th a t each logical inference is a sso c iated so m etim es w ith a n affirm ative a n d som etim es w ith a n eg ativ e conclusion. R oberge (1976b; 1978) has looked a t the evidence for negativ e-co n clu sio n bias. T h e an aly sis show n by R o b erg e (1976b) is p o te n tia lly confusing since he p re ­ sented th e su b je cts w ith th e opposite o f c o rre c t conclusions on h a lf the p ro b lem s - to w hich a co rre c t a n sw e r is a d en ial. H ow ever, if we look a t p ro b lem s w here the su b je c t is asked to e v a lu a te the a ctu al c onclusion o f th e a rg u m e n t, w h ich is sim ila r to E v a n s’s (1977a) m eth o d on c o n d itio n als, th en th ere is a ten d e n cy to m ake m ore c o rre c t T -F inferences w hen th e conclusion th a t m u st be e ndorsed is n eg ativ e (69 p e r cen t) ra th e r th a n affirm ativ e (49 p e r cent), b u t no effect o n F -T inferences. R o b erg e (1978) a rg u e s th a t

196

Propositional reasoning

the claim by E v an s (1977a) th a t th ere exists a b ias to n egative conclusions does n o t g en era lise to d isju n ctiv es, a lth o u g h he does find evidence for it on c o n d itio n als ( ' I f - th e n ’ a n d ‘only i f ) . H o w ­ ever, in th is e x p erim e n t he looked only a t F -T inferences o n the disjunctives. W h en the d isju n ctiv e d a ta a re tak en in to a cc o u n t the evid en ce o f a gen eral n eg ativ e-co n clu sio n bias is n o t very su b s ta n tia l. W h a t is clear is the ten d e n cy to m ak e m o re inferences w hich d e n y affirm ­ ative ra th e r th a n negative co m p o n e n ts. C o n sid e r th e follow ing v alid inferences: M T conditional I f the le tte r is n o t A th en th e n u m b e r is7 th e n u m b e r is n o t 7 th e le tte r is A T -F disjunctive (1) E ith e r th e le tte r is n o t A o r th e n u m b e r is 7 (2) th e n u m b e r is 7 T herefore, th e le tte r is A (1) (2) T herefore,

E ach o f th ese h as been found e m p irically h a rd for su b je cts, w ho tend to say th a t th e conclusion does no t follow. T h is could well arise from a d o u b le negative (cf. C h a p te r 8). In o rd e r to re a c h the affirm ative c onclusio n ‘T h e le tte r is A ’ th e su b je ct m u st first infer th a t ‘n o t A ’ c a n n o t be th e case. T h is ‘o p e ra tio n a l’ difficulty could a cco u n t for the p referen ce for n e g ativ e con clu sio n s o n inferences involving d e n ia l. T h e a sse rtio n th a t n eg ativ e c onclusions a re p re ­ ferred on all inferences (E v an s, 1977a) w as b ased o n th e a n aly sis o f AC inference ra te . T h a t finding could, p e rh a p s, be ex p la in ed as in in te rp re ta tio n a l effect, if su b je cts a re m o re in clin ed to tre a t a c o n ­ ditio n al as a n e q u iv a len c e if it h a s a n eg ativ e a n te c e d e n t. T h is hyp o th esis receives som e su p p o rt from c o n sid e ra tio n o f tru th -ta b le d a ta as well (see C h a p te r 8). T h e e x a m in a tio n o f d isju n ctiv e in ference stu d ies seem s, th en , to refine the an aly sis o f resp o n se -b ia s ten d en cies o n th e c o n d itio n al task. H ow 'ever, tw o c a u tio n a ry notes m u st be so u n d e d : (i) P o llard (1979a) h a s p ro v id ed extensive a n aly sis to su p p o rt a n d e x te n d the original c onclusion biases claim ed o n c o n d itio n als; a n d (ii) it seem s th a t the in tro d u c tio n o f n eg ativ es in to th e d isju n ctiv e d isru p ts the in te rp re ta tio n a l c o m p o n e n t o f p e rfo rm a n ce , in a d d itio n to a n y effect

Disjunctive reasoning

197

th a t it m ay hav e on resp o n se biases. F u rth e r c o n sid era tio n a b o u t the n a tu re o f d isju n ctiv e inference sh o u ld aw ait the in sp e ctio n o f d a ta from o th e r reaso n in g p a rad ig m s.

Disjunctive selection task and truth-table task V a n D u y n e (1973; 1974) h a s c riticised th e e x p la n atio n o f aspects o f con d itio n al re aso n in g p e rfo rm a n ce in term s o f ‘m a tc h in g b ia s’, on the g ro u n d th a t th is bias does n o t g en eralise to d isju n ctiv e reasoning p ro b lem s. T h e evidence for his claim is a low frequency of p,q c ard selections w hen the W aso n selection task is a d m in istere d w ith a rule o f th e form Either not p or q (V a n D u y n e, 1974). H ow ever, m a tc h in g b ias h a s alw ays been d e m o n s tra te d as a sta tistica l te n d ­ ency w h en logical factors a re held c o n sta n t. O n e needs to co m p a re rules in w hich th e p re sen c e o f n eg ativ e c o m p o n e n ts is v aried. T h e only se lec tio n -task e x p erim e n t th a t p rovides a n y re le v an t d a ta is th a t o f W aso n a n d Jo h n s o n -L a ird (1969). T h e y a d m in istere d the task w ith a n affirm ative ru le Either p or q a n d a n e g ativ e ru le Either not p or q, using a p p ro p ria te a b s tra c t m ate ria l; e.g. ‘E very c ard e ith e r h a s a n u m b e r w hich is (isn ’t) R o m an on one side, o r it has a le tte r w hich is c a p ita l on the o th e r sid e .’ T h e p ro c ed u re c o n tain ed som e u n u su a l fe atu res, su c h as a re stric tio n on th e n u m ­ b er o f c a rd s th a t could be selected, a n d a set to believe th a t th e rule w as tru e o r false. S u b jects w ere n o t specifically told to in te rp re t the rule inclusively, a lth o u g h asp e cts o f th e p ro c e d u re im p lied this. T h e a u th o rs assu m e a n inclusive d e finition for p u rp o ses o f d ecid in g ‘c o rre c t’ responses. L in d er such a d e finition the su b je ct should choose c a rd s w hich fa lsify each c o m p o n e n t (since F -T is the only valid type o f inference). T h u s on th e affirm ative rule su b je cts should choose p a n d q, a n d on th e negative ru le p a n d q. If, as on the co n d itio n al selection task , th ere w as a bias to select p an d q (th e m a tc h in g v a lu e s), o n e m ig h t expect th e n eg ativ e rule to be easier. In fact only 52 p e r cen t chose co rrectly on this rule as co m p ared w ith 75 p e r cen t on the affirm ative. W h ilst th is result a p p e a rs to pro v id e evidence a g a in st m a tc h in g bias, we m u st b e a r in m in d the co n fo u n d in g o f in te rp re ta tio n a l effects. A s n o ted e arlie r, the in tro d u c tio n o f a single negative a p p e a rs to confuse, a n d w as associated w ith c o n sid era b ly m ore logical e rro rs in th e R oberge inference tasks.

198

Propositional reasoning

M a tc h in g bias has been d e m o n s tra te d n o t only o n the c o n d itio n al selection task, b u t also on c o n d itio n al tru th -ta b le tasks. T h e first experim ent in w hich it w as observ ed (E v an s, 1972b) w as a tru th tab le c o n stru ctio n task w hich w as d e sc rib e d in C h a p te r 8. S ubjects w ere asked to c o n stru c t e x h au stiv e ex am p les o f verifying a n d falsi­ fying cases, so th a t u n c o n stru c te d cases could be in ferred to be ‘irre le v a n t’. Such n o n -c o n stru ctio n s w ere strongly asso ciated w ith m ism atch es betw een th e item s in th e in stan c e a n d those in th e rule. E vans a n d N ew stead (1980, E x p e rim e n t I) re p ea te d this e x p erim e n t w ith d isju n ctiv es in p lace o f c o n d itio n als, a n d all four p e rm u ta tio n s o f a ffirm ativ e/n e g ativ e co m p o n e n ts. (S ubjects w ere n o t in stru c te d on the in te rp re ta tio n o f e x c lu sio n /in c lu sio n .) T h e only o th e r c h an g e w as in th e m a te ria ls w hich involved le tte r-n u m b e r c o m b in a tio n s. It w as th o u g h t th a t a n e x a m in a tio n o f in itial c o n stru ctio n s w ould give a p a rtic u la rly pow erful test o f th e p resen ce o f m a tc h in g b ias in d isjunctive reaso n in g . C o n sid e r the follow ing rule:

E ith e r the le tte r is a D, o r th e n u m b e r is n o t a 6.

T h e su b je ct asked to c o n stru c t verifying exam ples o f th is rule should in clu d e a T F a n d a n F T case, reg ard less o f w h e th e r he in te rp re ts it inclusively o r exclusively. T F is p ro d u c ed by m a tc h in g both co m p o n e n ts, D 6, w h ereas F T re q u ire s a d o u b le m ism a tc h , e.g. L3. T h u s one w ould expect th a t even if th e su b je ct w ere to c o n stru c t both, he w ould tend to th in k o f th e m a tc h in g case first. N o such tendency w as observ ed . A c u rio u s fe atu re o f this e x p erim e n t w as a large p ro p o rtio n o f c o n tra d ic to ry resp o n ses, th a t is c o n stru c tin g the sam e logical case o n both verifying a n d falsifying task. N o t a single case o f such c o n tra d ic tio n w as o b serv ed in th e e q u iv a le n t c o n d i­ tional reaso n in g e x p e rim e n t, a lth o u g h se lf-co n trad ic tio n s a re not u n u su a l in o th e r e x p erim e n ts (see W aso n , 1977). T h e su b je c ts’ protocols suggested th e c au se o f c o n tra d ic tio n on the d isju n ctiv e task. T h e y w ould often claim th a t th e ru le w as tru e p ro v id ed th a t a t least one c o m p o n e n t w as tru e on th e verifying task - w hich is fair e n ough if you a ssu m e inclusive d isju n ctio n . Som e w ould also claim on th e falsifying task th a t th e ru le w as false if a t least one co m p o n en t w as false. T h is g e n era lisa tio n is only a c c u ra te if you take the rule to be a conjunctive (p and q). C o n se q u e n tly , th e cases

Disjunctive reasoning

199

T F an d F T w ere classified as b o th verifying a n d falsifying th e rule by som e subjects. W hile the a b sen ce o f m a tc h in g bias re q u ire s e x p la n atio n , we will first look a t th e E v an s a n d N e w ste ad d a ta in term s o f th e in te rp re t­ atio n al h y p o th eses a b o u t d isju n ctiv e reaso n in g . T h is is a id e d by a second e x p erim e n t in w h ich a tru th -ta b le e v alu atio n task w as used w ith a forced choice b etw een ‘tru e ’ a n d ‘false’. T h is p ro c e d u re w as felt to be ju stifie d since th e ‘irre le v a n t’ responses o f th e first ex p eri­ m ent w ere relatively in fre q u e n t a n d evenly d istrib u te d across logical cases. T h e re is no ‘d efective’ tru th tab le for d isju n ctiv es, unlike conditio n als, a n d a tw o-valued logic seem s a p p ro p ria te . A n a d v a n ­ tage o f this p ro c e d u re w as th a t it fa cilitate d th e collection o f re ­ sponse laten cies, w h ich w ere d iv id e d in to c o m p re h en sio n tim e (C T ) and verification tim e (V T ) by a sim ila r p ro c e d u re to th a t used by E vans a n d N e w ste ad (1977). Som e o f th e E v an s a n d N e w s te a d ’s (1980) d a ta is su m m a rise d in T a b le 10.5. T A B L E 10.5

Results from the study o f Evans and Newstead (1980)

E xperim ent I

M ean latency (E xperim ent II) (seconds) E xperim ent II C T VT

69 46 36 49

89 77 73 77

% correct* R ule E ith er E ith er E ith er E ith er

p or q p o r not q not p o r q not p o r not q

3.88 4.35 4.55 4.59

4.18 6.23 6.17 6.06

* E x c lu d in g th e T T case.

Since su b je cts w ere n o t in stru c te d on how to in te rp re t the rule, the a m b ig u o u s T T case w as excluded from th e an aly sis o f p e rc e n t­ age correct. C lassificatio n s o f th is case w ere tak e n as a n in d ic a tio n o f w h e th e r su b je cts p re fe rre d a n inclusive o r exclusive read in g . In b oth e x p erim e n ts a significant m ajo rity o f tru e o ver false classifi­ cations w as o b serv ed , sugg estin g a preference for a n inclusive re a d ­ ing. T h is acc o rd s w ith th e re su lts o f P aris (1973) b u t n o t those o f M an k telo w (1980), w ho fo u n d th e reverse preference. In e ac h stu d y the ru le clearly is a m b ig u o u s w ith c o n sid era b le s u p p o rt for b o th readings. T h e d a ta p re se n te d in T a b le 10.5 s u p p o rt th e c onclusions follow­ ing the e x a m in a tio n o f R o b e rg e ’s d isju n ctiv e inference stu d ies (T a ­

200

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ble 10.4). N eg ativ es cause p a rtic u la r difficulty, especially w hen one negative only is p resen t. T h e presence o f a negative in e ith e r com ­ po n en t in te ra c ts significantly in the a n aly sis o f v a ria n ce o f b oth frequency co rrect a n d resp o n se latency. T h is la tte r re su lt c o n tra sts w ith the a d d itiv e effect o f negatives o n a c o n d itio n al tru th -ta b le task (E v an s a n d N e w ste ad , 1977). E v an s a n d N e w ste a d ’s (1980) analyses also suggest th a t su b je cts m ay be co n v ertin g the d o u b le ­ negative ru le in to a n affirm ativ e form , w hich could a c c o u n t for its lack o f in cre asin g difficulty on b oth freq u en cy a n d laten cy m easures. T h e re is th u s a n e n co u ra g in g convergence betw een th e c onclusions o f the inference a n d tr u th ta b le stu d ies. T h is co nvergence in itself suggests th a t the effect o f n egatives is p rim a rily in te rp re ta tio n a l. W h a t, how ever, has h a p p e n e d to m a tc h in g bias? T h e bias a p p ea rs n o t to be in d e p e n d e n t o f lin g u istic stru c tu re , as proposed by E vans (1972a). D oes this p u t the w hole tw o-factor theory in je o p a rd y ? I th in k n o t. E v an s a n d N e w ste ad p o in t to tw o facts: (1) su b je cts’ e rro rs on th e negative rules a re co n sisten t w ith a tendency to ignore th e p resen ce o f n eg ativ es on all rules, a t least in E x p e ri­ m en t I. T h e y ten d to re sp o n d as i f all rules w ere affirm ative, w hich leads to m o re e rro r o n the sin g le-n eg ativ e rules th a n on th e d o u b le negative. (2) S u b je c ts’ p e rfo rm a n ce on all rules is well above c h an c e ra te w hich, for ex am p le, is 50 p e r c e n t in th e forced-choice task o f E x p erim en t I I. Ig n o rin g negatives is clearly n on-logical, b u t th e second o b se r­ vatio n e q u ally clearly reveals a logical c o m p o n e n t. M a tc h in g bias can also be re g a rd e d as a ten d e n cy to ignore negativ es, if we can explain w hy the bias to p a n d q sho u ld be th ere on the affirm atives. E vans a n d N e w ste ad a c c o u n t for the a p p a re n t linguistic d e p en d e n ce o f th e m a tc h in g effect in term s o f the a sso c iatio n al theory p u t forw ard by P o llard a n d E v an s (1981b, cf. C h a p te r 9). T h e c o n d i­ tional form I f p then q, from its ev ery d ay use, in d u ce s a set to expect a positive a sso ciatio n o f p a n d q. T h is in d u ces a n on-logical b ias to focus o n these values o n a b s tra c t c o n d itio n al-rea so n in g tasks. T h e d isjunctive Either p or q, how ever, in d u ce s a set for negative associ­ ation. ‘E ith e r /o r ’ lead s to a n e x p ec ta tio n o f p w ith o u t q o r vice versa. E v an s a n d N e w ste ad find a c le a r bias to choose pq o r pq as verifying cases w hen d a ta from all ru les teste d in th e ir first e x p eri­ m ent a re c o m b in e d . T h e y su m m arise th e a rg u m e n t as follows: O n b o th c o n d itio n als a n d d isju n ctiv es, su b je cts succeed

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p a rtially in tak in g a cc o u n t o f th e negatives a n d a rriv in g a t the correct an sw ers. T o th e e x te n t th a t th ey fail they resp o n d not ra n d o m ly , b u t sy ste m atica lly w ith a sso c iatio n al biases. T h e se are positive in the case o f c o n d itio n als b u t n egative in the case o f d isjunctives. T h e e x a m in a tio n o f d isju n ctiv e re aso n in g o n b o th inference a n d tru th -ta b le tasks h as, th en , su p p o rte d the tw o-factor theory, in th a t it a p p e a rs necessary to p o stu la te b o th a n in te rp re ta tio n a l (logical) com ponent a n d non-logical factors to e x p la in p erfo rm an ce. In each case, som e d isc rep a n cie s w ith b e h a v io u r on e q u iv a le n t c o n d itio n al reaso n in g tasks h as led to re-an aly sis o f the n a tu re o f the proposed response m ec h an ism s, a n d facilitated e x p la n a tio n o f th e ir origin.

Thematic disjunctives A re c u rrin g th em e o f in te re st in th is book h a s been the effect o f task content on re aso n in g p erfo rm an ce. W e hav e seen th a t th e m a tic co n te n t m ay fa cilitate p erfo rm an ce, b u t m ay also in d u ce non-logical biases, p a rtic u la rly w here beliefs a n d a ttitu d e s a re co n cern ed . N a tu ­ rally, we sh o u ld see w h a t evidence p e rtin e n t to this h as a risen in the study o f d isju n ctiv e reasoning. U n fo rtu n a te ly , th ere a re few such stu d ies a v ailab le. T w o stu d ies p e rm it th e a ssessm en t o f possible facilitatio n effects. V an D u y n e (1974) c o m p a re d selection-task p e rfo rm a n ce w ith a b stra c t rules such as: A c ard d o e sn ’t h a v e a P on o n e side, or it h a s a 2 on th e o th e r side. w ith c o n cre te ru les su c h as: A s tu d e n t d o e sn ’t stu d y F ren ch , o r he is a t L on d o n . T h e re w as no ev idence o f fa cilitatio n , w ith 5 /2 4 solving the a b stra c t form a n d 4 /2 4 solving th e th e m a tic form . R oberge (1978), testing T - F a n d F -T inferences, looked a t a b s tra c t a n d th e m a tic d isjunctives w ith all c o m b in a tio n s o f negatives, a n d w ith exclusive

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a n d inclusive fo rm u la tio n s. A n e x am p le o f a n affirm ativ e inclusive th em a tic ru le is: E ith e r J o a n is a th le tic o r she is rich (or b o th ). A b stra ct rules referred to le tte rs a n d n u m b e rs. H is resu lts c o n ­ tra d ic t V a n D u y n e ’s in th a t fa cilitatio n d id o c cu r on single-negative rules, a lth o u g h n o t on affirm ativ e o r d o u b le-n e g ativ e rules. T h is finding a ctu ally s u p p o rts the view th a t th e h igh e rro r ra te s n o rm ally observed on single n e g ativ e d isju n ctiv es a re d u e to special in te rp re t­ atio n al difficulty. P re su m a b ly , wrhen th e m a tic c o n te n t facilitates, it does so by a id in g th e o p e ra tio n o f th e in te rp re ta tio n a l c o m p o n e n t. In view o f th e stu d ies review ed in th e la st c h a p te r, how ever, it is ra th e r su rp risin g th a t R oberge found a n y facilitation a t all. H is ‘th e m a tic ’ ru les a re q u ite a rb itra ry a n d p lac ed in no se m a n tic context. R oberge (1977) h a s also looked a t belief-bias effects w ith th e m a tic disjunctives. H e tested T -F a n d F -T inferences on affirm ativ e in clu ­ sive rules, a n d w ith th ree types o f c o n te n t. T w o o f these, a b s tra c t a n d c o m p a tib le th e m a tic , w ere as used in th e 1978 stu d y . T h e th ird in co m p a tib le th em a tics p ro v id ed d isju n ctio n s betw een ite m s th a t w ere o p p o site in m ea n in g e.g. E ith e r J o h n is in te llig e n t o r h e is stu p id (or b o th ). R oberge found th a t a b s tra c t a n d c o m p a tib le m a te ria ls p ro d u c ed sim ila r p e rfo rm a n ce , a b o u t 80 p e r c e n t c o rre c t on b o th inferences. H ow ever, th e in c o m p a tib le g ro u p show ed m ark e d differences. O n the v alid F -T inference p e rfo rm a n ce rose to a b o u t 90 p e r c e n t b u t on the fallacious T -F inference it d ro p p e d to a b o u t 40 p e r cent. Since the T - F inference w ould be v alid if th e ru le w ere a n exclusive d isju n ctio n , the re su lts a re q u ite easy to e x p la in . T h e in c o m p a ti­ bility o f the term s ev id en tly im p o sed a semantic exclusiveness, w hich overrode the sy n ta c tic m odifier ‘o r b o th ’. A n o th e r a sp e ct o f th e m a tic m a te ria ls considered previously (see C h a p te r 8) re la te s to the influence o f c o n te x t u p o n sen ten c e in ­ te rp re ta tio n . S p rin g sto n a n d C la rk (1973) claim ed th a t th e d isju n c ­

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tive Either p or q ten d s to be in te rp re te d exclusively w hen used as a pseudoimperative as in th e follow ing: Flip th e sw itch o r the fan goes on. T h ey tested th is by p re sen tin g su b je cts w ith T -F a n d F -T infer­ ences, a n d claim ed ev idence for the h y p o th esis since all ten d e d to be end o rsed . U n fo rtu n a te ly , th is conclusion is u n w a rra n te d d u e to p o o r m ethodology. F o r e x am p le, a T - F inference m ig h t be tested by p re sen tin g the in fo rm a tio n th a t the sw itch is flipped a n d asking if the fan h as gone on. T h e c o rre c t a n sw e r is ‘c a n ’t sa y ’ b u t subjects w ere not given this a lte rn a tiv e - they h a d to m ake a forced choice Yes or N o. F a c ed w ith such a choice the sub ject has no o p tio n b u t to in te rp re t th e ru le exclusively so th a t he can m ak e a d e te rm in a te (No) response. A c o m p a ra b le m etho d o lo g ical e rro r h a s been d is­ cussed in C h a p te r 8, in T a p lin ’s co n d itio n al re aso n in g studies. S pringston a n d C lark also fail to c o m p a re th e use o f d isju n ctiv es as p seu d o im p e rativ es w ith th e ir use in o th e r contexts. T h e few av ailab le stu d ies o f th e m a tic d isju n ctiv es discu ssed above provide ev idence re aso n a b ly c o m p a tib le w ith th a t from the m ore tho ro u g h ly in v estig a te d syllogistic a n d c o n d itio n al re aso n in g tasks. O n e recen t stu d y , how ever, has p ro d u c ed m ost u n ex p ec te d results. M anktelow ' (1980) u sin g a tru th -ta b le e v alu atio n task, c o m p a red a b stra c t a n d th e m a tic disju n ctiv es, in clu d in g rules w ith negative com ponents. E x am p les o f his rules w'ere: Abstract E ith e r th ere is a T on one side o r a 3 on the o th er. Thematic E ith e r I e at chicken o r I d rin k b ra n d y . T h e in stan c es w ere w ritte n on c ard s for th e su b je ct to ev alu ate. H ence a T F case w ould be T 7 o r chicken, w ine. W ith a b stra c t d isjunctives, M a n k telo w found a p a tte rn o f resu lts sim ila r to those o f E vans a n d N ew stead (1980), except th a t su b jects ten d e d to w ard s an exclusive in te rp re ta tio n . W ith th em a tics the p a tte rn s ch an g ed entirely. S u b jects show'ed a m assive ten d en cy to classify all d o u b le m ism atch es p q as irre le v a n t, reg ard less o f th e p resen ce o f neg a­

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tives. In to ta l c o n tra s t to a b s tra c t d isju n ctiv es, th e th e m a tic s a p p e a r to have in d u ce d a stro n g m a tc h in g b ias, a lth o u g h M a n k telo w offers an in te rp re ta tio n a l e x p la n a tio n . M a n k te lo w also looked a t ‘if . . . th e n ’, a n d ‘ . . . only i f . . .’ c o n d itio n als. In e ac h case th e e x te n t o f m atc h in g bias, o bserved in the a b s tra c t form , significantly in creased w ith the food a n d d rin k s m ate ria l. T h ese findings a re som e o f the m o st d ra m a tic re p o rte d o n the effect o f c o n te n t on re aso n in g . O n e is tem p te d to sp e c u la te th a t ‘m atc h in g b ia s’ has a p e rc e p tu a l ba sis a n d is facilitated by th e use o f ‘im a g e ab le ’ c o n cre te c o n te n t. H ow ever, th ere m ay be so m e th in g p e cu liar a b o u t th e food a n d d rin k c o n te x t. It will be recalled from the last c h a p te r th a t th is p a rtic u la r c o n te n t p ro d u c ed a n u n re p re ­ sen tativ e lack o f fa cilitatio n o n th e W aso n selection task (M a n k telo w a n d E v an s, 1979). I t m ay be th a t su b je cts b rin g p a rtic u la r p re su p ­ positions a b o u t m eals to b e a r in this task. R e p lic atio n o f M a n k telow ’s re su lts w ith a v a rie ty o f o th e r th e m a tic c o n te n t is necessarybefore too m u c h im p o rta n c e is a tta c h e d to these results.

The THOG problem Before co n clu d in g th is survey o f d isju n ctiv e inference, we will look at som e w ork on a p ro b lem re ce n tly devised by W aso n , w hich involves th e logic o f exclusive d isju n c tio n (W’a so n , 1977a; 1978; W ason a n d B rooks, 1979). L ike th e selection task , ‘T H O G ’ is a m etainference task , th a t re q u ire s th e fo rm u la tio n a n d te stin g o f h ypotheses, in a d d itio n to a n a b ility to u n d e rs ta n d logical re la tio n ­ ships. T h e su b je ct is show n four d esigns: a blue d ia m o n d , a red d iam o n d , a blu e circle, a n d a red circle (see F ig u re 10.1). T h e in stru c tio n s used by W aso n a n d B rooks a re as follows: In front o f you a re four designs: B lue D ia m o n d , R ed D ia m o n d , Blue C ircle a n d R ed C ircle. Y ou a re to a ssu m e th a t I h a v e w ritte n d o w n o n e o f th e colours (blue o r red ) a n d one o f the sh a p e s (d ia m o n d o r circle). N ow re ad th e follow ing ru le carefully: If, a n d only if, a n y o f th e designs in clu d e s e ith e r th e c o lo u r I have w ritte n d o w n , o r th e sh a p e I h a v e w ritte n do w n , b u t n o t b o th , th e n it is called a T H O G . I will tell you th a t th e B lue D ia m o n d is a T H O G .

Disjunctive reasoning

F IG U R E 10.1

205

T h e four coloured shapes used in the T H O G problem

E ach o f th e designs can now be classified in to one o f the follow ing categories: A) D efinitely is a T H O G . B) In su fficien t in fo rm a tio n to decide. C ) D efinitely is no t a T H O G . T h e co rre c t a n sw e r is th a t red d ia m o n d a n d the b lu e circle c an n o t be T H O G S , a n d th e red circle m u st be a T H O G . A s on th e selection task (i) th e co rre c t so lu tio n is in freq u e n tly found w hen stu d e n t p o p u latio n s a re tested a n d (ii) th ere is a c h a ra c te ris tic ‘in tu itiv e e rro r’ w hich m an y su b je cts offer in stea d . In o rd e r to find th e c o rre c t so lu tio n , on e m u st first o f all g e n era te the possible ru les as h y p o th eses. Since th e b lu e d ia m o n d is a T H O G the e x p e rim e n te r m u st h a v e w ritte n d o w n e ith e r its c o lo u r o r its sh ap e b u t n o t b o th . H e n ce , he m u st hav e a d o p te d one o f th e fol­ low ing tw o rules: R1 R2

A T H O G is e ith e r B L U E o r C IR C L E , b u t n o t bo th . A T H O G is e ith e r R E D o r D IA M O N D , b u t n o t bo th .

O n ly th ese tw o ru les w ould define b lu e d ia m o n d as a T H O G . T h e next ste p is to e x am in e th e re m a in in g th ree designs a n d ask how th e ru les R1 a n d R 2 w ould classify th em . U n d e r R l , th e red d iam o n d c a n n o t be a T H O G b eca u se it h a s n e ith e r n a m e d a t­ trib u te , a n d th e b lu e circle c a n n o t be a T H O G b ecau se it h a s b oth.

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T h e red circle m u st, how ever, be a T H O G b ecau se it h a s one a ttrib u te (sh a p e). I f we now follow R 2, we a re forced to the sam e classifications. Red d ia m o n d c a n n o t be a T H O G b ecau se it has both a ttrib u te s , a n d blue circle c a n n o t be a T H O G b ecau se it has n eith er. A gain the red circle is b ecau se it has one a ttrib u te (colour). So w hichever ru le the e x p e rim e n te r a d o p te d th e classifications are the sam e. M o st su b je cts d o n o t succeed in fin d in g this answ 'er. O f the 56 tested by W aso n a n d B rooks (1979), for ex am p le, only 17 solved it, desp ite the in tro d u c tio n o f v a rio u s p ro c e d u re s d esig n ed to a id its u n d e rsta n d in g . W hy is it so difficult? I t seem s unlikely th a t it is d u e to a failure to a p p re c ia te th e logic o f exclusive d isju n ctio n , for tw'o reasons. F irstly, su b je cts show a low e rro r ra te w hen asked to d ra w inferences from such a rule, p ro v id ed , as in the T H O G p ro b lem , it is expressed affirm atively (see T a b le 10.4). Secondly, W 'ason a n d Brooks asked su b je cts in one e x p e rim e n t to c o n stru c t the tru th table o f an a n alo g o u s rule before a tte m p tin g the T H O G p ro b lem . T h e y h ad to devise a ru le o f th e sam e so rt - exclusive d isju n ctiv e - a n d in d icate w h a t p a tte rn s could o r co u ld n o t conform to it. A ll su b jects w ere ab le to d o th is co rrectly , b u t p e rform ed no b e tte r o n the su b seq u e n t T H O G th a n a c o n tro l g ro u p . T h e re is a d ire c t an alo g y here to the p a rad o x ica l findings on th e selection task th a t su b jects can all co rrectly e v alu ate th e logical c o n seq u en ces o f tu rn in g card s, b u t re q u irin g th em to d o so exerts lim ite d tra n sfe r on to a su b se ­ q u e n t selection task (cf. C h a p te r 9). W aso n a n d B rooks also tested the possibility th a t su b je cts a re u n a b le to co m p lete th e first ste p o f the co rrect so lution: g e n era tio n o f possible rules th a t th e e x p eri­ m en te r could be using. WThen asked to d o this, 9 o u t o f 14 w ere spo n tan eo u sly co rrect a n d the o th e rs h a d to be co ach ed . H ow ever, there w as a g ain no b enefit o f th is p ro c e d u re on a su b se q u e n t T H O G pro b lem , as c o m p a red w ith control. As on th e selection task, the c o m b in e d re q u ire m e n t b o th to g e n ­ e rate h y p o th eses a n d e v a lu a te th e ir logical c o n seq u en ces a p p e a rs to defeat m ost su b jects. O n the selection task th e ‘in tu itiv e e rro r’ is ch ara cte rised as m a tc h in g bias. W h a t is th e in tu itiv e e rro r on T H O G ? I t consists o f a ten d e n cy to say th a t red circle cannot be a T H O G , w h e rea s th e red d ia m o n d , a n d blue circle a re e ith e r in d e ­ te rm in a te o r else are T H O G S . T h e c h a ra c te ris tic e rro r tends, th en , to reverse the c o rre c t solution. W a so n ’s (1978) e x p la n a tio n o f this c h a ra c te ris tic e rro r so u n d s

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very like m a tc h in g bias. H e sta te s th a t, ‘T h e basic c o n ce p tu a l dif­ ficulty w ith the T H O G p ro b le m is th a t th e p e rso n try in g to solve it has to d e ta c h the n o tion o f possible p a irs o f defin in g features aw ay from th e a c tu a l designs w hich e x h ib it those fe a tu re s.’ T h e p o in t is th a t if the h y p o th esised ru le is say red o r d ia m o n d , th en the design c o n ta in in g b o th these featu res, th e red d ia m o n d , ‘c o u n te r-in tu itiv e ly ’, cannot be a T H O G . T h is m ig h t a c c o u n t for su b je cts’ failu re to sta te th a t the red d ia m o n d a n d b lu e circle c a n n o t be T H O G S . T h e failu re to see th a t the red circle m u st be, a n d indeed to say th a t it cannot be a T H O G , seem s b est ex p la in ed in term s o f w h a t B ru n e r, G o o d n o w a n d A u stin (1956) call th e ‘com ­ m on elem en t fallacy’. B ru n e r et al., in a stu d y o f d isju n ctiv e con cep t a tta in m e n t, found th a t su b je cts ten d e d to assu m e th a t tw o m em b ers of the sam e categ o ry sho u ld hav e a c o m m o n featu re. T h is ‘ru le ’ obviously fails w hen th e categ o ry is defined as exclusive d isju n ctio n . T h is e x p la n a tio n is also a k in to m a tc h in g bias. T h e T H O G p ro b lem is relatively new a n d little in v estig ated . It is, how'ever, useful to h a v e a n a lte rn a tiv e stru c tu ra lly sim p le task w hich h a s so m an y c h a ra c te ristic s in co m m o n w ith th e selection task. I t is w o rth y o f fu rth e r in v estig a tio n , b u t if it is to g a in e q u iv ­ alent success to th e selection task co n d itio n s m u st be found u n d e r w hich su b je cts can ach iev e re aso n a b le logical p erfo rm an ce.

Conclusions Studies o f d isju n ctiv e re aso n in g h a v e rev ealed a n u m b e r o f p a ralle ls to those o f c o n d itio n a l reaso n in g . F or e x am p le, reaso n in g p e rfo rm ­ ance is su b je ct to the in fluence o f sim ila r c o n te n t v a ria b le s. T h e re also a p p e a rs to be a m ix tu re o f logical success a n d non-logical biases d e m o n stra te d on a b s tra c t tasks. H o w ev er, th e fo rm u la tio n o f d is­ ju n c tiv e s w ith n e g ativ e c o m p o n e n ts does a p p e a r to be less lin g u ist­ ically n a tu ra l th a n a sim ila r tre a tm e n t o f c o n d itio n als. T h u s the in tro d u c tio n o f n eg ativ e c o m p o n e n ts leads to high logical e rro r ra te s unless, as on d o u b le-n e g ativ e exclusive rules, the su b je ct can avoid the p ro b lem by c onversion in to a n affirm ativ e form . T h e a b sen ce o f m a tc h in g b ias on the a b s tra c t d isju n ctiv e tru th table tasks h a s led E v an s a n d N ew stead (1980) to p o stu la te th a t the bias m ay be d e p e n d e n t on the linguistic c o n te n t set by the co n d itio n al. H o w ev er, th e re a re som e p o in ts on w'hich to defend a

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m ore g e n era l c o n cep t o f m atc h in g . F irstly , th e tec h n iq u e by w hich m atc h in g is m e a su re d o n c o n d itio n als - in tro d u c tio n o f n eg ativ e co m p o n en ts - causes confusion o f in te rp re ta tio n w ith disjunctives. W h en in te rp re ta tio n is a id e d by th e use o f th e m a tic c o n te n t, (M a n k ­ telow, 1979) m a tc h in g re tu rn s w ith a vengeance. Secondly, w'hen dealing w'ith a d isju n ctiv e p ro b lem , T H O G , w hich is a n alo g o u s in its psychological com plexity to th e selection task, the c h a ra c te ristic in tu itiv e e rro r a p p e a rs to re su lt from a fe a tu re -m a tc h in g ten d en cy . M ore gen eral th eo re tic al a rg u m e n ts for re ta in in g the n o tio n o f a general m a tc h in g b ias will be p re se n te d in th e next c h a p te r.

Part IV

Discussion

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On explaining the results of reasoning experiments

W e have now c o m p le te d the m ain review o f recen t e x p erim e n tal resea rc h e m p lo y in g d e d u ctiv e reaso n in g p a rad ig m s. T h e task o f this c h a p te r is to d ra w to g e th e r th e v a rio u s findings, c o n sid er e x p la n a ­ tions o f the m a in facto rs th a t have e m e rg ed , a n d assess th e useful­ ness o f v a rio u s g e n era l th eo re tic al a p p ro a c h e s. In C h a p te r 12, the d u a l process th eo ry o f re aso n in g , a risin g from w ork on th e selection task (C h a p te r 9), will be ex am in ed in d e ta il, to g eth e r w ith its b ro a d e r im p lica tio n s. L et us s ta rt w ith a b rie f resu m e o f th e m a te ria l covered in the review . In p a rt I, the focus w as on relatively sim ple re aso n in g tasks in w hich resp o n se laten cy is th e p rim a ry m ea su re o f in te rest. In b oth sen ten ce v erification (C h a p te r 3) a n d tran sitiv e inference tasks (C h a p te r 4) m o st a u th o rs ag ree on a g e n era l se q u e n tial m odel o f reaso n in g , w ith a re p re se n ta tio n stag e follow ed by a p rocess stage. In b o th cases, m u c h in te re s t has been focused on linguistic factors w hich a re th o u g h t to influence th e re p re se n ta tio n o f sen ten ces used in the p ro b lem s. T h e form at o f re p re se n ta tio n - p ro p o sitio n a l versus im a g e ry -b a se d - has also been a n issue, p a rtic u la rly in tran sitiv e inference. H ow ever, in line w ith o th e r fields o f cognitive psychology, this d e b a te h a s p ro v e d so m e w h a t in tra c ta b le , if n o t futile. O n e im p o rta n t conclusion o f the w'ork review ed in P a rt I w as th a t, d e sp ite th e im p o rta n c e o f linguistic factors in the c o m p re h e n ­ sion process, no satisfacto ry e x p la n a tio n o f even sim ple reaso n in g tasks can be a tte m p te d w ith o u t c o n sid e ra tio n o f th e p rocessing re q u ire m e n ts o f the task itself. Such a c onclusion will a fortiori ap p ly to th e m o re com plex tasks involved in syllogistic (P a rt I I ) a n d p ro p o sitio n a l (P a rt I I I ) reaso n in g . T w o im p o rta n t differences exist betw een th e types o f stu d y involved in these la te r sections a n d those

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Discussion

o f P a rt I. O n e is b e h av io u ral. In the la te r e x p erim e n ts the n a tu re o f su b je cts’ responses is m u ch m ore v a rie d , a n d becom es th e d e ­ p e n d en t o f v a ria b le o f m a in in te rest. T h e o th e r difference lies in the origin o f th e p ro b lem s, a n d h a s h a d a p ro fo u n d influence o n the c o n stru ctio n o f theories. F o r the e x p erim e n ts discussed in P a rts II a n d I I I th ere is alw ays a system o f fo rm al logic w ith in w hich to describe the p ro b lem stru c tu re . T h e d o m in a n t issue in P a rts I I a n d I I I has been the p resen ce o r absence o f logical re aso n in g processes. It is p e rh a p s a co n cern w ith rationality w hich h a s m o st d istin g u ish e d th e psychology o f re aso n in g from o th e r fields o f cognitive psychology (w ith one im p o rta n t ex­ ception to be considered below ). In g e n era l, cognitive psychology is c oncerned w ith th e cognitive m ec h an ism s u n d e rly in g b e h av io u r. T h e p ro b lem is to u n d e rsta n d the o rg a n isa tio n o f the b ra in as a n in fo rm a tio n -p ro c essin g system . F o r ex am p le, in m em o ry resea rc h people a rg u e a b o u t how m an y ty p es o f m em o ry sto re exist, how they a re accessed, how they a re co n n ec te d to one a n o th e r, etc. O n e does n o t assess th e b e h a v io u r by som e p red efin ed n o rm a tiv e system specifying w h a t is ra tio n a l. In a sense, ra tio n a lity in th e b e h a v io u r is im plicitly assu m e d . A lth o u g h th e processes o f p e rce p tio n , m em ­ ory, etc. a re c o n stra in e d by th e n a tu re o f th e cognitive m ec h an ism s availab le, such m ec h an ism s h av e p re su m a b ly evolved in a n a d a p ­ tive m a n n e r. T h e re w ould be little su rv iv al v a lu e in m ec h an ism s w hich p ro d u c e d a h ighly in a c c u ra te re p re se n ta tio n o f the real w orld. T h is pragmatic n otion o f ra tio n a lity is, how ever, very different from the normative type p ro v id ed by logic, a n d it will be a rg u e d th a t the p ra g m a tic n o tio n is m o re a p p ro p ria te also to the e x p la n a tio n o f reaso n in g b e h av io u r. A d a p tiv e b e h a v io u r m ay , o f course, arise from in d iv id u a l lea rn in g as well as from th e evolution o f m ec h an ism s. T h e a ssu m p tio n th a t logicality c o rre sp o n d s to ra tio n a lity in th e p ra g m a tic sense is h ighly d isp u ta b le . T h e re is n o t one b u t m an y a lte rn a tiv e system s o f form al logic. E ven ‘s ta n d a r d ’ logic is highly sim plified c o m p a red w ith th e su b tle co m plexities o f n a tu ra l language. A lso, th ere is no necessary reaso n w hy peo p le sho u ld benefit from a logical asse ssm e n t o f a rg u m e n ts , a n d hence have learn ed to d o it. T h e id en tific atio n o f fo rm al logicality w ith ra tio n ­ ality is, therefore, ex trem ely d u b io u s. M a n y o f the ‘lo g ical’ th eo rists - in clu d in g those influenced by H enle - p o stu la te u n d e rly in g m ec h an ism s in the form o f re p re se n ­ tatio n a n d p ro cess m odels. I w ould a rg u e th a t th e n a tu re o f the

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m ech an ism s p ro p o sed is m o tiv ated not p rim a rily by a de sire to explain th e o bserved b eh av io u r, b u t by a w ish to see th e su b je c ts’ b eh av io u r as ra tio n a lly d e te rm in e d (th is m o tiv a tio n h a s been d e ­ m o n stra te d re p ea te d ly in P a rts I I a n d I I I o f this book). I f form al logic p ro v id es the c riterio n for ra tio n a lity , th en this exercise is unlikely to be very useful. T h e re is, o f course, no a rg u m e n t a b o u t the fact th a t th e observed behaviour on syllogistic a n d p ro p o sitio n a l re aso n in g tasks is fre­ q u en tly illogical. W h a t is in te restin g , th o u g h , is the n u m b e r o f factors w hich a p p e a r to affect re aso n in g p e rfo rm a n ce . T h e se include the linguistic stru c tu re o f th e sen ten ces used to express a logical relation, influences o f c o n te x t a n d c o n te n t, a n d v a rio u s a p p a re n tly non-logical fe atu res o f the tasks used. T h e th eo re tic al task is to explain w hy people b e h av e as they d o on these tasks - reg ard less o f logicality - a n d to infer so m e th in g a b o u t th e cognitive m e c h a n ­ ism s a n d processes involved. In the In tro d u c tio n (C h a p te r 1) it w as sta te d th a t on e objective o f the book w as to place reaso n in g re sea rc h in th e g e n era l con tex t o f cognitive psychology. So fa r this h a s been a tte m p te d in d e ta il only in P a rt I. In o rd e r to achieve th is o bjective for th e la te r w ork, we m ust forget th e issue o f logicality for th e tim e being, a n d look a t the stru c tu re o f th e tasks. T h e re seem to be tw o a lte rn a tiv e g eneral fram ew 'orks in to w hich these tasks could be p laced problem-solving a n d decision-making. A b rie f c o n sid era tio n o f th e m ain features o f each a p p ro a c h is re q u ire d in o rd e r to c o n sid er th eir a p p lic atio n s to re aso n in g research.

Problem-solving or decision-making? T h e m ost influ en tial th eo ry o f p ro b lem -so lv in g in c o n te m p o ra ry psychology is th a t o f N ew ell a n d S im on (1972; for re ce n t d ev elo p ­ m ents see S im on, 1979). T h e ir th eo ry is d eriv ed from w ork in artificial intelligence, a n d in som e cases they w rite a c tu a l c o m p u te r p ro g ram s to sim u la te the b e h av io u rs they a re c o n cern ed w ith. T h e ir a p p ro a c h is c o n te n t-o rie n te d in th a t th ey begin w ith a d e ta ile d task analysis, in o rd e r to specify how the p ro b lem m ay be re p re se n ted in te rn ally , a n d w h a t stra te g ie s m ay be a p p ro p ria te to its solution. P sychological difficulty is seen to a rise e ith e r th ro u g h in a d e q u a te re p re se n ta tio n o f the task e n v iro n m e n t o r th ro u g h th e a p p lic a tio n

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o f in a p p ro p ria te stra te g ies. A n im p o rta n t c o n ce p t in this a p p ro a c h is th a t o f problem space (also called se a rc h sp ace). T h is consists o f an in itial sta te , one o r m o re goal sta te s a n d a set o f possible in te r­ m ed iate sta te s. P ro b lem -so lv in g is th u s defined as a se a rc h th ro u g h the pro b lem sp ace for a solu tio n p a th , le a d in g from in itial to goal states. In o rd e r to illu stra te th e a p p lic a tio n o f th is a p p ro a c h to reaso n in g , let us c o n sid er th e W aso n selection task (cf. C h a p te r 9). T ask analysis w ould in d ic a te th a t th e possible c o m b in a tio n s o f va lu e s on eith er side o f th e c ard sh o u ld be c o n sid ere d , a n d th e ir effect o n the tru th v alue o f the ru le e v a lu a te d in o rd e r to solve th e pro b lem . U nlike th e p ro b lem s stu d ie d by N ew ell a n d Sim on (1972) th e pos­ sibilities a re very few', so a n e x h au stiv e c o n stru c tio n a n d se a rc h o f the p ro b lem space sh o u ld be very easy. T h e full p ro b lem sp a c e is show n in F ig u re 11.1 (a). E ach c ard is c o n sid ere d , to g e th e r w ith eith er logical v alu e th a t c a n a p p e a r on th e back o f it. E a c h o f th e eight p a th s is th en e v a lu a te d for its effect on the tru th value o f the rule - in F ig u re 1 1 .1 a defective tru th tab le is assu m e d . I f su b jects u n d e rsta n d the falsification p rin cip le, they sh o u ld choose o nly those cards w hich hav e a p a th lea d in g to ‘false’ e v a lu a tio n - i.e. p a n d q. T h is m u ch is task an aly sis. N ow , how d o we exp lain a com m on e rro r p a tte rn such a s p , q? W aso n (1966) p ro p o sed th a t su b jects a tte m p t to verify ra th e r th a n falsify. I f they se a rc h th e co rre c t pro b lem sp a c e (F ig u re 11.1 (a )), b u t w ith this fau lty p rin cip le, they will choose p a n d q since only these lead to a ‘tru e ’ e v alu atio n . A n a lte rn a tiv e cause o f e rro r is in the c o n stru c tio n o f th e p ro b lem space. W hen Jo h n s o n -L a ird a n d W aso n (1970) claim th a t su b je cts w ith o u t insight focus on th e n a m e d v alues, they are in effect su g g estin g a re stric te d p ro b lem sp a c e as show'n in F ig u re 11.1 (b ). In th is space su b jects only se a rc h b ra n c h e s s ta rtin g w ith th e c a rd s p a n d q. T h e tw o c h a ra c te ristic e rro rs o f su b je cts w ith ‘no in sig h t’ a re to choose p alone o r else to choose p a n d q. In sp e c tio n o f the p ro b lem space in F igure 11.1 (b) w ould fa v o u r th e h y p o th esis th a t th e form er ap p ly only a falsification p rin cip le, w h ereas th e la tte r a re looking for verifying a n d falsifying c ard s. J o h n s o n -L a ird a n d W aso n - w ho did n o t refer to such a p ro b lem sp a c e explicitly - gave a n o th e r e x p la n atio n for th e difference, w'hich w as in te rn a lly in co n siste n t (see C h a p te r 9). U n d e r p a rtia l in sig h t o r c o m p lete in sig h t su b je cts are su p p o sed to c o n sid er all c a rd s, i.e. sw itch to the full se arch space. T h e difference b etw een th e tw o w ould a g a in lie in th e use o f

On explaining the results o f reasoning experiments

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START

Card

(a) Full p ro b lem space

START

Card

Other side

q

q

P

P

Evaluation*

(b) L im ited p ro b lem space

F IG U R E 11.1 Possible problem spaces for th e W ason selection task, for a ru le o f the form I f p then q ‘ A ssum es a defective tru th table

verification a n d falsification p rin cip les - lea d in g to p , q, q, o r the falsification p rin cip le alone - lead in g to p, q. T h e above an aly sis is n o t in te n d e d as a co m p lete theoretical e x p la n atio n o f p e rfo rm a n ce on the W aso n selection task - indeed th ere are v a rio u s a sp e cts o f th e d a ta for w h ic h it w ould n o t acco u n t. T h e p o in t o f th e exercise is sim ply to illu stra te the a p p lic a b ility o f the pro b lem -so lv in g theory o f N ew ell a n d S im on, a n d to show its m ain a d v a n ta g e - th e d istin c tio n betw een e rro rs o f re p re se n ta tio n an d e rro rs o f process o r stra te g y . T h e H e n le h y p o th esis, w h ich w as e v a lu a te d in P a rts I I a n d I I I o f this book, c an be view ed w ith in this fram ew ork. E ssentially, the

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H enle claim is th a t all re aso n in g e rro rs a rise d u rin g re p re se n ta tio n o f the p ro b lem in fo rm a tio n , ra th e r th a n in the e xecution o f s tr a t­ egies. T h e la tte r a re a ssu m e d alw ays to a cc o rd w ith form al logic. T h is highly re stric tiv e use o f the re p re se n ta tio n -p ro c e ss d istin c tio n seem s to lack a priori ju stific a tio n , o th e r th a n a b elief in m a n ’s in h ere n t logicality. N ew ell a n d S im on (1972) certain ly re g a rd dif­ ficulties in the a p p lic a tio n o f a p p ro p ria te se a rc h m eth o d s, ra th e r th an p ro b lem re p re se n ta tio n , to be th e m a jo r c au se o f p ro b le m ­ solving difficulty. T h e pro b lem -so lv in g a p p ro a c h assu m e s th a t su b je cts a re a tte m p t­ ing to solve th e p ro b le m as in stru c te d - w h a t N ew ell a n d Sim on call ‘in te n d e d ly ra tio n a l b e h a v io u r’. O n e o f th e p ro b le m s w ith reasoning e x p erim e n ts is th a t in stru c tio n s p re su p p o se a know ledge o f logic in th e ir su b je cts. S u b jects will be asked to decid e w h e th e r a conclusion ‘necessarily follow s’, for e x am p le, a n d th e ex p licit use o f the term ‘logic’ is n o t u n c o m m o n . T h is c o n tra sts m ark e d ly w ith Newell a n d S im o n 's ow n ‘logic’ p ro b lem s, in w hich su b je cts a re given a n explicit set o f rules for m a n ip u la tin g logical sym bols, a n d th en asked to prove th eo re m s. In these e x p erim e n ts, su b je cts are never told th a t the sym bols re p re se n t logical re la tio n sh ip s. T h e reaso n in g e x p erim e n ts d e sc rib e d in th is book a re th e n really tests o f the e x te n t to w hich su b je cts u n d e rs ta n d , a n d a re a b le to ap p ly , logical prin cip les. B ecause so m u ch o f the p ro b lem -d efin itio n is im plicit, a n d left to th e su b je c t’s u n d e rsta n d in g , it is relatively difficult to disco v er w h a t p ro b lem sp ace people m ay a ctu ally be using. A lso, these e x p erim e n ts h a v e n o t g en erally used ‘th in k in g a lo u d ’ tec h n iq u es, fav o u red by N ew ell a n d Sim on to trac e th o u g h t processes in in d iv id u a ls (m o re o f this in C h a p te r 12). F in ally , N ew ­ ell an d S im o n ’s theo ries a re n o t m e a n t to a p p ly to g ro u p d a ta , w hich is th e u su a l form in w hich re aso n in g re su lts a re p re sen te d . F or all these reaso n s, a d e ta ile d p ro b lem -so lv in g a n aly sis o f re aso n ­ ing e x p erim e n ts - as c u rre n tly c o n d u c te d - is n o t likely to be very easy. All re aso n in g e x p erim e n ts re q u ire a decision to be m ad e . T h e sub ject is asked to d e cid e w h e th e r a ru le is tru e o r false, given c ertain evidence, w h e th e r o r n o t a conclusion follows logically, w h e th er o r n o t a c ard need be tu rn e d over. I t is w o rth co n sid erin g , then, w h a t g e n era l p rin cip les hav e been d eveloped to a cc o u n t for d e cision-m aking in g e n era l. Decision theory, as dev elo p ed by eco n o ­ m ists a n d m a th e m a tic ia n s, h a s m an y a p p lic a tio n s in psychology

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(see Lee, 1971; Slovic, F isch h o ff a n d L ic h ten ste in , 1977). T h is is the o th e r field in w hich ra tio n a lity is a d o m in a n t issue. H e re ra ­ tionalism is defined n o t by logicality b u t by the p rin cip le o f m ax ­ im isation o f u tility (p erso n al subjective g a in ). ‘R a tio n a l m a n ’ is a fu n d a m e n ta l c o n cep t in econom ic theory. R a tio n a l m an considers the con seq u en ces o f his possible lines o f a ctio n , e v alu ate s the chances a n d costs o f v a rio u s ou tco m es, a n d chooses in a m a n n e r m axim ally beneficial to him self. V a rio u s decision ru les o r stra te g ies m ay be a p p lie d a cc o rd in g to th e situ a tio n . In risky choice - such as g a m b lin g - ra tio n a l m a n m axim ises exp ected u tility (i.e. chooses the ou tco m e th a t w o u ld , on av era g e, yield th e larg e st g a in ). U n d e r ra tio n a l c o m p e titio n writh a n o th e r p lay e r, he m ay choose so as to m inim ise his m a x im u m loss. F o r ex am p le, in a g a m e o f chess you should choose th e m ove th a t g a in s you m ost on the a ssu m p tio n th a t y o u r o p p o n e n t chooses th e b est possible reply from his p o in t o f view. T h e n o tio n o f ra tio n a l choice is as easy - a n d as h a rd ! —to dism iss as th a t o f logical re aso n in g . J u s t as o n e can easily d e m o n s tra te th a t people re aso n illogically, so one can d e m o n s tra te th a t they choose gam bles w ith objectively expected losses. T h e d e cisio n -m ak in g e q u iv a len t o f th e H e n le hyp o th esis, how ever, p o stu la te s th a t people choose ra tio n a lly , given th e ir su b jectiv e in te rp re ta tio n o f the w orld. F or exam ple, it is ra tio n a l to bet on the football pools, if you e ith e r o v erestim ate the c h an c e o f w inning, o r o v erv alu e th e p rize m oney relative to th e stak e. F o r th is reaso n , m u ch in te re st has focused o n the subjective u n d e rsta n d in g o f c h an c e a n d p ro b a b ility , w'hich a re d isto rte d in m an y resp ects. In this a re a a th eo re tic al a p p ro a c h based on n o n -ra tio n a list p rin cip les h a s been dev elo p ed , a n d th is is o f co n sid era b le relev an ce to re aso n in g research . T h e im p o rta n t w ork is th a t in itiate d by K a h n e m a n a n d T v ersk y (1972). T h e y p ro p o se d th a t su b je c ts’ a ssessm en ts o f p ro b a b ility a re based, n o t o n a n u n d e rs ta n d in g o f th e m a th e m a tic s o f p ro b a b ility , b u t on c e rta in ‘h e u ris tic s’ o r sh o rt-c u ts devices, w hich m ay lead to c o n sid era b le in ac cu ra c ie s. F o r ex am p le, if su b je cts a re asked to assess the likelihood o f a given set o f sta tistic a l d a ta , they are assum ed to use a h e u ristic called representativeness. T h a t is, they exam ine th e d e g ree to w h ic h sa lie n t c h a ra c te ris tic s o f th e sam p le, such as m ea n o r p ro p o rtio n , m a tc h th e c o rre sp o n d in g c h a ra c te ris­ tics o f the p a re n t p o p u la tio n . In th e p rocess they ignore sta tistica lly relev an t factors such as sa m p le size. A n o th e r p ro p o sa l is th a t s u b ­

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jec tiv e likelihood is re la te d to th e availability o f item s for re triev a l from m em ory' (T v ersk y a n d K a h n e m a n , 1973). F o r e x am p le, th e finding th a t people o v e re stim a te th e likelihood o f se n sa tio n a l causes o f d e a th , e.g. from a e ro p la n e c rash e s (L ic h ten ste in et al., 1978), could be d u e to d isp ro p o rtio n a te coverage o f su c h events in the m edia, c o m p a red w ith co m m o n cau ses o f d e a th su ch as strokes. I f re aso n in g e x p erim e n ts a re looked a t in term s o f d ecision th eo ry , we need to ask w h a t the u tilities a re for the decisions m ad e. A nyone w ho h a s ru n su c h e x p e rim e n ts know s th a t how ever su b je cts m ay be in stru cte d to th e c o n tra ry , they re g a rd su c h e x p erim e n ts as tests o f intelligence, a n d are freq u e n tly very co n ce rn ed a b o u t how w ell they have p erfo rm ed . I t is a fa ir a ssu m p tio n , th en , th a t su b je cts choose in o rd e r to m ax im ise th e ir c h a n c e o f bein g ‘rig h t’. T h e fact th a t they so freq u e n tly fail to d o so m u st be a ttrib u te d to a n in a b ility to u n d e rsta n d th e p ro b lem o r to b a se th e ir responses o n a ra tio n a l, i.e. logical, base. T h e tw o im p o rta n t q u e stio n s a risin g a re a s follow's: (i) w hy is su b je c ts’ logical co m p e ten c e a p p a re n tly so lim ited a n d situ a tio n -d e p e n d e n t a n d (ii) if su b je c ts’ choices a re n o t b ased on logic, on w'hat a re they b ased? T h e a n sw e r to th e second q u e stio n m ay well lie in the a p p lic a tio n o f m ore o r less a p p ro p ria te h eu ristics, in te n d e d to m ax im ise c h an c es o f success. F irstly , how ever, w e co n ­ sider the g e n era l n o tio n o f logical com p eten ce.

Logical competence T h e re are tw o w ays o f d efin in g c o m p e ten c e. T h e easy b u t u n in te r­ esting w ay is task-specific. P eo p le’s co m p e ten c e to solve a given logical task can easily be assessed. H o w ev er, the term ‘logical com ­ p e te n ce ’ is n o rm ally used to define so m e th in g m u ch m o re a b s tra c t. I t refers to a h y p o th e tic a l system o f logic w hich th e in d iv id u a l ‘possesses’. I t im plies a p o te n tia l c a p a b ility to p e rfo rm a n y task w hose logical stru c tu re is a m e n a b le to so lu tio n by th e system . T h is does not m ea n th a t all su c h p ro b le m s will be solved, how ever. T h e tra n sla tio n o f co m p e ten c e in to p e rfo rm a n c e is su b je ct to the o p e r­ ation o f a p e rfo rm a n ce system . T h e c o m p e te n c e /p e rfo rm a n c e d istin c tio n w as dev elo p ed by C hom sky in his lin g u istic th eo ries (see C h a p te r 2). In th a t case, a g ra m m a tic a l th eo ry w as seen as a d e sc rip tio n o f th e lan g u a g e u se r’s com petence. P ro d u c tio n o r u n d e rs ta n d in g o f lan g u a g e w ould how ­

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ever be su b je ct to p e rfo rm a n ce lim ita tio n s such as m em ory cap a city , w hich could cau se, for ex am p le, u n g ra m m a tic a l (in co m p ete n t) u t­ terances. T h e a p p lic a tio n o f this d istin c tio n to logic a n d re aso n in g raises v a rio u s p ro b lem s. A s in th e lin g u istic c o n te x t, th e co m p eten ce m odel does n o t c o n stitu te a n em p irically testa b le th eo ry , unless the p erfo rm an ce c o m p o n e n t is also fully specified. Since p e rfo rm a n ce factors a re liable to be task specific, th ey m ay not be easy to define a priori. T h e re is also th e q u e stio n o f th e c o m p eten ce system itself: should it be b ased on form al logic, o r on a lte rn a tiv e ‘n a tu r a l’ logic (see, for e x am p le, B ra in e , 1978)? I f form al logic is tak e n as th e basis o f th e co m p eten ce system , then this a p p ro a c h m ig h t be seen as a n o th e r a tte m p t to preserve the notion o f logicality in th e face o f o vertly illogical b e h av io u r. In this case, th e d e v ia tio n s a re a ttrib u te d to ‘p e rfo rm a n ce fa cto rs’. T h e la tte r m ig h t in clu d e v a rio u s non-logical biases discu ssed in this book, e.g. a preference for negative c onclusions (C h a p te r 8) o r a bias to a cc ep t a rg u m e n ts w hose c onclusions you believe (C h a p te r

6 ). T h e E v an s tw o-factor reaso n in g th eo ry could be in te rp re te d in this fram ew ork i / i t w ere a ssu m ed th a t the logical c o m p o n e n t w as ta sk -in d e p en d e n t; a n d th e sto c h astic reaso n in g m odel (cf. E vans, 1977b; a n d C h a p te r 9) could be seen as a d e sc rip tio n o f the w ay in w hich logical ten d e n cie s a risin g from c o m p eten ce co m b in e w ith task-specific p e rfo rm a n ce factors. E v id e n tly , th en , the p re serv a tio n o f logicality by this device is ra th e r different from th e m u ch m a ­ ligned (in this book) H e n le a p p ro a c h . A lth o u g h H en le d id indeed a ssum e th a t su b je cts possess a co m p eten ce b ased on form al logic, she u n n ecessarily re stric te d th e so u rce o f p e rfo rm a n ce e rro rs to the in te rp re ta tio n a l stage. T h e im p o rta n t p o in t a b o u t logical com p eten ce, w h e th e r form ally or n a tu ra lly b ased , is its in d ep e n d en c e o f task c o n te n t. T h is m ea n s th a t c o m p eten ce c a n nev er be assessed w ith reference to a given situ atio n unless one know s a priori the n a tu re a n d effect o f all p erfo rm an ce factors. T h e o b se rv atio n th a t a su b je ct fails to give a correct a n sw e r to a m o d u s tollens (M T ) p ro b lem , for ex am p le, does not e n title on e to say th a t th is su b je ct does n o t possess th e co m ­ p etence to m ak e M T . W h a t is less often recognised is th a t giving the correct a n sw e r does n o t im ply th a t the su b ject h a s the com ­ petence e ith e r; he m ay hav e g uessed, o r b een in d u ce d to give a spuriously c o rre c t a n sw e r by a non-logical stra te g y , su c h as the

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alleged a tm o sp h e re effect in syllogistic re aso n in g (C h a p te r 6). As Pollard (1979a) co rrectly p o in ts o u t, we a re obliged to e x p la in w hy people get p ro b lem s right, a n d n o t sim p ly to e x p la in logical erro rs. All o f this m ea n s th a t th e pro cess o f in ferrin g c o m p eten ce from p erfo rm an ce is ex trem ely tricky. F o r ex am p le, it w as show n in C h a p te r 8 th a t m ost peo p le can m ak e M T w ith a n a b s tra c t ru le o f the form I f p then q, b u t n o t w ith a ru le o f the form I f not p then q. T h e a ttrib u tio n o f the logical failure in the second case to a difficulty in m ak in g a d e n ia l o f a n eg ativ e p re su p p o se s th e ex istence o f com ­ petence for M T - th e affirm ative form allow s such co m p e ten c e to be expressed, a n d the negative su p p re sses it. H o w ev er, it could equally be a rg u e d th a t we d o not h a v e c o m p eten ce for M T a n d th a t the n egative form gives th e ‘tru e ’ p ictu re; the inference is only a p p a re n tly m ad e on th e affirm ativ e rule, ow ing to a non-logical bias to w ard s a rg u m e n ts w ith n eg ativ e conclusions. T h is la tte r in te rp re t­ atio n seem s less a ttra c tiv e , b u t m u st be tak e n seriously in the light o f recent re su lts by P o llard a n d E v an s (1980). T h e y found no evidence o f c o rre latio n betw 'een th e a b ility to m ak e M T inferences on sy n ta ctica lly d istin c t rules. T h e m ost in flu en tial theory p o stu la tin g the ex istence o f a co m ­ petence system based in form al logic is th a t o f P iaget. A n u n d e r­ sta n d in g o f logic is seen as g row ing in th e child th ro u g h v a rio u s cognitive stages, re ac h in g c o m p le tio n in th e a d u lt sta g e o f form al operations, w hich is d e sc rib e d in d e ta il by In h e ld e r a n d P ia g et (1958). In the p e n u ltim a te stag e, th e sta g e o f concrete operations, th e child learns to a p p ly logical o p e ra tio n s in p a rtic u la r co n tex ts. T h is is then su p p o sed to evolve in to a g e n era l a b s tra c t system , in w hich the a d u lt is c a p a b le o f re p re se n tin g a given situ a tio n in a p ro p o si­ tional m a n n e r, a n d a p p ly in g form al logical rules to its solution. W aso n (1977b) h a s a tta c k e d the viab ility o f P ia g e t’s theory o f form al o p e ra tio n s on th e basis o f a d u lt re aso n in g e x p erim e n ts, p a r ­ ticu larly those em plo y in g th e W 'ason selection task. H e c laim s th a t c ertain logical o p e ra tio n s o f w'hich in te llig e n t a d u lts sh o u ld be c a p ­ able, su c h as the a p p re c ia tio n o f rev ersib ility , o r the a b ility to a p p ly a combinatorial analysis (ex h au stiv e se a rc h o f logical po ssib ilities), are m anifestly a b se n t on these tasks. W aso n also p o in ts to the fact th a t logical p e rfo rm a n ce is h ighly d e p e n d e n t on the n a tu re o f th e task c o n te n t, a n d is only relatively ‘g o o d ’ w hen th e m a te ria l is th em a tic. O th e r re ce n t c ritics o f P iag et, su c h as D o n a ld so n (1978) hav e also focused on th e ta sk -d e p e n d e n t n a tu re o f su b je c ts’ resp o n ses, b u t in

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a ra th e r different w ay. T h e claim is th a t c erta in v a ria tio n s on the co n v en tio n al P ia g e tia n p a ra d ig m s can p ro d u c e p e rfo rm a n ce beyond th a t o f w h ich y o u n g c h ild ren a re su p p o sed to be cap a b le . T h e c o n te n t-d e p e n d e n t n a tu re o f reaso n in g is itself a m a tte r o f g reat in te re st, a n d wall be discu ssed la te r in the c h a p te r. C a n P iaget escape his critics, how ever, by reference to the c o m p e ten c e/p erfo rm ance d istin c tio n ? Its use in defence o f P iag et is illu stra te d by F lavell an d W ohlw ill (1969), w'ho use it to e x p la in in co n siste n t p e rfo rm ­ ances on v a rio u s tasks a t c e rta in stages (horizontal décalage). It is conceivable, p e rh a p s, th a t th e p o o r a n d c o n te n t-d e p e n d e n t n a tu re o f reaso n in g responses could be a ttrib u te d en tirely to ‘p e rfo rm a n ce factors’, b u t to d o so on this scale g re atly w eakens the e x p la n ato ry pow er o f th e o rig in a l th eo ry . P iaget h im self d id seem to m ove som e w ay to w a rd s recognising th e c o n te n t-d e p e n d e n t n a tu re o f a d u lt thought: In o u r in v estig a tio n s o f form al th in k in g wre used ra th e r specific types o f e x p erim e n tal situ a tio n s w hich w ere o f a physical an d lo g ic a l-m ath e m a tic al n a tu re . . . it is possible to q u e stio n w h e th e r th ese situ a tio n s w ere, fu n d a m e n ta lly , very g e n era l a n d therefore a p p lic a b le to a n y school o r professional e n v iro n m en t. L et us c o n sid er th e ex am p le o f a p p re n tic e s to c a rp e n te rs, locksm iths o r m ec h an ic s . . . I t is highly likely th a t they will know how to re aso n , in a h y p o th etica l m a n n e r in their speciality . . . faced w ith o u r e x p erim e n tal situ a tio n s, th e ir lack o f know ledge . . . w ould h in d e r th em from re aso n in g in a form al w ay (P ia g et, 1972, ita lic s m in e). T h e sugg estio n th a t fo rm al o p e ra tio n a l th o u g h t is re stric te d to g e n ­ eral a re a s o f know ledge, if n o t specific c o n te n t, seem s to be a m ajo r change o f d irec tio n in P ia g e t's th in k in g , a n d is m u ch less su sce p tib le to W a so n ’s criticism s th a n is P ia g et’s e a rlie r theo risin g . In effect, Piaget is say in g th a t, a lth o u g h we possess logical co m p eten ce in the p o ten tial for form al th o u g h t a n d h y p o th etica l reaso n in g , th is is only likely to be m an ifested in re aso n in g p e rfo rm a n ce w hen the c o n te n t relates to th e g e n era l fields o f experience a n d in te rest o f the subjects. I f he is rig h t, th en a b s tra c t reaso n in g tasks such as the m ajo rity review ed in this book will necessarily u n d e re stim a te th e a c tu a l co m petence o f th e su b je cts tested . F u rth e rm o re , the fa cilitatio n o f reaso n in g by th e m a tic c o n te n t, w hich is fu n d a m e n ta l in W a s o n ’s

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(1977b) c ritiq u e, is to be exp ected in th is revised th eo ry o f form al o p erations. In g e n era l, how ever, th e n o tio n th a t form al logic m ay form the basis for a c o m p eten ce system h a s been criticised by v a rio u s a u th o rs, since it does n o t c o rre sp o n d well to o u r use o f n a tu ra l lan g u ag e (see W aso n a n d Jo h n s o n -L a ird , 1972; O sh e rso n , 1975; J o h n s o n -L a ird , 1975; B rain e, 1978). N o rm a lly , the logic referred to is o f the ‘s ta n d a r d ’ p ro p o sitio n a l form , the e lem en ts o f w hich w ere describ ed in C h a p te r 7. T h e a rg u m e n t h ere defines c o m p eten ce in a m a n n e r a n alo g o u s to C h o m sk y ’s lin g u istic use, in w hich the language u se r is su p p o sed to hav e a n in tu itiv e a b ility to d ecide w h e th er o r n o t a n u tte ra n c e is g ra m m a tic a l. T h u s it is a rg u e d th a t various featu res o f form al logic a re in tu itiv ely u n a c c e p ta b le . F o r exam ple, in form al logic a n im p lica tio n p^> q is alw ays tru e if its a n te ce d e n t is false o r its c o n se q u en t tru e. T h e re is n o real linguistic e q u iv a len t w hich h a s this p ro p e rty . C o n sid e r th e follow ing ‘I f . . . th en . . .’ sentence: I f 2 + 2 = 5 th en th e w orld is sq u a re I f this w ere a m a te ria l im p lica tio n , th e n th e sen ten ce w ould have to be d e em ed ‘tru e ’. L in g u istica lly it is m eaningless. S im ilarly , how m an y people w'ould c o n sid er this to be a ‘lo gical’ a rg u m e n t: E n g la n d is th e larg e st c o u n try in th e w'orld, L o n d o n is the c a p ita l o f the larg e st c o u n try in th e w orld, T h erefo re, L o ndon is the cap ital o f E n g la n d . T h is m u st be a logically valid a rg u m e n t since it can only be invalid w hen it is possible for th e c onclusion to be false, w'hile all the prem ises a re true. T h e in a b ility o f ‘s ta n d a r d ’ form al logic to acc o u n t for p e o p le ’s u n d e rsta n d in g o f lin g u istic re la tio n s is d e m o n s tra te d by th e need to p o stu late a th ird ‘irre le v a n t’ tru th v alue, in o rd e r to e x p la in p e o p le ’s co m p reh en sio n o f c o n d itio n al sta te m e n ts (cf. C h a p te r 8). I f form al logic is rejected as a c o m p e ten c e m odel, th en p e rh a p s a n a lte rn a tiv e ‘n a tu r a l’ logic m ig h t be p ro p o sed . F o r som e recen t a tte m p ts to do this the re a d e r is referred to Jo h n s o n -L a ird (1975), E n n is (1976) an d B ra in e (1978). T h e p ro b lem w'ith all su ch schem es is th e ir testab ility . U n less d e ta ile d a priori p e rfo rm a n ce a ssu m p tio n s are

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b u ilt in, it is n o t c le ar how an y such th eo ry w'ill g e n e ra te testa b le p red ictio n s. B ra in e , in p a rtic u la r, seem s u n a w a re o f the n u m b e r an d m a g n itu d e o f p e rfo rm a n ce factors th a t w ould n eed to be tak en into a cc o u n t, a n d fails to cite m u ch o f th e re le v a n t lite ra tu re . H ow does th e c o m p e te n c e /p e rfo rm a n c e issue re la te to the p ro b lem -so lv in g a n d d ecisio n -m ak in g analyses? N ew ell a n d Sim on (1972) claim th a t p ro b lem -so lv in g processes a re closely re la te d to task c o n te n t, a n d can be u n d e rsto o d only a fte r d e ta ile d task a n a ly ­ sis. H ow ever, as wras p o in te d o u t e arlie r, m u ch o f the task in s tru c ­ tion in re aso n in g p ro b le m s is im p licit a n d rests on th e su b je c t’s u n d e rsta n d in g o f logic. T h u s th e p o te n tia l c a p a b ility to c o n stru ct an a p p ro p ria te p ro b le m space a n d se a rc h it correctly w ould rest upon the su b je c t’s com p eten ce. P erfo rm an c e d e v ia tio n s could be acco u n ted for in term s e ith e r o f th e re p re se n ta tio n a l sta g e (a la H enle) o r th e p ro cessin g stage. If, a lte rn a tiv e ly , we su p p o se th a t the subject is try in g to m ax im ise co rrect d ecisions, th en his a b ility to do so can also be seen as reflecting c o m p e ten c e/p erfo rm a n ce factors. Since a su b je c t’s b e h a v io u r is n o t o nly freq u e n tly illogical, b u t also in co n siste n t across tasks, it is cle ar th a t m u c h o f th is b e h a v io u r reflects p e rfo rm a n ce factors. W e will c o n se q u en tly tak e a closer look at som e o f th e m a jo r v a ria b le s w hich affect reaso n in g p e rfo rm a n ce , a n d c o n sid er th e e x p la n a tio n o f th eir origin.

Linguistic factors It w as suggested e a rlie r th a t the c o m p e te n c e /p e rfo rm a n c e d istin c ­ tion m ig h t re la te to the d istin c tio n b etw een logical a n d non-logical factors in reaso n in g . H o w ev er, the ‘lo g ic a l’ c o m p o n e n t does not necessarily im p ly logically correct b e h av io u r. I t m erely refers to th a t p a rt o f the d a ta w hich v a rie s w ith th e logically defined stru c tu re o f the task. T h is c o m p o n e n t has been show n to be su b je ct to the influence o f linguistic factors, a n d in d ee d , in som e co n tex ts, it has been term ed the interpretational c o m p o n e n t o f p erfo rm an ce. L in g u istic influences a re them selves ex tra-lo g ical factors in the d e te rm in a tio n o f re aso n in g p e rfo rm a n ce . E vid en ce for th e im p o rt­ ance o f such facto rs can be found th ro u g h o u t this book. F o r ex­ am ple, in C h a p te r 3 it wras o bserved th a t n e g a tio n serves a linguistic function - th a t o f d e n y in g p re su p p o sitio n s. N eg ativ es used in a

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lin guistically a p p ro p ria te c o n te x t a re p rocessed m o re easily. In C h a p te r 4, lin g u istic factors w ere seen to be im p o rta n t in influencing tran sitiv e inference. C lea rly , p ro b le m s c o n ta in in g lexically u n ­ m ark ed ad jectiv es a re e asie r to p ro cess th a n those using m ark e d adjectives, w 'hether o r n o t wre a ssu m e th e use o f im a g e ry -b a se d strategies. S uch a n effect m u st be ex p la in ed by lin g u istic usage or o rg a n isatio n - th e re is no logical d istin c tio n involved. T h e re has b een little in v estig a tio n o f sy n ta ctic factors in syllogistic reaso n in g (C h a p te r 6), a lth o u g h se m a n tic c o n te n t facto rs hav e been stu d ied (see below ). T h e p ro p o sitio n a l re aso n in g lite ra tu re (P a rt I I I ) , how ever, p ro v id es v a rio u s e x am p les. T h u s , c o n d itio n a l se n ­ tences hav e been show n to possess a d ire c tio n a lity w'hich is d e p e n ­ den t u p o n th e ir exp ressio n in th e ‘I f . . . th en . . .’ o r ‘. . . only if . . .’ form . T h e re is a lso ev idence th a t th e in te rp re ta tio n o f such sentences is influenced by the use o f co n te x ts specifying tem p o ral o r causal conn ectio n s. D isju n c tiv e sen ten ces, unlike c o n d itio n als, are tre a te d relatively sy m m etrica lly , b u t prove very h a rd to in te rp re t w hen n eg ativ e c o m p o n e n ts a re in tro d u c e d . C learly, th en , th e su b je c t’s know ledge o f lan g u a g e influences his re aso n in g responses. T h e g e n era l p rin c ip le seem s to be th a t the n o rm al linguistic usage o f a p a rtic u la r sy n ta c tic form a p p e a rs to influence its in te rp re ta tio n a n d use in a n a rtificial e x p erim e n t. In c onsidering th e role o f semantic factors, how ever, we m u st c o n sid er the su b je c t’s know ledge o f the w orld (se m an tic m em ory) as well as lang u ag e, a n d c o n sid er n o n -lin g u istic influences o n b e h av io u r. F o r exam ple, su b jects m ay be a p p ly in g le a rn e d stra te g ies to o p tim ise the role o f m ak in g c o rre c t decisions. I t is w ith this b ro a d e r a p p ro a c h in m in d th a t we now tu rn to a c o n sid e ra tio n o f c o n te n t a n d c o n te x t effects.

Effects of content and context T h e c o n te n t-d e p e n d e n t n a tu re o f re aso n in g responses has been a l­ luded to e a rlie r in th e c h a p te r. W e look h ere a t the specific types o f effect th a t h a v e a risen . T h re e g e n era l classes o f effect hav e been claim ed: (i) In som e c irc u m stan c es it a p p e a rs th a t th e m a tic o r ‘re alistic ’ con ten t c an fa cilitate logical p e rfo rm a n ce . T h is w as o riginally claim ed by W ilkins (1928) in h e r early syllogistic re aso n in g e x p eri­

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m ents; recen t c o n firm atio n com es m ain ly from w ork o n the W aso n selection task (C h a p te r 9). (ii) W h ere su b je cts hav e beliefs a b o u t the tr u th o r falsity o f s ta te m e n ts e m b e d d e d in re aso n in g p ro b lem s, th e ir re sp o n ses m ay be biased a cco rd in g ly . A n u m b e r o f syllogistic re aso n in g e x p eri­ m en ts hav e d e m o n s tra te d a b ias to a cc ep t o r reject th e conclusion o f an a rg u m e n t on th e ba sis o f a priori beliefs ra th e r th a n logical v alidity (see C h a p te r 6). R ecent selectio n -task e x p erim e n ts also show effects o f th e su b jectiv e tru th s ta tu s o f th e ru le bein g tested (especially P o llard , 1979a; P o llard a n d E v an s, 1981, discu ssed in C h a p te r 9). (iii) T h e se m a n tic c o n te x t in w hich a sen ten c e is used m ay affect its in te rp re ta tio n a n d c o n se q u en tly affect inferences a sso c iated w ith it; for e x am p le, c o n d itio n a ls a re m o re likely to be in te rp re te d as equivalences in c au sal o r th re a t/p ro m is e co n tex ts (C h a p te r 8). O u r co n cern h ere is to seek som e g e n era l e x p la n a tio n o f w hy such effects arise. W e will c o n sid er the m erits o f the prob lem -so lv in g a n d decisio n -m ak in g view s o f re aso n in g in tu rn . It will be recalled th a t p ro b lem re p re se n ta tio n is a n im p o rta n t concept in the p ro b lem -so lv in g a p p ro a c h . A fu n d a m e n ta l difference could a rise in re p re se n tin g a b s tra c t a n d th e m a tic p ro b lem s. I t w as noted in C h a p te r 9 th a t th e m a tic m a te ria ls m ay only fa cilitate selection-task p e rfo rm a n ce w hen they a re also realistic, i.e. p e rta in in g to likely a re a s o f the su b je c t’s p e rso n al ex perience. I n su c h cases subjects w'ill h av e a p re -e x istin g know ledge system o r se m an tic m em ory', to w hich th e p ro b le m relates. I t is therefore possible th a t the re p re se n ta tio n o f th e p ro b lem is assisted by ex istin g asso ciatio n s in se m an tic m em o ry . In effect, th e su b je ct reaso n s w ith a n a u g ­ m en ted p ro b lem sp a c e, e n ric h ed by re le v an t p e rso n al experience. T h e d ra m a tic ‘fa c ilita tio n ’ in th e envelope a n d sta m p version (Jo h n so n -L a ird , L eg ren zi a n d L eg ren zi, 1972) a n d its e q u ally d r a ­ m atic failu re to tra n s fe r to a s u b s e q u e n t a b s tra c t task, is a good illu stra tio n . I f fa ilu re on th e a b s tra c t task arises from th e failu re to inclu d e the q c a rd in th e p ro b lem sp ace, th en the e x p la n a tio n is sim ple. In the realistic c o n d itio n th e su b je ct know s from experience th a t a n envelope w ith a low -valued sta m p m u st be in sp e cted , since it is only so m etim es legal. H e m ay also exclude th e q c a rd from the sea rc h sp a c e (com m only m istak en ly selected in the a b s tra c t task) since a n envelope w ith a h ig h -v alu ed sta m p is always legal. M o re difficult to e x p la in is th e use o f ‘to w n s a n d tra n s p o rt m a ­

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te ria l’ w hich a p p a re n tly facilitate selections (W aso n a n d S h a p iro , 1971) a lth o u g h one recen t stu d y h as failed to re p lica te this (M a n k ­ telow a n d E v an s, 1979). It is highly im p ro b a b le th a t su b je cts will have had an y experience w'hich re la te s specifically to a ru le su ch as ‘E very tim e I go to M a n c h e ste r th en I travel by tra in ’. H ow ever, they will c ertain ly hav e h a d m o re ex p erien ce o f trav e llin g to d e sti­ n atio n s by v a rio u s m ea n s o f tra n s p o rt th a n o f tu rn in g c a rd s w ith letters a n d n u m b e rs on th em . T h is m ay fa cilitate the im a g in a tio n o f a lte rn a tiv e possibilities sufficiently to c o u n te ra c t the 'm a tc h in g b ias’, c h a ra c te ris tic o f a b s tra c t selection tasks, a n d to p e rm it in clu ­ sion o f n o n -m a tc h in g v alues in th e se a rc h space. T h e idea th a t th e c o n stru c tio n o f p ro b lem spaces is influenced by existing a sso ciatio n s in se m an tic m em o ry is also a p p lic a b le to co n ­ text effects. C o n sid e r th e ‘in v ite d in fere n ce ’ effects w-ith th re a ts a n d prom ises: ‘I f y o u m ow th e lawrn th e n I ’ll give you five d o lla rs’ seem s to im ply th a t ‘I f you d o n ’t m ow the law n th en I w o n ’t give you five d o lla rs’. E x p erien ce will hav e ta u g h t us —from early ch ild h o o d — to exclude c erta in logical p o ssibilities in c o n te x ts involving th re a ts a n d prom ises. If, c o n se q u en tly , th e given se n ten c e lead s us to d isre g a rd the possibility o f receiving five d o lla rs for not mow ing the law n, th en the inference n a tu ra lly follows. I t is n o t a form al tru th ta b le b u t a p ra ctic a l experience o f p o ssibilities th a t d e te rm in e s o u r responses. It is en tirely re aso n a b le th a t we sh o u ld th in k in p ro b lem spaces th a t are a u g m e n te d o r re stric te d by re le v a n t p rev io u s experience. P e rc ep tio n , m em ory a n d th o u g h t a re all sh a p e d a n d d ire c te d by experience a n d e x p ec ta tio n s. It is, how ever, a m ista k e n sim p lifica­ tion to sug g est th a t, in g e n era l, realistic c o n te n t improves o u r re a so n ­ ing. M o st evidence for fa cilitatio n by re alistic c o n te n t d eriv es from w ork on the selection task, in w hich a b s tra c t p e rfo rm a n ce pro v id es a n e x tra o rd in a rily low logical base ra te for c o m p a riso n . T h e p ro ­ cesses resp o n sib le for th e a b s tra c t task p e rfo rm a n ce will be d is­ cussed later. T h e poin t a b o u t realistic m a te ria ls is th a t they in d u ce responses th a t a re appropriate to o u r experience, w hich m ay o r m ay n o t c o rre sp o n d to a logical d efin itio n o f v alidity. T h e belief-bias effects a re h a rd e st to e x p la in in this se m i-ra tio n a l pro b lem -so lv in g a p p ro a c h . T o e v a lu a te a conclusion on its a priori tru th v a lu e seem s to involve a ‘failu re to a cc ep t the logical ta s k ’ (H enle, 1962). It is re aso n a b ly exp licab le if, like P o llard (1979a), we re g ard a ‘r a tio n a l’ resp o n se as a ten d e n cy to m axim ise c o rre c t decisions. In effect, in a re aso n in g task one is asked to e v a lu a te the

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tru th o f a s ta te m e n t (conclusion) on th e basis o f th e evid en ce given (prem ises). If, how ever, o n e know s th e a n sw e r a priori it is q u ite re aso n a b le to ignore th e evidence. T h is is c e rta in ly c h a ra c te ris tic o f m uch real-life b e h a v io u r. W h y , for e x am p le, sh o u ld one take the tro u b le to stu d y th e a rg u m e n ts o f political o p p o n e n ts, w h e n one alread y know s th a t th e ir conclusions a re w rong! T h is a rg u m e n t supposes little u n d e rs ta n d in g o f the c o n cep t o f v a lid ity in subjects o f these e x p erim e n ts. H o w ev e r, P o llard a rg u es th a t a n u n d e rs ta n d ­ ing o f v a lid ity is o f little p ra c tic a l use. It w o u ld only be o f v a lu e in real life if one co u ld e v a lu a te th e p rem ises o f a n a rg u m e n t m ore easily th a n its c onclusion. T o p u t his a rg u m e n t in to perspective, how ever, one m u st recall th a t belief-bias effects in syllogistic re a so n ­ ing are relatively w'eak w h en c o m p a red w ith , say, a tm o sp h e re /c o n ­ version effects. In a sense, th e in te rp re ta tio n o f c o n te n t a n d c ontext effects is fairly o bvious a n d stra ig h tfo rw a rd . O u r th o u g h t is g u id ed in w ays a p p ro p ria te to o u r p rev io u s ex perience, re la te d to th e m ate ria l. H ow ever, th is leaves a fu n d a m e n ta l p ro b lem unsolved. Is all th o u g h t a fu n c tio n o f specific experience? Is it n o m o re th a n g en ­ eralised lea rn in g , o r is th ere tru ly a n u n d e rly in g sy stem o f re aso n in g com petence, w h ich is c o n te n t in d e p e n d e n t, b u t m odified b y p e r­ form ance factors w hich a re c o n te n t d e p e n d e n t? T h e p ro b lem is th a t even the lea rn in g a p p ro a c h w ould lead one to ex p ec t a com m on factor o f p e rfo rm a n ce a cro ss situ a tio n s. T h is is b ecau se c erta in logical inferences (e.g. m o d u s p onens) w ill h old in all situ a tio n s a n d thus will h a v e been u n iv ersally lea rn ed . Since all re alistic reaso n in g tasks p e rm it the sugg estio n th a t su b jects a re g e n era lisin g le a rn e d responses, it can n e v er be estab lish e d th a t reasoning, in th e p h ilo ­ sophical sense, is o c c u rrin g a t all. All o f this lead s to th e view th a t it is m ost necessary' to stu d y a n d u n d e rsta n d w h a t h a p p e n s in abstract re aso n in g tasks - a fo rtu n a te conclusion, p e rh a p s, since m ost o f the e x p erim e n ts in th e lite ra tu re fall in to th is categ o ry . N ev erth eless, the conclusion is forced. I f m an has th e c a p a c ity to re aso n , as op p o sed to m ake le a rn e d responses, th en th is m u st m an ifest itse lf in p ro b lem a re a s w here he c an n o t m ake d irec t use o f p re v io u s ex perience. I t is, th en , to a c o n sid era tio n of such a b s tra c t task p e rfo rm a n ce th a t w e now tu rn .

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A b stra ct r e a s o n in g : n o n -lo g ic a l b ia s e s Several a p p a re n tly non-logical biases a p p e a r to affect a b s tra c t reasoning p e rfo rm a n ce , a n d it is obviously im p o rta n t to try to u n d e rsta n d th e ir origin. I f we a re to re ta in a n y n o tio n o f u n d e rly in g logical co m p eten ce, th en these biases m u st be ex p lain ed in on e o f tw o w ays: e ith e r they a re ta sk -d e p e n d e n t ‘p e rfo rm a n ce ’ factors, o r else a n illusion c rea te d by th e su b je c ts’ logical tre a tm e n t o f a m is­ in te rp re te d p ro b lem . T h is la tte r view , the H e n le h y p o th esis, w as considered a n d rejected as o v ersim plified in review ing th e w ork on syllogistic a n d p ro p o sitio n a l reaso n in g . W e will therefore explore the form er type o f e x p la n atio n . A g e n era l ten d en cy for su b je c ts’ th o u g h t to be influenced u n d u ly by fe a tu re -m a tc h in g processes h a s been observ ed . In th e W aso n selection task a n d in c o n d itio n al tru th -ta b le tasks, su b je cts ten d to focus a tte n tio n on the item s n a m e d in the p ro b lem se n ten ces, re ­ gardless o f th eir a c tu a l logical sta tu s . T h is ‘m a tc h in g b ia s’ is n o r­ m ally d e m o n s tra te d by m a n ip u la tin g th e presence o f n egative c o m p o n en ts in th e sentences. T h e ten d e n cy to focus o n th e n a m e d item , w h e th e r o r n o t it is n e g ated , c a n be re la te d to som e o f the psychological stu d ies o f neg atio n discu ssed in C h a p te r 3. B ecause negatives a re n o rm ally used to d e n y p re su p p o sitio n s a b o u t affirm ­ atives, a s ta te m e n t like ‘T h e le tte r is n o t A ’ is still psychologically a sta te m e n t a b o u t the le tte r A, r a th e r th a n the letters B to Z. W e are n o t accu sto m e d to th in k in g in term s o f negativ e classes o r events. W h e n task in stru c tio n s force us to d o so, th e n e x tra p sy c h o ­ logical difficulty is d e m o n s tra te d (cf. C h a p te r 2). F e a tu re -m a tc h in g ten d en cies, how ever, arise in o th e r contexts, w here they c a n n o t be a ttrib u te d to difficulties in u n d e rsta n d in g negatives. F o r e x am p le, th e ‘a tm o sp h e re effect’ in syllogistic infer­ ence (C h a p te r 6) a p p e a rs to d e m o n s tra te th a t su b je cts p refer to endorse c onclusions w h ich sh a re c o m m o n featu res w ith prem ises. O f course, th e a tm o sp h e re effect, th o u g h w ell su p p o rte d e m p irically , is highly c o n tro v e rsial. M a n y a u th o rs a ttrib u te the resu lts to illicit conversions, a lth o u g h th is h y p o th esis does n o t fare too well on a lte rn a tiv e p a ra d ig m s . F u rth e r evid en ce for featu re m a tc h in g com es from w ork on W a s o n ’s new T H O G p ro b lem (C h a p te r 10). It seem s th a t in tu itiv e e rro rs in d isju n ctiv e re aso n in g can re su lt from a fal­ lacious e x p ec ta tio n th a t m em b e rs o f the sam e c ateg o ry sh a re co m ­ m on features.

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O n e line o f e x p la n a tio n for these effects lies in th e d e v elo p m en t o f T versky a n d K a h n e m a n ’s (1973) h e u ristic -b ia s ‘a v a ila b ility ’ (see P o llard , 1979a for a d e ta ile d a p p lic a tio n to re aso n in g ). T h e ir use o f this concept, as m en tio n ed e arlie r, refers to the ease o f retriev al o f item s from m em ory. P o llard (1979a) used it also in th is sense w hen discussing biases affecting th e m a tic reaso n in g . W ith a b s tra c t reaso n in g , w h ere re le v a n t a re a s o f se m a n tic m em ory are n o t stim u ­ late d , how ever, P o llard su g g ested th a t th e p rim a ry d e te rm in a n t o f the elem ents av ailab le to th o u g h t are fe atu res o f the task itself. T h u s the m en tio n o f p a rtic u la r letters a n d n u m b e rs in a c o n d itio n al reasoning task in creases th e ir av ailab ility , re su ltin g in m atc h in g bias. S im ilarly , th e sy n ta c tic featu res o f syllogistic prem ises d e te r­ m ine th e a v ailab ility o f a lte rn a tiv e conclusions, p ro d u c in g an ‘a tm o sp h e re effect’. T h e fact th a t th o u g h t can be influenced in this w ay is s u p p o rte d by a n e x p erim e n t o f K u b o v y (1977) in w hich subjects h a d to g e n e ra te dig its b etw een zero a n d nine. I f su b jects are asked to sta te th e ‘first one-d ig it n u m b e r th a t com es to m in d ’, far m ore choose ‘o n e ’ th a n if asked to sta te th e ‘first d ig it th a t com es to m in d ’. T h e effect a p p e a rs to be u n conscious, how ever, in th a t if a p a rtic u la r n u m b e r is given as a n ex am p le o f a d ig it b etw een zero an d n in e, th en significantly few er choose th a t n u m b e r. M a tc h in g bias could, th e n , be th e re su lt o f a n u n c onscious resp o n se -p rim in g process. H o w ev er, the fact th a t a n item is m a d e a v ailab le to th o u g h t does n o t m ea n th a t it w'ill necessarily be selected. W h a t it does m ean is th a t a m ism atching item is less likely to be selected. T h is in te rp re ta tio n is q u ite co n sisten t w ith th e d a ta , a n d in fact on tru th -ta b le tasks m a tc h in g is n o rm ally m e a su re d by th e in cre asin g n u m b e r o f ‘irre le v a n t’ classifications (o r n on-selections) o f u n n a m e d item s. P o lla rd ’s (1979a) a p p lic a tio n s o f the a v aila b ility h e u ristic to o th e r reasoning d a ta a re also w o rth y o f a tte n tio n . C o n sid e r, for exam ple, the facilitation o f selectio n -task p e rfo rm a n ce o n p ro b lem s w here the test sen ten ce is believed to be false (P o llard , 1979a; P o llard a n d E vans, 1981; cf. C h a p te r 10). Since the T A -F C a sso ciatio n is a v ail­ able from prev io u s experience, w hile th e T A -T C a sso ciatio n is not, correct c o n se q u e n t selection is facilitated . W ith e x p erim e n tally train ed ex p erien ce on a n a b s tra c t task , P o llard (1979a) found th a t this bias co m p eted w ith m a tc h in g bias, a n d could only be d e m o n ­ stra te d by m a n ip u la tio n o f n egative c o m p o n e n ts to c ontrol the la t­ ter. H e re g a rd s th e lea rn ed a sso ciatio n a n d th e fe atu re -m a tc h in g

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tendencies as influences w hich co m b in e in th e d e te rm in a tio n o f the a v ailab ility o f card s. T h e fig u ral b ias o b serv ed on syllogistic re aso n in g tasks is ra th e r different (C h a p te r 6). H e re su b je cts d o n o t match featu res o f the task, b u t th eir th in k in g is n e v erth ele ss influenced by th e m a n n e r in w hich th e task in fo rm a tio n is p re se n te d . It a p p e a rs th a t su b je c ts’ th in k in g m oves in a d irec tio n d e te rm in e d by th e o rd e r in w hich item s a re p re se n te d in the p rem ises. All else bein g e q u a l, a c o n clu ­ sion w hose o rd e r o f item s is c o n g ru e n t w ith th eir a p p e a ra n c e in the p rem ises is likely to be p referred . A n o th e r non -lo g ical b ias th a t h a s been d e m o n s tra te d in c o n d i­ tional reaso n in g tasks is a p referen ce for n e g ativ e conclusions. T h e e x p la n atio n offered by P o llard a n d E v a n s (1981) is in line w ith the g eneral n o tion o f h e u ristic biases. It will be recalled (see C h a p te r 8) th a t in th e ir stu d y su b je cts w ere a sk ed to d e cid e w h e th e r o r not one c o n d itio n al sen ten c e w;as im p lied by a n o th e r. W ith th is tec h ­ niq u e, the e q u iv a le n t o f a n eg ativ e-c o n clu sio n bias is a preferen ce for en d o rsin g a sta te m e n t w ith a n e g ativ e c o n se q u en t. P o llard a n d E vans also fo u n d a p referen ce for e n d o rsin g sta te m e n ts w ith affirm ­ ative a n te ce d e n ts. T h u s , w ith logical v a lid ity c o n tro lled , th e re w as an overall b ias to say th a t sta te m e n ts o f th e form I f p then not q should be inferred from o th e r sta te m e n ts, w hile sta te m e n ts o f the form I f not p then q w ere least likely to be en d o rsed . P o llard a n d E v an s’s e x p la n a tio n o f th is fin d in g is a n alo g o u s to th e a p p a re n t e x p la n atio n o f belief-bias effects in th e m a tic reaso n in g . T h a t is, they supposed th a t, in ste a d o f m ak in g a v a lid ity ju d g m e n t, su b je cts are a tte m p tin g to e v a lu a te th e tru th o f the conclusion d irectly . T h e bias is, in fact, to w a rd s th e least falsifiable sta te m e n t. As P o p p e r (1959) p o in ts o u t, a c o n d itio n al is m o re falsifiable, the m ore g e n era l its a n te ce d e n t a n d th e m o re specific its c o n se q u en t. T h u s , th e sta te ­ m en t I f the letter is A then the number is not 4 c a n only be false w ith respect to o n e c o m b in a tio n , A4. O n th e o th e r h a n d th e s ta te m e n t I f the letter is not D then the number is 7 is false if a n y except o n e le tte r is p a ire d w'ith a n y ex ce p t one n u m b e r. T h u s P o llard a n d E v an s suggested th a t su b je cts a p p ly a c a u tio n h e u ristic , in w'hich c o n clu ­ sions a re re g a rd e d as safer if they c a n n o t easily be falsified. H a v in g e x am in ed som e possible cau ses o f n on-logical biases, we now c o n sid er th e ev idence for logical influences on p e rfo rm a n ce .

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The logical component T h e q u e stio n we m u st now ask is w h e th er, tak in g all these ‘p erfo r­ m an c e ’ factors in to a c c o u n t, th ere is still evidence o f som e u n d e r­ lying logical c o m p e ten c e. I t w ould be su rp risin g , not to say w orrying, if th e re w ere n o t su ch evidence. T h e v a rio u s stu d ies c o n d u cted by th e a u th o r a n d his colleagues hav e alw ays found evidence o f som e c o n sisten t re sp o n d in g to the logical s tru c tu re o f the task, w h en fe atu res eliciting non -lo g ical biases a re b a la n ce d the so-called ‘lo g ical’ o r in te rp re ta tio n a l c o m p o n e n t. I t is also su g ­ gested th a t th e logical a n d non-logical co m p o n e n ts co m b in e in a n a d d itiv e sta tistic a l m a n n e r. T h e form al m odel o f E v an s (1977b) h as been a p p lie d only to selectio n -task d a ta (see C h a p te r 9), a lth o u g h its gen eral stru c tu re is a ssu m e d to u n d e rlie p e rfo rm a n ce on o th e r con d itio n al re aso n in g tasks (see F ig u re 9.1). T h e a p p a re n tly parallel n a tu re o f th e tw'o c o m p o n e n ts will be c o n sid ere d in C h a p te r 12. O u r c oncern h ere is to try to see w-hether th is logical c o m p o n e n t reveals th e b asis o f a possible c o m p e ten c e system . In C h a p te r 8, th e ev idence for a com m on logical c o m p o n e n t un d erly in g inference a n d tru th -ta b le tasks w as assessed . T h e re w as evidence o n b o th tasks o f a ten d e n cy for su b je cts to tre a t a b s tra c t c o n d itio n als as e q u iv alen ces. T h e re also a p p e a re d to be a co m ­ petence to p e rfo rm M P a n d to ju d g e c o rrectly th a t T T verifies a n d T F falsifies th e rule. T h e a ssu m p tio n th a t m an y su b je cts tre a t the co n d itio n al as a n e q u iv a len c e ex p la in s th e relatively h ig h ra te o f AC inference a n d F T ‘false’ classifications. W h a t th is co m p eten ce a m o u n ts to is sim ply a n a b ility to su p p o se th e a n te c e d e n t a n d see th a t th e c o n se q u e n t is a necessary c onsequence. E v idence o f a b ility to m ake M T (or D A for th e converse ru le), w hich re q u ire s sim ila r reaso n in g , is none too good. T h e ‘logical’ c o m p o n e n t o f selectio n -task p e rfo rm a n ce (C h a p te r 10) ties in well w ith these conclusions. Follow ing P o lla rd ’s (1979b) rean alysis o f the E v an s (1977b) p a ra m e te rs, it becom es cle ar th a t subjects a re c o m p e te n t o nly in re aso n in g from a n te c e d e n t to c o n ­ seq u en t a n d n o t vice versa. O v e rall, a b s tra c t c o n d itio n al reaso n in g p erfo rm an ce in d ic a te s n o m ore th a n a superficial u n d e rsta n d in g o f the sentence I f p then q, a n d little ev idence o f an y d e p th o f reasoning. W ith d isju n ctiv e re aso n in g , e rro r ra te s a re very high on inference tasks involving n eg ativ e c o m p o n e n ts (T a b le 10.4), a lth o u g h su b jects are generally a b o v e c h an c e on tru th -ta b le e v alu atio n (T a b le 10.5).

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T h e a p p a re n t c o m p eten ce d e m o n s tra te d w ith affirm ative d isju n c ­ tives is n o t m an ifest on W a s o n ’s T H O G p ro b lem , b u t a rg u a b ly this is p ro b a b ly d u e to th e failure to g e n e ra te a n a p p ro p ria te h y p o th esis-te stin g stra te g y , ra th e r th a n a m is u n d e rs ta n d in g o f d is­ ju n c tiv e logic per se. T h e evidence for logical c o m p eten ce on syllogistic tasks is not good e ith e r. S u b je cts d o perfo rm q u ite well on valid syllogism s b u t not necessarily for the rig h t reasons. P o llard (1979a) h as p o in te d o u t th a t the g re a t m ajo rity o f valid syllogism s w ould be en d o rsed on th e ba sis o f a tm o sp h e re bias. H e suggests in fact th a t th e efficacy o f the b ias on v alid p ro b lem s m ay be a cause o f its in a p p ro p ria te a p p lic a tio n o n fallacious p ro b lem s. So fa r a s th e fallacious syllog­ ism s are co n ce rn ed , a su b s ta n tia l logical c o m p o n e n t can be inferred only if th e c onversion h y p o th esis is a cc ep te d . As we saw in C h a p te r 8, how ever, th is h y p o th esis does n o t g e n era lise across p a ra d ig m s . O n ly in P a rt I o f th e book h a v e th e p ro b lem s a p p e a re d to lie generally w ith in su b je c ts’ c o m p e ten c e, a lth o u g h e rro r ra te s c a n be q u ite high even on tran sitiv e inference (see, for e x am p le, D e Soto, L on d o n an d H a n d e l, 1965). T h e tasks involved d o n o t re q u ire subjects to u n d e rs ta n d form al logic. In C h a p te r 3, we looked at pro b lem s w h ere affirm ativ e a n d n e g ativ e sta te m e n ts n e ed e d to be ev alu ate d a g a in st evidence. In C h a p te r 4 we e x am in ed p e o p le ’s a bility to a rra n g e item s alo n g tra n sitiv e scales. In su ch stu d ies it a p p e a rs th a t su b je cts a re a b le to fo rm u la te successful stra te g ies, a lth o u g h som e p ro b lem s take c o n sisten tly longer to solve th a n others. In co m m o n w ith th e m ore com plex re aso n in g p ro b lem s, difficulty is influenced by task-specific fe atu res, c o n te n t a n d co n tex t. T h e effects a re p rin c ip a lly u p o n sp eed , ra th e r th a n acc u rac y , h o w ­ ever. W e will now m ove to som e g e n era l conclusions.

Conclusions In this c h a p te r, we hav e been co n ce rn ed w ith th e e x p la n a tio n o f reaso n in g -task p e rfo rm a n ce . It w as a rg u e d th a t su ch tasks sho u ld be re g ard e d as p ro b lem -so lv in g o r d e cisio n -m ak in g tasks, a n d view ed in th e c o n te x t o f th e g e n era l fram ew o rk o f su ch a p p ro a c h e s. C e rta in ly , th e idea th a t su b je cts c o n stru c t a n d se a rc h a p ro b lem space is a p p lic a b le to som e o f this w ork, a lth o u g h it is difficult to identify su b je c ts’ re p re se n ta tio n s. T h e d e cisio n -m ak in g a p p ro a c h

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h a s also p ro v e d u se fu l, e sp e c ia lly in th e n o tio n th a t d e c isio n s m ay be in flu e n c e d by h e u ris tic biases. In e x a m in in g re a so n in g p e rfo rm a n c e , w e in e v ita b ly need to be a w a re o f th e issu e o f lo g ic a lity a n d th e view s o f m a n y , in c lu d in g P ia g et, th a t in te llig e n t a d u lts possess a c o m p e te n c e for fo rm al logi­ cal re a so n in g . S u c h c o m p e te n c e , on th e basis o f e v id e n ce from re a so n in g e x p e rim e n ts , is s u rp risin g ly - n o d o u b t to so m e - dep re ssin g ly lac k in g . A ll th e e v id e n ce p o in ts to c o n te n t-d e p e n d e n t th o u g h t p ro c esses o n th ese task s. W ith th e m a tic c o n te n t, p rio r p re ju d ic e a n d b e lie f in flu e n ce s ju d g m e n t; logical b e h a v io u r is e n ­ h a n c e d or in h ib ite d a c c o rd in g to c o n te x t. A b s tra c t-re a s o n in g task p e rfo rm a n c e is m a rk e d by th e in flu e n ce o f task fe a tu re s , in a m a n n e r w h ich is in d e p e n d e n t o f th e ir logical sig n ific a n ce . B o th th e c o n te n t a n d d ire c tio n o f th o u g h t p ro c esses a p p e a r s to be h ig h ly s tim u lu sbound. T h e r a tio n a lis t a p p ro a c h to re a so n in g re se a rc h a p p e a rs to a rise from a priori beliefs a b o u t m a n ’s ra tio n a lity . I t is a rg u e d th a t we c o u ld n o t h a v e evolved o u r c iv ilisa tio n w ith o u t o u r a b ility to re aso n . O u r in te llig e n c e is d e m o n s tra b ly p ro v e n . W h e n I s ta rte d m y re ­ se a rc h in to re a so n in g , my ow n view s w e re sim ila r. W h a t c h a n g e d m y m in d , from th e e a rlie st e v id e n c e o f re sp o n se b iases in m y ow n e x p e rim e n ts, w a s th e s h e e r w e ig h t o f ev id e n ce . I still believ e m a n to be a h ig h ly in te llig e n t, a d a p tiv e sp ecies, so how sh o u ld the p a ra d o x be reso lv ed ? I m u st h e re a g re e w ith the v iew s o f A llp o rt (1980a; 1980b) w h o believ es th a t th e se a rc h for g e n e ra l p u rp o s e m e c h a n ism s by c o g n itiv e p sy c h o lo g ists is m isco n c eiv e d . I t is in the very n a tu r e o f c o g n itiv e p ro c esses, he a rg u e s, to be c o n te n t specific. C e rta in ly A llp o rt’s ra d ic a l su g g e stio n s a rc fully s u p p o r te d by th is review' o f re a so n in g re se a rc h . T h e p o sitiv e a s p e c t o f th e w ork o n re a so n in g is th a t it h a s p ro ­ v id ed c o n sid e ra b le e v id e n c e a b o u t th e n a tu r e o f th o u g h t p ro cesses. In th e n e x t a n d final c h a p te r , w e will c o n sid e r th e b ro a d e r im p li­ c a tio n s o f th e re se a rc h for th e p sy c h o lo g y o f th in k in g , w'ith p a r tic u ­ la r refe re n ce to th e p o ssib ility o f d u a l m e c h a n ism s o f th o u g h t.

Dual processes and beyond

In C h a p te r 9, the sugg estio n w as m ad e th a t tw o d istin c t types o f th o u g h t m ig h t be involved in selectio n -task e x p erim e n ts. F ro m early ‘th e ra p y ’ stu d ies, it a p p e a re d th a t th ere w as a re m a rk a b le degree o f in d ep e n d en c e b etw een th e p rocess o f selectin g c a rd s a n d the verb al e v alu atio n s o f p ossible selections offered by th e subjects. S im ilarly, W aso n a n d E v an s (1975), a n d E v an s a n d W aso n (1976), found th a t v e rb a l ju stific a tio n s o f selections w ere rationalisations, ra th e r th a n a c c u ra te e x p la n a tio n s o f selection p e rfo rm a n ce . T h is led to a theory o f d u a l th o u g h t processes w hich h a s b ro a d im p li­ cations, not only for th e psychology o f reaso n in g , b u t for cognitive theory in g e n era l. T h e a p p lic a tio n o f the theory to re aso n in g d a ta has b een revised re ce n tly (E v an s, 1980a; 1980b), b u t we will first c o n sid er the o rig in al W aso n a n d E v an s (1975) version.

The Wason and Evans theory of dual processes W ason a n d E v a n s (1975) p ro p o se d th a t c a rd selections - a n d m ore g enerally re aso n in g responses - a re u n co n scio u sly d e te rm in e d . T h e processes re sp o n sib le a re labelled ‘T y p e 1’ by E v an s a n d W aso n (1976). W h en a su b je ct is asked to ‘in tro s p e c t’ a n d gives a verb al e x p la n atio n o f his p e rfo rm a n ce , th en a ‘T y p e 2 ’, v e rb a l ju stific a tio n is involved. T h e th eo ry , a s sta te d , w as p rin cip ally c o n ce rn ed w ith the e x p la n a tio n o f d isc re p a n c e b etw een p e rfo rm a n ce a n d in tro sp e c ­ tion. T h u s, it w as assum ed: (1) T h e processes u n d e rly in g th e re aso n in g p e rfo rm a n ce , e.g. m atc h in g bias, a re n o t g en erally a v a ila b le for in tro sp ec tiv e re p o rt. 234

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(2) In tro sp e c tiv e re p o rts o f p e rfo rm a n ce reflect a ten d en cy for the subject to construct a ju stific a tio n o f his ow n b e h a v io u r c o n sisten t w ith his know ledge o f th e situ atio n . W ason a n d E v an s a re a rg u in g here for a rev ersal o f com m on-sense th in k in g in w hich in tro sp ec tio n s a re a ssu m e d to reveal the causes o f b eh av io u r. T h e y a rg u e th a t it is th e b e h a v io u r w hich d e te rm in e s the n a tu re o f th e in tro sp ec tio n . T h e su b je ct, in effect, is a n sw e rin g the q u e stio n ‘G iven w h a t I d id , a n d th e n a tu re o f th e task an d in stru ctio n s, w h a t is th e best e x p la n a tio n o f m y b e h av io u r? ’ In labelling this ‘ra tio n a lis a tio n ’ we seem to hav e b een m isu n d ersto o d as d e n ig ra tin g o u r su b je cts (see, e.g. Fellow s, 1976). In fact, these v e rb alisatio n s p ro v id e th e best ev idence o f a b ility to reason w hich has been observ ed o n re aso n in g tasks. In sp e ctio n o f the p rotocols qu o ted in C h a p te r 9 rev eals d istin c tly logical th o u g h t. If, on a given task, th e su b je c ts’ b e h a v io u r is logically co n sisten t w ith falsifying the rule, th en they e x p la in it in such term s. I f it is co n sisten t w ith verification, they e x p la in it likew ise. T h e p uzzle is th a t if subjects possess su c h c ap a city for logical reaso n in g , w hy d o they n o t use it to m ake th e c o rre c t re sp o n ses in the first place? W e shall re tu rn to this p o in t in d u e course. I f th e W a s o n /E v a n s view o f in tro sp ec tio n can be gen eralized , then it h a s im p o rta n t im p lica tio n s. M u c h resea rc h in social science is based o n th e c o m m o n -sen se a ssu m p tio n th a t peo p le can identify causes o f th e ir ow n b e h av io u r. Is it, in fact, v alid to ask people why they m a d e c e rta in d ecisions, such as to vote for a political p a rty , o r to live in a p a rtic u la r d istric t? Is th e re a n y reaso n to su p p o se, in gen eral, th a t w e a re n o t a w a re o f the basis o f o u r decisio n -m ak in g , b u t are a d e p t in c o n stru c tin g post hoc ex p la n atio n s? T h e p ro b lem s o f in te rp re tin g in tro sp ec tiv e re p o rts h a v e a lre ad y been m e n tio n e d in th e c o n te x t o f v isu al im ag ery (C h a p te r 2; see also E v an s, 1980b). I t is p e rtin e n t to th is discu ssio n , how ever, to look beyond the b o u n d a rie s o f cognitive psychology. N isb e tt a n d W ilson (1977; see a lso N isb e tt a n d R oss, 1980) hav e la u n c h e d a m ajo r th eo re tic al a tta c k o n th e use o f in tro sp ec tiv e re p o rts by cog­ nitive social psychologists. T h e ir a rg u m e n ts p arallel those o f W aso n an d E v an s in tw o respects: (i) they look a t su b je c ts’ re p o rts on tasks w here the a c tu a l c a u sa l factors hav e been d e te rm in e d e x p eri­ m en tally , a n d c o n clu d e th a t th e su b je cts a re n o t aw-are o f th em , (ii) they a rg u e th a t th e re p o rt p ro d u c e d is a co n seq u en ce o f the su b je c ts’

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a tte m p t to e x p la in th e ir ow n b eh av io u r. T h e y suggest th a t the subject is th eo risin g a b o u t his b e h av io u r, in a sim ila r m a n n e r to the ex p erim e n ter. H e may give the c o rre c t e x p la n a tio n , if he has the rig h t theory, b u t not b e ca u se he h as w h a t R yle (1949) term ed ‘p riv i­ leged acc ess’ to p riv a te m en ta l processes. It is a p p ro p ria te in this con tex t to rep ly to a criticism o f m y ow n, very sim ila r, p o sitio n offered by Fellow s (1976). H e claim ed th a t ‘I f E vans dism isses th e su b je c t’s re p o rts as ra tio n a lisa tio n s, then logically he m u st also dism iss his ow n e x p la n a tio n s in th e sam e w av.’ H e is q u ite rig h t to infer th a t one m u st eng ag e in T y p e 2 thinking in o rd e r to w rite the d iscussion o f a n e x p e rim e n ta l p a p e r. In a sense it is a ra tio n a lisa tio n , in th a t one is try in g to c o n stru ct an e x p la n atio n to m ak e sense o f th e resu lts. T h e re aso n th a t the a u th o r is m o re likely to g et it rig h t th a n th e su b je ct is th a t he has access to in fo rm a tio n th a t th e su b ject does not. T h e su b je ct does not have a tra in in g in e x p e rim e n ta l psychology, a know ledge o f the relev an t lite ra tu re o r a n u n d e rsta n d in g o f the n a tu re a n d p u rp o se o f the e x p erim e n tal design. In this c o n te x t it is the e x p erim e n ter, n o t the su b je ct, w ho enjoys p rivileged access. S m ith a n d M ille r (1978) criticise N isb e tt a n d W ilson (1977) on the g ro u n d s th a t the su b je cts w'ere d e n ie d access to in fo rm a tio n they w ould need to assess the c au se o f th eir b e h av io u r, e.g. the e x p erim e n tal tre a tm e n t offered to o th e r su b jects. In view o f the above p o in ts th is c riticism is so u n d , if th e q u e stio n o n e is in te re ste d in is w h e th e r peo p le n o rm ally know' th e cause o f th e ir b e h av io u r. I t does n o t, o f course, affect th e a rg u m e n t th a t su b je cts h a v e no d irect access to th e ir m e n ta l processes. T h e view' tak e n h e re, a n d by N isb e tt a n d W ilson, is sim ila r to th a t expressed by R yle (1949), ‘o u r know ledge o f o th e r people a n d ourselves d e p e n d s u p o n n o ticin g how they a n d we b e h a v e .’ In m y view it is im p o rta n t to d istin g u ish tw o types o f in tro sp ec tiv e re p o rt. I believe th a t su b je cts a re a b le , to som e e x te n t, to m ake phenomenal reports, i.e. to re p o rt w h a t they a re experien cin g . W h a t they c a n n o t d o is to re p o rt the process o r stra te g y u n d e rly in g th eir b eh av io u r. T a k e , for e x am p le, th e p h e n o m e n o n o f size con stan cy . U nless they hav e stu d ie d e x p e rim e n ta l psychology, p e o p le will not be aw are o f th e fact th a t objects a re p h e n o m e n ally en la rg ed to c o m p en sate for th eir d ista n c e . W h a t they are a w are of, a n d can re p o rt, is how big they look. I t is th e product, r a th e r th a n th e process, o f size co n stan c y th a t is a v ailab le to in tro sp ec tio n .

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N isb e tt a n d W ilson m ake a sim ila r d istin c tio n w hich is d isp u te d by S m ith a n d M iller (1978), w ho cite as an e x am p le N ew ell a n d S im on’s (1972) c ry p ta rith m e tic p ro b lem s, in w'hich su b je c ts’ v e rb al re p o rts a p p e a r to reveal th e p rocess o f th o u g h t bein g used. I w ould argue w ith th is ex am p le, how ever, since I d o n o t believe th a t the ‘th in k in g a lo u d ’ p rotocols used by New'ell a n d Sim on a re th e sam e th in g as in tro sp ec tiv e re p o rts (see also B yrne, 1977). N ew ell a n d S im on’s task is as follows: DONALD + GERALD D = 5 ROBERT T h e su b je ct has to decid e w hich d ig it is re p re se n ted by each le tte r in o rd e r to m ake a legal sum . N ow , it is tru e th a t th e su b ject ‘th in k in g a lo u d ' does tra c e a fairly c le ar p a tte rn o f his th o u g h t process. H ow ever, th is is n o t in tro sp ec tio n . T h e p o in t a b o u t a p ro b lem like this is th a t it b re ak s do w n in to a series o f su b -p ro b le m s, each o f w hich is solved by a su b -p ro cess. F o r ex am p le, p rocessing the last c o lu m n , w ith the in fo rm a tio n th a t D = 5, will quickly lead to the conclusion T = 0. T h e fact th a t the su b je ct can say this is hard ly re m a rk a b le - m an y pro b lem -so lv in g processes p ro d u c e a verbal o u tp u t. I t is like ask in g som eone to sta te th e so lu tio n o f an an a g ra m . It is not, how ever, like ask in g th em to e x p la in how they solved the a n a g ra m . T h a t, if it w ere possible, w ould be intro sp ectio n . In brief, p ro b lem s o f th e so rt stu d ie d by N ew ell a n d Sim on a re am e n ab le to stu d y by th in k in g a lo u d pro to co ls, since they a re co m ­ posed o f a n u m b e r o f su b -p ro b le m s w hich have verb al o u tp u ts. R ecording the o u tp u ts o f su ch in te rm e d ia te stages facilitates the co n stru ctio n o f a n o verall p ic tu re o f th e pro b lem -so lv in g process. If, how ever, a th o u g h t pro cess h a s no in te rm e d ia te stages w'hich p ro d u ce v e rb al o u tp u ts , th en the tec h n iq u e will n o t be helpful. I strongly su sp ect th a t selectio n -task responses com e in to th is c a t­ egory. I once ra n a n e x p e rim e n t in w hich su b je cts w ere asked to think alo u d p rio r to m ak in g th e ir choices on the W aso n selection task. T h e e x p e rim e n t h a d to be a b a n d o n e d , since su b je cts sim ply could n o t com ply w ith th e in stru ctio n ! T h e d iscu ssio n to d a te h a s focused m ain ly o n the issue o f in tro s­ pective access to cognitive processes. I f people d o n o t have such access, why d o they p ro d u c e a ra tio n a lisa tio n (W aso n a n d E vans)

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o r a p p ly a cau sal th eo ry to th e ir ow n b e h a v io u r (N isb e tt a n d W il­ son)? W h y d o su b je cts n o t sim ply sta te th a t they d o not know ? W ason a n d E v an s im p ly th a t su b je cts a re m o tiv a te d to c re a te a n illusion o f ra tio n a lity . S u b je cts c onvince them selv es th a t th ey a re in control o f th e ir b e h a v io u r a n d know w hy th ey h a v e d o n e things. P e rh a p s peo p le h av e a need to e x p la in th e ir o w n b e h av io u r. T h e ‘cognitive co n sisten c y ’ th eo ries o f social psychologists w ould su p p o rt such a view , in th a t peo p le a re seen to be m o tiv a te d to g e n era te in te rn ally co n sisten t e x p la n a tio n s o f th e w o rld , in c lu d in g th e ir ow n b e h a v io u r in it (see Z ajo n c, 1968). H o w ev er, in th e m o re recently fashionable a ttrib u tio n theory, m o tiv a tio n a l co n ce p ts a re de-em phasised (e.g. K elly, 1967; 1972). I t could be th a t su b je cts c o n stru c t e x p la n atio n s (or m ak e c a u sa l a ttrib u tio n s) to e x p la in th e ir b e h a v ­ iour, sim ply b e ca u se th e e x p e rim e n te r has re q u ire d th em to d o so. T h e fact th a t one asks th e su b je ct to e x p la in th is b e h a v io u r im plies th a t he o u g h t to be a b le to d o this. I t w ould be a b ra v e su b je ct w ho refused to com ply. T h e W aso n a n d E v an s d u a l process th eo ry is n o t, how ever, in ­ ten d ed sim ply as a c ritiq u e o f in tro sp ec tio n . T h e suggestion is th a t the th o u g h t processes u n d e rly in g decision (T y p e 1) a re q u a lita tiv e ly d istin c t from those g e n e ra tin g v e rb al a c c o u n ts (T y p e 2). T y p e 2 processes d o n o t sim ply g e n e ra te in tro sp ec tiv e re p o rts. T h e y are also seen as resp o n sib le for v e rb al e v alu atio n s o f the conseq u en ces o f selections. F u rth e r ev idence for d u a l processes is found in a n in d u ctiv e re aso n in g task orig in ally fo rm u la te d by W aso n (1960). Subjects a re told th a t th e e x p e rim e n te r h a s a ru le in m in d w hich classifies tria d s o f dig its. T h e y are told th a t 2 4 6 com plies w ith the rule, a n d asked to g e n e ra te o th e r tria d s in o rd e r to disco v er w h a t the rule is, a n d only to a n n o u n c e th e ru le w hen th ey a re su re o f being rig h t. T h e e x p e rim e n te r sim ply tells th e su b je ct if e ach tria d conform s to th e ru le o r n o t. I f the su b je ct a n n o u n c e s a w ro n g rule, he is asked to c o n tin u e. T h e a c tu a l ru le is ‘an y a sc en d in g se q u e n c e ’. T h e e x am p le given 2 4 6, d e lib e ra te ly c rea te s a m isle a d in g set to ex p ect a m o re specific rule. Since su b je cts ten d to ex am in e only positive ex am p les o f th eir c u rre n t hy p o th eses, th ey find it h a rd to e lim in a te th em (see W aso n , 1968; a n d for th e m ost re ce n t stu d y T w e n ey et al., 1980). T h e in te restin g asp e ct from o u r p o in t o f view is th a t m an y su b jects p ersist in g e n e ra tin g in stan c es from th e sa m e rule, d e sp ite bein g

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told th a t th e ir v e rb a l a n n o u n c e m e n t is w rong. T h e y th en a n n o u n c e ‘o th e r’ rules th a t a re a c tu a lly re fo rm u latio n s o f th e sa m e one. F or e x am p le, one o f W a s o n ’s (1960) su b jects g e n e ra te d tria d s such as 2 6 10 a n d 1 50 99 a n d a n n o u n c e d th e rule: The rule is that the middle number is the arithmetic mean o f the other two. O n being told th a t th is w as w rong, she g e n e ra te d 3 10 17 a n d th en a n n o u n ce d : The rule is that the difference between two numbers next to each other is the same. O n being told th a t th is w as w'rong, she tested a fu rth e r tria d a n d th en a n n o u n c e d : The rule is on adding a number, always the same one, to form the next number. T h e fre q u e n t o c c u rre n ce o f such cases gives ev idence for d u a l processes. I t is su p p o sed th a t th e g e n era tio n o f tria d s is co n tro lled by a T y p e 1 pro cess, a n d th e v e rb al fo rm u la tio n o f rules by a T y p e 2 process. T h e re is a close an alo g y h ere to th e se lec tio n / e v alu atio n -p ro ce ss d istin c tio n o n th e selection task. T h e re is also a clear ele m en t o f ra tio n a lisa tio n in th e ru le fo rm u la tio n s. T h e su b ­ je c ts d o n o t seem to be a w a re th a t they a re p e rsistin g w'ith th e sam e rule, a n d the a lte rn a tiv e fo rm u la tio n s w ould seem to m a in ta in the self-deception. T h e g e n era l co n clu sio n w o u ld seem to be th a t T y p e 2 processes arise w h e n ev e r a v e rb a l e x p la n a tio n is re q u ire d , w h e th e r o r not such a n a c c o u n t w o u ld be in te n d e d as a n in tro sp ec tiv e re p o rt. A ctual re sp o n ses o r decisions a re , how ever, seen as d e te rm in e d by T y p e 1 processes. T h e tw o processes a re in d e p e n d e n t, a lth o u g h the b e h av io u ral c o n seq u en ces o f a T y p e 1 p rocess m ay form a n in p u t to the T y p e 2 process.

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T h e r e v ise d d u a l p r o c e s s th e o r y In recen t p u b lic a tio n s, E v an s (1980a; 1980b) has revised a n d ex­ ten d e d th e d u a l p rocess th eo ry so m ew h at. F irstly , th e reference to T y p e 1 processes as u n c o n sc io u s a n d T y p e 2 processes as conscious has been rejected. I f by ‘u n c o n sc io u s’ o n e m eans n o n -in tro sp ec tib le, th en b o th processes a re u n conscious. T y p e 2 processes u n d e rlie so-called in tro sp ec tiv e re p o rts, b u t th ey a re not, them selves, re ­ p o rtab le. In s te a d , T y p e 2 processes hav e been c h a ra c te ris e d as verbal a n d T y p e 1 as non-verbal. T h is does n o t m ea n th a t T y p e 2 processes co n sist o f w o rd s, b u t m erely th a t th e ir fu n c tio n is to g e n era te v e rb al resp o n ses. B ecause su ch v e rb aliz a tio n s a p p e a r to be in d e p e n d e n t o f a sp ects o f decision processes, it is assu m e d th a t the T y p e 1 processes a re n o n -v e rb a l. T h e d istin c tio n im plies th a t th ere m ay be d isc rete cognitive system s o r m ec h an ism s from w h ich T y p e 1 a n d T y p e 2 processes o rig in a te. T h is d istin c tio n is c o m p lica te d by th e second revision o f the theory. In the W a s o n /E v a n s versio n , all reaso n in g resp o n ses w ere a ttrib u te d to T y p e 1 processes. In th e revised version, th e d u a l processes a re linked to th e E v an s tw o -facto r th eo ry o f reaso n in g . H ence, T y p e 1 processes a re c o n sid ere d to u n d e rlie th e n o n-logical response processes, su c h as m a tc h in g b ias, b u t a re not seen as resp o n sib le for th e lo g ic a l/in te rp re ta tio n a l c o m p o n e n t o f p e rfo rm ­ ance. T h is is a ttrib u te d in ste a d to T y p e 2 processes. In essence, th e revised th eo ry envisages T y p e 2 processes as a risin g from a v e rb a l-ra tio n a l sy ste m o f th o u g h t. O n a b s tra c t reaso n in g tasks, th is sy stem h a s only p a rtia l c o n tro l o f b e h a v io u r - g e n e ra tin g the ‘lo g ical’ c o m p o n e n t - a n d m u st c o m p e te w ith n o n -v e rb a l T y p e 1 processes w hich g e n e ra te th e n on-logical co m ­ p o n en t. T h e m a th e m a tic a l m odel o f E v an s (1977b) c an be seen as a form al d e sc rip tio n o f twro p a ralle l, c o m p e tin g processes (see F ig u re 9.2). T h e w e ig h tin g fa cto r a , in d ic a te s the b a la n c e b etw ee n th e tw o processes. I f a is in cre ased , for e x am p le, by use o f re alistic m a te ria ls, th en it is p ossible for p e rfo rm a n ce to com e m ain ly u n d e r the c o n tro l o f v e rb a l-ra tio n a l (T y p e 2) processes. A n a d v a n ta g e o f th is refo r­ m u la tio n o f th e th eo ry is th e a b ility to e x p la in p e o p le ’s a b ility to reason c o m p e ten tly , w hen d e alin g w ith p ro b le m a re a s w ith in th eir n o rm a l experience. In th e revised versio n , v e rb a lisa tio n s a re still seen as p rim a rily arisin g from T y p e 2 processes. T h e re is som e influence o f T y p e 1

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thin k in g as well, th o u g h as evidenced by th e 'se c o n d ary m a tc h in g b ias’ o b serv ed on th e W aso n selection task (cf. C h a p te r 9).

Dual processes: the broader context In the next section we will c o n sid er som e re sea rc h desig n ed to give e x p erim e n tal test o f th e revised d u a l pro cess th eo ry . F irst, th o u g h , we look a t som e o th e r id eas a n d w ork in th e psychology o f cognition w hich re la te to th e theory'. T h e s e stu d ies suggest som e a d d itio n a l h ypotheses a b o u t th e n a tu re o f th e d u a l processes w'hich c a n also be exam ined. T h e lite ra tu re in th e psychology o f th in k in g is littere d w ith d i­ chotom ies. O n e o f th e m ost fu n d a m e n ta l is the F re u d ia n d istin c tio n betw een th e p rim a ry a n d se c o n d ary process. P rim ary -p ro c ess th o u g h t is free associative, lad e n w ith im ag ery a n d c h a ra c te ris tic o f d re am s a n d fan tasies. T h e seco n d ary p rocess is re ality -b a se d , goal-d irected , p ro b lem -so lv in g th o u g h t. T h is ty p e o f d istin c tio n arises e a rlie r (in philo so p h y ) a n d la te r, in v a rio u s guises. A rtistic th in k in g is c o n tra ste d w ith scientific, crea tiv e th in k in g w ith problem -solving, d iv e rg e n t w ith co n v erg e n t, in sig h t w ith triala n d -e rro r, etc, etc. T h e m ere p ro life ratio n o f such d ich o to m ie s does n o t e stab lish the case for d isc rete m ec h an ism s, b u t th ere m ay be som e fire b e n e a th all this sm oke. T w o m o d e rn th eo ries o f th in k in g w o rth y o f a tte n tio n a re those o f N eisser (1963) a n d P aivio (1975). N eisser review ed v a rio u s dichotom ous classifications o f th o u g h t, su c h as those m en tio n ed above, an d c oncludes, ‘T h e c o m m o n core o f all th ese th eo re tic al d ich o to ­ m ies seem s to be th e d istin c tio n b etw een a relativ ely w e ll-ordered, easily d e sc rib a b le , a n d efficient th o u g h t process on o n e side, a n d superficially confused profusion o f activ ity on the o th e r.’ H e wre n t on to develop a th eo ry o f th in k in g b a se d on the an alo g y to in fo rm a tio n -p ro c essin g system s - a relatively novel p ro c e d u re at th a t d a te . In p a rtic u la r, he d rew on the d istin c tio n betw een se­ q u e n tia l a n d p a ralle l processes. H e d e sc rib e d seco n d ary -p ro cess th o u g h t as th e main sequence b u t su b je ct to th e influence o f parallel or m u ltip le ‘p re co n sc io u s’ processes. T h e m u ltip le processes w ere seen as resp o n sib le for in tu itiv e , crea tiv e a n d d iv erg e n t thinking. N eisser d id n o t explicitly specify th a t th e m ain seq u en ce is verbal in n a tu re , b u t ra th e r a sso c iated it w ith consciousness. H ow ever,

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‘conscious’ m en ta l a ctiv ities a re often defined by a sso c iatio n w ith lang u ag e, a n d it m ay be th a t it is th e p o te n tia l for v e rb alisatio n th a t N eisser h a d in m in d . T h is suspicion is su p p o rte d by his a sse rtio n th a t the effect o f ‘th in k in g a lo u d ’ e x p erim e n ts (cf. N eisser, 1963) is to re stric t th o u g h t to th e m a in process. Paivio (1975), in a d e v elo p m en t o f his d u a l c oding th eo ry o f m em ory (cf. C h a p te r 2), d e sc rib e d tw o system s o f th o u g h t w ith sim ilar fu n ctio n al c h a ra c te ris tic s to those o f N e isse r’s. H ow ever, he referred to verb al a n d im ag ery system s, ra th e r th a n to conscious an d preco n scio u s system s. H e defined the system s as follows: T h e im ag ery system is assu m e d to be specialized for p rocessing n o n v e rb al in fo rm a tio n in th e form o f im ages, th a t is m em o ry re p re se n ta tio n s c o rre sp o n d in g ra th e r d irec tly to co n cre te things. . . . T h e v e rb al sy stem , o n the o th e r h a n d is specialized for d e a lin g w ith a b s tra c t lin g u istic u n its, w'hich involve d isc rete, se q u en tially a rra n g e d in fo rm a tio n a l u n its th a t a re only in d irectly a n d a rb itra rily re la te d to th in g s, a c c o rd in g to the con v en tio n s o f lan g u a g e. S u ch fu n c tio n s d istin g u ish th e verb al system as a n a b s tra c t, logical m ode o f th in k in g , c o m p a re d to the co n crete, an alo g ica l m o d e th a t a p p a re n tly c h a ra c te riz e s im agery. T h e fu n c tio n al re la tio n to N e isse r’s th eo ry is seen in th e follow ing q u o ta tio n , ‘the im ag ery system is sp ecialized for sy n c h ro n o u s o r­ g a n iz atio n a n d p a ra lle l pro cessin g o f n o n -v e rb a l in fo rm a tio n w hereas v e rb a l processes involve se q u e n tia l o rg a n iz a tio n o f lin g u is­ tic u n its .’ P a iv io ’s v e rb a l system does seem to re la te th e W aso n an d E vans T y p e 2 process. C o n sid e ra tio n o f N e isse r’s a n d P a iv io ’s th eo ­ ries suggest tw o possible c h a ra c te ristic s o f T y p e 1 processes th a t we m ight look for - firstly they m ay be p a ralle l (m u ltip le , sy n c h ro n o u s), a n d secondly they m ay involve c o n cre te visual th in k in g (im ag ery ). F irst, th o u g h , I w o u ld like to in tro d u c e a fu rth e r id e a in to the discussion. T h e re is a n in cre asin g in te re s t in re sea rc h in to th e dif­ fe re n tia tio n o f fu n c tio n betw een th e tw o h e m isp h e res o f th e b ra in . T h e left h e m isp h e re (in rig h t-h a n d e rs ) is o f course specialised for lan g u ag e a n d speech. T h e re is in cre asin g evid en ce th a t cognitive processes o f a v e rb al n a tu re take place in th e left h e m isp h e re , a n d those o f a n o n -v e rb a l, in clu d in g visu al, n a tu re in th e rig h t h e m i­ sphere. S uch ev idence d eriv es from stu d ies o f p a tie n ts w ith ‘sp lit

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b ra in s ’, o r less d ra m a tic a lly w ith localised b ra in d a m a g e, a n d from ex p erim e n tal stu d ies o f n o rm a l su b jects (see C o h en , 1977). In the last category, it is often re p o rte d th a t p e rfo rm a n ce on a cognitive task is d e p e n d e n t u p o n th e h e m isp h e re to w hich the p ro b lem is initially p re sen te d . P re se n ta tio n to rig h t e a r, h a n d , o r visual h e m i­ sphere goes to the left h e m isp h e re, a n d vice versa. F or re ce n t ex­ am p les in p ro b lem -so lv in g a n d re aso n in g the re a d e r is referred to G olding, R eich a n d W aso n (1974), V a n D u y n e a n d S ass (1979) an d K a tz (1980). T h e evidence for d iscrete cognitive system s w ith such a c le ar a n a to m ic a l basis is q u ite ex citing a n d sh o u ld not be ignored sim ply b ecau se the re sea rc h is at su c h a n early stage. T h e possibility th a t P a iv io ’s im ag ery a n d v e rb al system s - a n d p e rh a p s T y p e 1 a n d T y p e 2 processes - a re located in the rig h t a n d left h em isp h eres respectively, m u st be seriously considered. T h e discussion in th is section leads to th e follow ing g e n era l co n ­ clusions. T h e id e a o f tw o d istin c t ty p es o f th o u g h t is not novel to the W a s o n /E v a n s d u a l process th eo ry (or its revision) b u t is co m ­ m on th ro u g h o u t th e lite ra tu re on th in k in g . T y p e 2 processes m ig h t be p a rt o f a system specialised for v e rb al, se q u e n tial th o u g h t a n d this m ig h t be localised in the left h em isp h e re. T h e n o n -v e rb a l, T y p e 1, system m ay be m u ltip le in n a tu re , a sso c iated w ith im ag ery a n d , p e rh ap s, located in th e rig h t h e m isp h e re o f the b ra in . W e m u st now ask w h a t ev idence th ere is th a t th e T y p e 1 a n d T y p e 2 processes, as defined in the re aso n in g c o n te x t, m ig h t possess som e o f these o th e r c h ara cte ristics.

Evidence for dual mechanisms O n e su g g estio n th a t has a risen is th a t T y p e 2 th o u g h t m ay be intrin sically se q u e n tial. T h is is su p p o rte d to som e e x te n t by the review o f e le m en tary re aso n in g tasks (P a rt I). Since those tasks are w ithin the su b je c ts’ co m p eten ce, it w ould be a ssu m ed in the revised theory th a t they a re e n tirely u n d e r the c ontrol o f T y p e 2 processes. In such cases, w'e found th a t se q u e n tia l stag e m odels g en erally gave a good fit to th e latency d a ta . T h e re is also evidence o f p a ralle l processing on tasks w h ere b e h a v io u r is strongly influenced by non-logical factors (a ttrib u te d to T y p e 1 processes). B oth E vans (1977b) a n d P o llard (1979a) have found c o n sid era b le evidence th a t responses o n th e a b s tra c t selection task a rc statistically independent.

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F or exam ple, k now ing th a t a su b je ct h as chosen T C does not help you to guess w h e th e r o r n o t he h a s also chosen F C . S im ilarly, Pollard a n d E vans (1980) have found little evidence o f c o rre latio n betw een su b je c ts’ p e rfo rm a n ce on different tasks o f re la te d logical stru c tu re . T h e fact th a t responses a p p e a r to be p ro b a b ilistic a n d in d e p e n d e n t (th o u g h not ra n d o m ) could well result from p a ralle l processing by a n in trin sic a lly in d e te rm in a te system . T h e second m ain h y p o th esis re la te s to the m o d ality o f the tw o processes. I t h as been p ro p o sed th a t T y p e 2 processes a re v e rb al an d T y p e 1 processes n o n -v e rb a l in n a tu re . P aivio’s w ork fu rth e r suggests th a t the T y p e 1 processes m ig h t be im a g e ry -re lated , a n d hence visual in n a tu re . Som e re ce n t e x p erim e n ts w'hich the a u th o r has d esigned in c o lla b o ra tio n w ith P. G. B rooks pro v id e evidence re le v an t to b o th these h y p o th eses. L et us consider, first o f all, the suggestion th a t T y p e 2 processes re su lt from a v e rb al cognitive system . W e ho p ed to d is ru p t selectively th e ‘lo gical’ c o m p o n e n t o f p e rfo rm a n ce (a ttrib u te d to T y p e 2 processes in the revised theory) by use o f a c o m p e tin g task o f a v e rb a l n a tu re . T h e in te rfere n c e task used - c o n c u rre n t a rtic u la tio n o f irre le v a n t v e rb al item s - w as suggested by th e re sea rc h o f H itc h a n d B addeley (1976). T h e y set ou t to test th e w o rk in g m em ory m odel o f B addeley a n d H itc h (1974) w hich is c om posed o f a c e n tra l executive a n d a n a rtic u la to ry loop. I f such a w’o rk in g m em o ry is used in reaso n in g , they a rg u e d , th en c o n cu rre n t in terferen ce tasks w hich affect its function sh o u ld d is ru p t re aso n in g p erfo rm an ce. T h e y used th ree co nditions:

C o n tro l N o in terferen ce A rtic u la tio n S u b jects w’ere in stru c te d to sp eak alo u d c o n tin u o u sly e ith e r digits (1 2 3 4 5 6 re p e a te d ) o r ‘th e th e the. . .’ w hile p e rfo rm in g the re aso n in g task. M em o ry S u b jects w ere p re se n te d w ith a different six d ig it n u m b e r to re p ea t o n e ac h tria l. T h is a d d s a s h o rt­ term m em o ry load to the c o n c u rre n t a rtic u la tio n task.

A ccording to B addeley a n d H itc h , c o n c u rre n t irre le v a n t a rtic u ­ latio n sh o u ld su p p re ss use o f th e a rtic u la to ry loop. A sh o rt-te rm m em ory load sho u ld fu rth e r in te rfere w ith the c en tra l executive.

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T h e ir re aso n in g task w as a sim p le v erification task, in w h ich s u b ­ jec ts h a d to m ak e tru e /fa lse ju d g m e n ts to p ro b lem s su c h as: A p reced es B

BA

T h e in te rfere n c e tasks d id n o t d is ru p t re aso n in g p erfo rm an ce, b u t they d id lea d to in cre ased laten cies, w ith m ea n s in the o rd e r control less th a n a rtic u la tio n less th a n m em o ry . H o w ev er, th e ir task w as very sim p le, a n d b o th they a n d we m ig h t ex p ect interferen ce w ith p e rfo rm a n ce o n m o re com plex c o n d itio n al re aso n in g tasks. From th e view p o in t o f th e revised d u a l p rocess th eo ry , th e H itc h an d B addeley in te rfere n c e tasks, b e in g o f a v e rb al n a tu re , sho u ld d isru p t the logical c o m p o n e n t o f p e rfo rm a n ce . R esp o n se-b ias effects - a ttrib u te d to a n in d e p e n d e n t n o n -v e rb a l system - sh o u ld n o t be d isru p te d . I f a n y th in g su ch effects sh o u ld have increased stre n g th since they h a v e less co m p e titio n from th e v e rb al system . (In term s o f the E vans, 1977b, m odel th is m ea n s a d ecre ase in th e w eig h tin g p a ra m e te r, a .) A series o f c o n d itio n a l-re a so n in g e x p e rim e n ts have been ru n by E vans a n d B rooks w ith g ro u p s o f su b je cts tre a te d u n d e r con tro l, a rtic u la tio n a n d m em o ry co n d itio n s. In all e x p erim e n ts ru les w ere used w ith all p ossible p e rm u ta tio n s o f n e g ativ e c o m p o n en ts: I f p then q, I f p then not q, I f not p then q, I f not p then not q. T h is e n ab les logical a n d non-logical c o m p o n e n ts o f p e rfo rm a n ce to be se p a ra te d (cf. C h a p te r 8). In E x p e rim e n t I a n inference task w as used in w hich n e g ativ e-co n clu sio n b ias is th e p re v ailin g n o n-logical te n d ­ ency. T h re e fu rth e r e x p erim e n ts em ployed tru th -ta b le e v alu atio n tasks, in w hich m a tc h in g b ias is th e m a in n on-logical effect. E x p erim en t I is re p o rte d by E v an s a n d B rooks (1981) a n d full re p o rts o f th e o th e rs a re in p re p a rtio n . T h e re su lts p re se n te d here are selected for th e ir relev an ce to the th em e o f this c h a p te r (see T a b le 12.1). A lth o u g h the freq u en cy d a ta hav e been a n aly se d in term s o f b o th logical a n d n o n-logical c o m p o n e n ts, th e d a ta show n in T a b le 12.1 (i) re la te to th e fo rm er a n aly sis only. T h e p re d ic tio n w as th a t th is logical p e rfo rm a n ce w'ould be in h ib ited by c o m p e tin g verb al tasks. In E x p e rim e n t I, th e ty p e o f inference (M P , D A , A C , M T ) p ro d u c e d a sig n ifican t m ain effect, sim ila r to th a t o b serv ed in previous stu d ies. I t d id not, how ever, significantly in te ra c t w ith groups. T h u s th e re is n o ev idence h e re th a t c o m p e tin g v e rb al tasks interfere w ith logical p e rfo rm a n ce .

246

Discussion T A B L E 12.!

Results o f the Evans and Brooks interference experiments

(i) R esponse frequencies All d a ta are a v era g ed across four c onditional rules in w hich th e presence an d a b sen ce o f n e g ated c o m p o n e n ts is p e rm u ted . Inference ra te (% o f a rg u m e n ts accepted) E x p erim en t I C A M

MP

DA

AC

MT

97 92 87

55 57 63

81 69 85

55 51 68

92

58

79

59

T r u th ta b le ev a lu a tio n (% c o rrect responses) In sta n ce

E x p erim en t II

C A M

V e rb al 93 79 83

Pictorial 97 82 90

95 8! 87

C A M

85 V erba! 88 68 71

90 Pictorial 91 90 82

90 79 77

76

87

T T as ‘tru e ’

T F as ‘false’

E x p erim en t I I I

T T as ‘tru e ’

In stan ce

C A

V e rb al Pictorial C o n g ru e n t In c o n g ru e n t 81 83 92 79_________ 85________ 83 80

T T as ‘false’

C A

84 88 V e rb al Pictorial C o n g ru e n t In c o n g ru e n t 73 77 92 60 73 88

85 82

67

75

90

81 74

Dual processes and beyond

247

E x p erim en t IV T T as ‘tru e’ 86 89 81

C A M (ii)

R esponse latencies (seconds) E x p erim ent E x p erim en t E x p erim ent E x p erim ent

K ey

T F as ‘false’ 80 81 78

I II III IV

C 8.58 8.38 7.11 11.11

A 6.13 6.96 6.59 9.32

M 11.62 9.05 -

12.03

C - C o ntrol - no interference A - C o n c u rren t articu latio n M - C o n c u rren t articu latio n w ith m em ory load

T h ese conditions w ere adm in istered to se p ara te groups in all experim ents.

In the o th e r th ree e x p erim e n ts, th e freq u en cy o f co rrect classifi­ c ations o f T T as ‘tr u e ’ a n d T F as ‘false’ w ere a n aly se d se p a ra tely . In E x p e rim e n t I I it c a n b e seen th a t p e rfo rm a n ce d id d ro p u n d e r b o th a rtic u la tio n a n d m em ory co n d itio n s, a n d the effect w'as sig­ nificant in b o th an aly ses. In E x p e rim e n t I I I w h en n o m em o ry g ro u p w'as ru n , p e rfo rm a n ce d ro p p e d u n d e r a rtic u la tio n in b o th a nalyses, b u t n o t significantly so. T h e re w'as no ev idence o f in te r­ ference in E x p e rim e n t IV . T h e significance o f the v e rb a l/p ic to ria l d istin c tio n in T a b le 12.1 (i) will be ex p la in ed late r. So far as the v erbal in te rfere n c e task s a re co n ce rn ed , th e o verall ev idence su g ­ gests th a t logical p e rfo rm a n ce m ay be affected, b u t th e effect is relatively w eak a n d u n re lia b le . In g e n e ra l, the u su a l non-logical biases w ere o b serv ed a n d , w ith th e ex cep tio n o f one o d d resu lt, w ere n o t affected by th e p re sen c e o f c o m p e tin g tasks. T h e lack o f interference w ith re sp o n se biases acc o rd s w ith the d u a l process pred ictio n s. Follow ing H itc h a n d B ad d eley (1976) we m ig h t, th en , expect to find interferen ce reflected in th e late n cy o f re sp o n d in g . T h e s e re ­ sults, su m m a rise d in T a b le 12.1 (ii), w ere m ost su rp risin g . In E x­ p e rim en ts I a n d I I , th ere w as a sig n ifican t m ain effect o f g ro u p s b u t the o rd e r w as a r tic u la tio n fa ster th a n co n tro l fa ster th a n m em ­ ory. B reak d o w n a n aly sis co n firm ed th a t th e u n ex p ec te d a cc ele ratio n

248

Discussion

o f solution tim es u n d e r a rtic u la tio n w as sig n ifican t re la tiv e to co n ­ trol. A lth o u g h the g ro u p s facto r w as n o t significant in E x p erim en ts I I I an d IV , the m ea n s w ere in the sa m e d irec tio n , a n d co n sisten tly so w hen bro k en do w n by v a rio u s c o n d itio n s n o t show n in T a b le s 12.1 (ii). T h e E v an s a n d B rooks e x p erim e n ts cause p ro b lem s for vario u s theories, n o t least for th e w orkin g -m em o ry m odel o f B addeley a n d H itch . A d d itio n a l v a ria b le s w ere in tro d u c e d in to E x p e rim e n t IV a n d o th e r e x p erim e n ts to test th e im p lica tio n s for th e ir m odel, b u t it w ould be a n u n ju stifia b le d iv ersio n to discuss th a t w ork in this context. T h e relative lack o f in te rfere n c e w ith logical p e rfo rm a n ce u n d e r a rtic u la to ry su p p re ssio n seem s also to cause p ro b lem s for the theory th a t a d u lt th o u g h t is based on in te rn a lise d speech (V ygotsky, 1962). W h a t th e a c c e le ra te d so lu tio n tim es suggest is th a t we a re in the h a b it o f su b -v o calisin g on such p ro b lem s, b u t th a t th is h a s little fu n c tio n al v a lu e a n d ten d s to slow us do w n . W h en im p licit a rtic u la tio n is su p p re sse d , w'e sp eed u p w ith little loss o f a ccu racy . I t m ay well be th a t th e effect is re stric te d to v e rb al p ro b lem s o f the sort involved in c o n d itio n al reaso n in g . N o evidence o f facilitatio n u n d e r a rtic u la to ry su p p re ssio n w as found in a n a g ra m -so lv in g in a fu rth e r e x p e rim e n t by B rooks. O n th e a n a g ra m task a m u ch sm a lle r p ro p o rtio n o f so lu tio n tim e is d ev o te d to re ad in g a n d pro cessin g v e rb al m ate ria l. W h ere does this leave the revised d u a l p rocess theory? T h e re is som e evidence o f a ten d e n cy for th e logical c o m p o n e n t to be affected relative to the n on-logical c o m p o n e n t, b u t the evidence is far from conclusive. I n p a rtic u la r, th e sp eed in g u p o f so lu tio n u n d e r c o n ­ c u rre n t a rtic u la tio n suggests th a t w h a te v e r it ‘su p p re ss e s’ is no t vital to th e re aso n in g process. W e c a n n o t dism iss th e th eo ry on the basis o f th is ev idence, how ever. I t m ay be th a t th e v e rb al system - o r th a t p a rt o f it c o n n ec te d w ith re aso n in g - is in d e p e n d e n t o f a rtic u la to ry processes per se. W h a t o f th e sugg estio n th a t T y p e 1 processes m ay be re la te d to an im ag ery system ? T h e role o f im ag ery in re aso n in g h a s only received sy ste m atic stu d y in the stu d y o f tra n sitiv e inference. T h e conclusion o f C h a p te r 4 w as th a t th e re w as little good e vidence th a t im agery, in th e sense o f a visual in fo rm a tio n -p ro c essin g system , w as involved. P e rh a p s th is is ju s t as well if w e are to a ttrib u te the competent re aso n in g w hich o ccu rs o n su c h p ro b lem s to th e T y p e 2 system . By th e sa m e token, how ever, we m ig h t ex p ect som e o f the

Dual processes and beyond

249

non-logical facto rs fo u n d o n o th e r tasks to be im a g in al o r p e rc e p tu a l in n a tu re . It w as n o ted in th e p re v io u s c h a p te r th a t o n e o f the m ost fu n d a m e n ta l asp e cts o f n on-logical b e h a v io u r is th e u n d u e influence o f specific fe atu res o f th e task. In this c ateg o ry , ‘m a tc h in g b ia s ’, in p a rtic u la r, seem s re la te d to c o n cre te , p e rc e p tu a lly b a se d th o u g h t. T h e ten d e n cy for th o u g h t to be fixated on the item s n a m e d c ertain ly fits well w ith P a iv io ’s d istin c tio n , a n d m o re g en erally to th e idea th a t b e h a v io u r is u n d e r the influence o f a co n crete ra th e r th a n a b stra c t th o u g h t process. I f we ask w h e th e r o r n o t im ag ery is involved in syllogistic o r p ro p o sitio n a l re aso n in g , th e sim p le a n sw e r is th a t we d o n o t know , because n o e x p erim e n ts h a v e b een c o n d u c te d to find o u t. T h e fact th a t th e m a tic m a te ria ls m ay fa cilitate re aso n in g (cf. C h a p te r 9) is h a rd to in te rp re t in th is co n tex t. S o-called ‘a b s tr a c t’ m a te ria ls a re in a sense q u ite c o n cre te . F o r e x am p le, in W a s o n ’s (1969a) selection-task e x p e rim e n t, th e rules referred to co lo u red sh a p e s d ra w n on c ard s, w hich m ig h t be re g ard e d as highly im a g e ab le. T h e only w ork th a t h a s d e lib e ra te ly m a n ip u la te d a fa cto r re la te d to the v isu a l/v e rb a l is th a t o f E v an s a n d B rooks. In tw o o f th e tr u th tab le ex p erim en ts ( I I a n d I I I ) they v a rie d th e form in w hich th e in stan c e w as p re sen te d . T h u s , given th e rule: If it is n o t a tria n g le, th e n it is red, the F T case w as re p re se n te d to th e v e rb al g ro u p by th e w o rd s ‘red tria n g le ’ a n d to th e p ic to ria l g ro u p by a c o lo u re d d ra w in g d e p ic tin g a red tria n g le. T h e id ea w as th a t th e use o f p ic to ria l re p re se n ta tio n m ig h t e n co u ra g e th e use o f a visual o r im agery' code a s o p p o se d to the use o f a v e rb al code. T h is re la te s to P a iv io ’s (1971) e a rlie r su p p o sitio n o f d u a l m em o ry codes (see C h a p te r 2). W h a t p re d ic tio n s does th is entail? A c co rd in g to the d u a l process theory (e ith e r v ersion) m a tc h in g is a ttrib u te d to a T y p e 1 process. I f such a pro cess is re la te d to P a iv io ’s im ag ery sy stem , th e n any factor e n co u ra g in g use o f th is system sh o u ld in cre ase m a tc h in g responses. As in o th e r re sp ec ts, th e E v an s a n d B rooks d a ta w ere unex p ected a n d su rp risin g . T h e n o rm a l effects o f m a tc h in g bias w ere o b se rv ed , b u t d id n o t in te ra c t w ith th e v e rb a l-p ic to ria l p re ­ se n tatio n as p re d ic te d . H o w ev e r, in E x p erim en t I I , logical p e rfo rm ­ ance w as sign ifican tly improved w'hen th e in sta n c e w as picto rial ra th e r th a n v e rb al. It w as th o u g h t th a t th is re su lt m ig h t be artifac-

250

Discussion

tu al, since th e o rd e r o f reference to th e sh a p e a n d c o lo u r o f the figure is in c o n g ru e n t b etw een th e sen ten c e a n d in sta n c e in the verb al c o n d itio n (see above e x am p le). P re su m a b ly , w ith p icto rial p re se n ta tio n , th e su b ject can e x tra c t th e re le v an t featu res in an o rd e r d e te rm in e d by the sen ten ce. E x p erim en t I I I w as desig n ed to control for th is possibility. I t can be seen from T a b le 12.1 (i) th a t p erfo rm an ce w as a g a in b e tte r in the p icto rial c o n d itio n th a n v e rb al, w h e th e r o r no t the la tte r w as c o n g ru e n t. In the case o f th e T F analysis, th e su p e rio rity o f th e p ic to ria l c o n d itio n w as sta tistica lly significant. T h ese resu lts c o n tra s t w ith those em plo y in g a sim ila r tec h n iq u e on e lem en tary sen ten ce-v erificatio n tasks (cf. C h a p te r 3). In th a t context we noted th a t S e y m o u r (1975) d id n o t find e vidence o f d u a l coding, a n d fav o u red C la rk a n d C h a se ’s (1972) a ssu m p tio n o f a com m on a b s tra c t p ro p o sitio n a l code u n d e rly in g p e rfo rm a n ce o f such tasks. I f o u r v e rb a l a n d p ic to ria l d isp lay s wrere en co d ed in such a com m on form , how ever, th e differences we h a v e o bserved sho u ld n o t have a risen . T h e only w ay th a t a C la rk a n d C h a se type m odel could a c c o u n t for o u r re su lts is a t th e e n co d in g sta g e itself. T h ey w ould hav e to a ssu m e th a t m o re e rro rs o c cu r in c o d in g a verb al d e sc rip tio n th a n a p ic tu re in to its p ro p o sitio n a l re p re se n ta ­ tion. T h is e x p la n a tio n seem s r a th e r im p la u sib le , how ever, since the instances used - co lo u red sh a p e s - a re so sim ple th a t one w ould expect negligible c o ding e rro rs in e ith e r form . O n th e o th e r h a n d , if d u a l codes are a ssu m e d a n d th e e rro rs a rise a t th e processing stage, th en it m u st be a d m itte d th a t d ire c tio n o f effect is w rong. T h e final po ssib ility to e x am in e is th a t d u a l re aso n in g processes m ight re la te to h e m isp h e ric sp e c ia lisatio n . T h e re is som e evidence to su p p o rt this h y p o th esis. G o ld in g et al. (1974) found som e sugges­ tive evidence th a t evid en ce p re se n te d to th e left h e m isp h e re (via a rig h t-h a n d tac tile stim u lu s) w as m o re effectively used in a re aso n in g task, th a n w h en it w as p re se n te d to th e rig h t h e m isp h e re. M u c h m ore im pressive, how ever, a re som e re ce n t resu lts o f G o ld in g , in w hich the W aso n selection task w as a d m in iste re d to b ra in -d a m a g e d p a tie n ts. In the first stu d y she a d m in iste re d the task to p a tie n ts w ith e ith e r left- o r rig h t- h e m isp h e re lesions a n d to a c o n tro l g ro u p (G olding, 1981). W h ilst c o rre c t so lu tio n s wrere m in im al in th e left h e m isp h e re a n d c o n tro l g ro u p s, those w ith rig h t-h e m is p h e re d a m ­ age p erform ed significantly better. F o r ex am p le, selection o f the FC cards w as m ad e by 50 p e r cen t o f this g ro u p , as c o m p a re d w ith 0

Dual processes and beyond

251

p e r cent o f co n tro ls. 50 p e r cen t is well a b o v e the n o rm a l b a se ra te in e x p erim e n ts u sin g h e a lth y in te llig e n t a d u lts. In a second stu d y (G olding, 1980), she show ed th a t p a tie n ts wrho hav e the fu n c tio n o f the n o n -d o m in a n t (n o rm ally rig h t) h e m isp h e re tem p o rarily in ­ h ib ited by E C T also show a d ra m a tic a lly h ig h e r so lu tio n ra te th a n controls. T h ese re su lts obviously invite the inference th a t logical p e rfo rm ­ ance o n th e selection task is n o rm ally in h ib ite d by c o m p e tin g influ­ ences from th e rig h t h e m isp h e re - a c onclusion m o st h a p p ily in line w ith th e revised d u a l p rocess th eo ry . F u rth e rm o re , G o ld in g (1981) found th a t p a tie n ts choosing co rrectly in th e rig h t-d a m a g e d g ro u p w ere those w ho possessed a p a rtic u la r ty p e o f p e rc e p tu a l deficit. G olding, herself, sugg ests th a t th e c o m p e tin g re sp o n se th a t h a s been elim in ated is m a tc h in g bias. In view o f these resu lts W aso n a n d I recently d esig n ed a n e x p e rim e n t w ith B rooks, in o rd e r to see if sim ilar re su lts could be o b ta in e d w ith n o rm al su b jects. T h e task w as a m odified version o f th e selection task in w hich c a rd s w ere p resen ted in d iv id u a lly to e ith e r h e m isp h e re, a n d in w hich decisions w ere in d ic a te d by a key press w ith e ith e r left o r rig h t h a n d . B oth v a ria b le s affected re sp o n d in g w ith th e m o st strik in g re su lts a risin g from the la tte r. F o r e x am p le, w hen in d ic a tin g choices w ith th e left h a n d , su b je cts chose th e in co rre ct T C c a rd o n 44 p e r cen t o f oc­ casions a n d th e c o rre c t F C o n 46 p e r cen t o f occasions. W ith a forced choice (u n d e r tim e p ressu re) th is could be re g a rd e d as r a n ­ dom re sp o n d in g . W ith the rig h t h a n d , how ever, su b je cts chose T C on 29 p e r cent a n d F C on 68 p e r c e n t o f occasions - yielding a significant h a n d X c a rd in te ra c tio n . T h is looks like im p ro v ed logical p e rfo rm a n ce w ith rig h t h a n d (co n tro lled by left h e m isp h e re ). T h e re w as n o t, how ever, a c o rre sp o n d in g im p ro v e m en t in a n te c e d e n t se­ lections, a lth o u g h a g a in it w as only the rig h t h a n d th a t d isc rim i­ n a te d th e logical significance o f th e c ard s. R e sp o n d in g w as also significantly m ore re la te d to the logical stru c tu re o f the task w hen card s w ere p re se n te d to th e left h e m isp h e re (via th e rig h t visual hem ifield). T h e e x p e rim e n t d id n o t, how ever, pro v id e a n y evidence th a t m a tc h in g b ias is m ed ia te d by the rig h t h e m isp h e re. Possibly d u e to th e u n u su a l p re se n ta tio n o f th e task, th e n o rm a l m a tc h in g response w as n o t observ ed . T h e re is, th e n , som e evid en ce th a t selectio n -task p e rfo rm a n ce reflects c o m p e tin g processes a risin g from th e tw o h em isp h e res o f the b ra in . T h is is the best ev idence review ed in th is section to

252

Discussion

su p p o rt th e idea th a t d u a l processes on re aso n in g tasks reflect the o p e ratio n o f d istin c t cognitive m ec h an ism s. T h e co n n ec tio n w ith the v e rb al a n d im ag ery system s o f P aivio (1975) lacks c le a r su p p o rt in the E v an s a n d B rooks stu d y . H ow ever, e x p erim e n ts o f this so rt are n o t all th a t easy to in te rp re t, a n d it w ould c ertain ly be p re ­ m a tu re to dism iss such a co n n ec tio n w ith o u t fu rth e r research . T o search for u n d e rly in g m ec h an ism s on such com plex tasks is, p e r­ h a p s, ra th e r a m b itio u s, b u t it is surely im p o rta n t to m ake the a tte m p t. A final c o n sid era tio n is th a t th e q u a lita tiv e difference b e ­ tw een T y p e 1 a n d T y p e 2 processes is e stab lish e d by the kind o f evidence d e sc rib e d a t th e b eg in n in g o f th e c h a p te r. T h is evidence sta n d s, even if the se a rc h for u n d e rly in g m ec h an ism s sho u ld u lti­ m ately fail. T h e d istin c tio n is d irec tly a n alo g o u s to th a t discussed in P a rt I; in the im ag ery versus p ro p o sitio n s d e b ate. F o r e x am p le, the s tru c tu re o f th e im ag ery theory' o f tra n sitiv e inference w as su p ­ p o rted , d e sp ite th e lack o f evidence for a visual m ec h an ism o f re p re se n ta tio n . L ikew ise, it is a rg u e d th a t it is not ev idence for the existence o f d u a l processes w hich is o p en to q u e stio n , b u t ra th e r the evidence re la tin g to th e ir n a tu re a n d origin.

Overview and new directions In this final section, I shall a tte m p t to su m m arise the m ain c o n clu ­ sions o f the book as a w hole, a n d p o in t to som e d irec tio n s in w hich future re sea rc h m ig h t fruitfully develop. A t th e o u tse t (C h a p te r 1) it w as p o in te d o u t th a t a lth o u g h th e book w as in te n d e d to survey the c u rre n t sta te o f re sea rc h using re aso n in g tasks, it w as n o t sim ply a b o u t reaso n in g processes. In th e first place, the issue o f w h e th e r reaso n in g - in the sense o f logical, d e d u ctiv e th o u g h t processes actu ally occurs on such tasks w as seen as a n e m p irica l q u e stio n . Secondly, re aso n in g e x p erim e n ts w ere perceived as u sin g cognitive tasks sim ila r to pro b lem -so lv in g a n d d ecisio n -m ak in g talks, a n d liable to influence by th e sa m e k in d s o f factors. R e aso n in g research should, therefore, be view ed w ith in th e c o n te x t o f cognitive psy­ chology as a w hole. T h e issue o f ra tio n a lity , a n d th e se a rc h for som e k ind o f logical com petence, h a s been co n sid ered th ro u g h o u t th e book, a n d d is­ cussed in d e ta il in the last c h a p te r. T h e g e n era l c onclusion is th a t th ere is little ev idence o f an y im pressive c o m p e ten c e, w hile a w hole

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host o f p e rfo rm a n ce factors h a v e been identified. E ven on th e el­ e m e n tary re aso n in g tasks discu ssed in P a rt I, w h ich d o lie w ith in the su b je cts’ c o m p eten ce, th ere a re m a n y su c h p e rfo rm a n ce factors influencing th e latency o f resp o n d in g . T h e th eo re tic al m odels p ro ­ posed to a c c o u n t for su c h effects te n d e d to be h ig h ly p a ra d ig m specific - a p ro b lem e n c o u n te re d also in la te r p a rts o f the book. I believe th a t this reflects som e general p ro b lem s w ith cognitive ex­ p erim en ts. F irstly , th ey a re reactive, in th a t the a ct o f m e a su rin g a cognitive p rocess ten d s to exert a larg e influence on the process being ‘m e a su re d ’. T h e second pro b lem is a lack o f ecological validity. It is very h a rd to g e n era lise from th e re su lts o f a n y p a rtic u la r experim ent. I t is for this very reaso n th a t it is im p o rta n t to survey a large range o f re la te d p a ra d ig m s , as in the p re sen t book. O n ly in th is w ay can one h ope to a b s tra c t g e n era l features. F o r ex am p le, the se q u e n ­ tial re p re se n ta tio n a n d process m odel o f reaso n in g a d o p te d w ith som e success in P a rt I, c a n n o t be a p p lie d to m u ch o f the d a ta in P a rts II a n d I I I . O n e c a n n o t claim th a t, in general, people solve reasoning tasks by successive stages o f re p re se n ta tio n o f pro b lem in fo rm atio n in to a n a b s tra c t p ro p o sitio n a l code, follow ed by a p p li­ cation o f re aso n in g stra te g ies. A ll one c an say is th a t it is possible to m odel b e h a v io u r on some tasks w ith this kind o f a p p ro a c h . It has been su g g ested e a rlie r th a t re aso n in g e x p erim e n ts assess peo p le’s in tu itiv e u n d e rs ta n d in g o f logic, in th a t the c o n cep t o f logical a rg u m e n t is n o t e x p la in ed in th e in stru ctio n s. T h e e x p eri­ m en tal w ork on syllogistic (P a rt II ) a n d p ro p o sitio n a l (P a rt I I I ) reaso n in g , suggests e ith e r th a t people h a v e little such in tu itiv e u n ­ d e rsta n d in g , o r else th a t logical ten d e n cie s c o m p ete ra th e r b a d ly w ith v a rio u s n on-logical influences. P eople d o not seem to be aw are o f th e lack o f ra tio n a lity in th eir ow n b e h av io u r, how ever, ju d g in g from the d iscussion o f in tro sp ec tio n in th e e arly p a rt o f this c h a p te r. W h e th e r o r n o t they d e lu d e them selves in to believing th e ir b e h a v ­ iour to be ra tio n a lly d e te rm in e d , they d o seem to have deceived the a u th o rs o f m an y p a p e rs on re aso n in g in to j u s t su c h a belief. T h e evidence th a t u n d e rm in e s th e ra tio n a list p o sitio n arises a g ain from v a ria tio n s in th e n a tu re o f the p a ra d ig m s used. T h e se d e m o n s tra te non-logical b iases th a t c a n n o t be ex p lain ed by an y ra tio n a list sleight o f h a n d , a n d inco n sisten cies in the p e rso n al ‘in te rp re ta tio n s ’ o f sentences th a t a re su p p o sed to u n d e rlie p e rfo rm a n ce . E ven in the E vans tw o-factor a p p ro a c h , th e lo g ic a l/in te rp re ta tio n a l c o m p o n e n t

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th a t can be d iv in e d , w ith d u e a llo w a n ce for n on-logical factors, d e m o n stra te s (i) in co m p lete a w are n e ss o f logical p o ssibilities an d inferences a n d (ii) su sce p tib ility to ex tra-lo g ical factors, p a rtic u la rly o f a lin g u istic n a tu re . W e are forced to th e c onclusion th a t people m anifest little a b ility for gen eral d e d u ctiv e re aso n in g in th ese e x p erim e n ts. V e ry little b e h av io u r can be a ttrib u te d to a n a priori system th a t is in d e p e n d e n t o f th e p a rtic u la r task c o n te n t a n d stru c tu re . T h is does n o t m ean th a t peo p le c a n n o t re aso n c o rrectly in co n tex ts w h ere they have re le v an t a n d a p p ro p ria te ex p erien ce - indeed som e ev idence su g ­ gests th a t they c an . I t does m e a n , how ever, th a t a d u lts ’ re aso n in g a bility is far m ore c o n cre te a n d c o n te x t-d e p e n d e n t th a n h a s been generally believed. T h e p o sitiv e a sp e cts o f re a so n in g re se a rc h lie in th e v a rio u s p e r­ form ance factors th a t have b een id entified (see p re v io u s c h a p te r). O f these, th e m o st im p re ssiv e a re , p e rh a p s, th e lin g u istic a n d p ra g ­ m atic influences. R e aso n in g e x p erim e n ts p ro v id e som e o f th e m ost useful situ a tio n s in w hich to stu d y th e re la tio n betw een lan g u a g e a n d th o u g h t. W e hav e seen a n u m b e r o f ex am p les o f sy n ta c tic a n d c o n te x tu al facto rs w h ich hav e influenced re aso n in g p e rfo rm a n ce , a n d w h ich a re clearly in te rp re ta b le w ith in a p sy ch o lin g u istic fram e ­ w ork. I t is th e very context-specific n a tu re o f re aso n in g responses th a t b o th u n d e rm in e s th e ra tio n a list a n d gives su ch scope to the p sycholinguist. T h e p re v alen c e o f non -lo g ical facto rs a n d resp o n se biases, p a r­ tic u larly in a b s tra c t tasks, m ay be w o rry in g to som e re a d e rs. H o w ­ ever, if b e h a v io u r is c o n sid era b ly influenced by irre le v a n t task features, th en it is im p o rta n t to know this, lest th e d a ta be m isin ­ terp re te d in term s o f som e m ore g e n era l factor. P erso n ally , I feel th a t these biases a re o f c o n sid era b le in te re st in th e ir ow n rig h t. I n the p rev io u s c h a p te r, it w as p o in te d o u t th a t th e psychology o f decisio n -m ak in g a n d su b jectiv e p ro b a b ility h a s becom e increasin g ly concerned w ith ju d g m e n ta l biases, a n d th e a p p lic a tio n o f m o re o r less a p p ro p ria te h eu ristics. A n a tte m p t w as m a d e to view th e nonlogical biases o b serv ed on re aso n in g tasks in a sim ila r light. T h e fact th a t re aso n in g - a n d d e cisio n -m ak in g - processes a re often influenced by inappropriate h e u ristic s lead s to som e in te re s tin g q u e s­ tions. F o r ex am p le, w h e re d o su c h h e u ristic s o rig in a te; a re they lea rn ed in a c o n te x t w h e re they a re a p p ro p ria te , a n d th en tra n s ­ ferred to one w here they no lo n g er w ork?

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T h e final k in d o f issue to a rise in this book h a s been th e q u e stio n o f w h a t cognitive m ec h an ism s m ay u n d e rlie b e h a v io u r o n these tasks. In P a rt I, we discu ssed ev idence for the use o f d u a l m em ory codes, w ith p a rtic u la r reference to v isu al im ag ery . In th is c h a p te r, the evidence for possible d u a l m ec h an ism s u n d e rly in g q u a lita tiv e ly d istin c t fe atu res o f task b e h a v io u r h a s also been e x am in ed . In n e ith e r case has th e evidence proved conclusive, b u t in e ac h case sufficiently suggestive to en co u ra g e fu rth e r research . T h is type o f research is obviously a m b itio u s, w hen on e co n sid ers the difficulties e n co u n tere d in d e cid in g w h a t m ec h an ism s u n d e rlie m u ch sim p ler cognitive p h e n o m e n a , su c h as those o f sh o rt-te rm m em ory'. T h e m ethodology involved, e.g. in terferen ce tasks, also ten d s to be co m ­ plex a n d gives rise to p ro b lem s o f in te rp re ta tio n . F inally, th en , how can re sea rc h in to th e psychology o f reaso n in g usefully develop? M y suggestions a re very m u ch d e te rm in e d by the above conclusions. I see little p u rp o se , for ex am p le, in p u rsu in g the search for logical c o m p e ten c e, o r in a tte m p tin g to e x p la in p e rfo rm ­ ance in a n en tirely ra tio n a listic m a n n e r. O n c e th e n o n -ra tio n a l an d c o n te n t-d e p e n d e n t n a tu re o f th e b e h a v io u r is recognised, new d i­ rections o f resea rc h a re in d ic a te d . T h e re is m u ch th a t needs c la ri­ fication, p a rtic u la rly the o rig in o f n o n-logical biases, a n d the precise n a tu re o f c o n te n t a n d c o n te x tu al factors. I f we d o a b a n d o n th e se a rc h for com p eten ce, th en the ju stific atio n for the p a ra d ig m a p p e a rs to d im in ish . W hy give som eone a task o f a given logical stru c tu re if one can m ak e no g e n era l conclusions a b o u t p e o p le ’s a b ility to u n d e rs ta n d it? A c co rd in g to this discussion, there is little ev idence o f a g e n era l co m p eten ce to p erform a n y given inference. O n e m ay o r m ay n o t be ab le to d o so d e p e n d in g upon the linguistic form , the c o n te x t, the n a tu re o f p re v ailin g response biases, etc. I f re aso n in g e x p erim e n ts d o n o t elicit re aso n in g , in an a priori sense, th en w'hy b o th e r to d o th em a t all? I w ould a n sw e r these p o in ts as follows. F irst o f all, it h a s been necessary to engage in su c h re se a rc h in o rd e r to show th a t one cannot d e d u c e logical a b ility . W h en a field o f resea rc h becom es d o m in a ted by false a ssu m p tio n s, th en it is im p o rta n t th a t this be d e m o n stra te d . S econdly, these e x p erim e n ts h a v e pro v ed useful a n d in te restin g in o th e r respects. As sta te d e arlie r, the p a ra d ig m s have proved well su ited to the in v estig a tio n o f lin g u istic a n d p ra g m a tic factors. A lso, c e rta in re aso n in g tasks, n o tab ly th e W aso n selection task, have pro v ed to be very co nducive to the stu d y o f th o u g h t

256

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processes. I see no re aso n w hy su c h re sea rc h sh o u ld n o t c o n tin u e a n d develop, provided th a t th e e x p e rim e n te rs recognise the tasks for w h a t they a re - specialised p ro b lem -so lv in g o r d e cisio n -m ak in g tasks. Such reco g n itio n , how ever, h a s im p lica tio n s th a t go bey o n d the decline o f ra tio n a lism . I f re aso n in g e x p e rim e n ts a re specialised cog­ nitive tasks, th en th e ir resu its sh o u ld be re la te d th eo re tic ally to those from o th e r cognitive p a ra d ig m s . A lso, an y g e n era l h y p o th eses a b o u t cognitive processes o r m ec h an ism s sho u ld be assessed on o th e r tasks, w hich need n o t be d efined as d e d u ctiv e re aso n in g ex­ p erim en ts. In o th e r w ords, we sh o u ld be less co n ce rn ed w ith ex­ p lain in g p e rfo rm a n ce o n p a rtic u la r p a ra d ig m s , a n d m o re c o n cern ed w ith u n d e rs ta n d in g th e n a tu re o f th e c ognitive m ec h an ism s an d processes th a t u n d e rlie th em . F o r e x am p le, cognitive psychologists in terested in ju d g m e n ta l processes sh o u ld look a t a v a rie ty o f dif­ ferent p a ra d ig m s , in clu d in g those used by cognitive social p sy ch o l­ ogists (see N isb e tt a n d R oss, 1980). T h e d isa d v a n ta g e s o f lim itin g o n eself to a p a rtic u la r p a ra d ig m - o r class o f p a ra d ig m s - are tw o-fold. F irstly , on e is d e n ie d access to the know ledge a c c u m u la te d by o th e r re se a rc h e rs stu d y in g the sa m e processes by different m eans. Secondly, it is very difficult to tell w h ich a sp e cts o f th e d a ta are parad ig m -sp ecific, a n d w h ich in d ic a tiv e o f m o re g e n era l fe atu res o f the cognitive system u n d e r stu d y . M y re c o m m e n d a tio n s in this respect h a v e im p lica tio n s for th eo ry c o n stru c tio n , also. T h e c u rre n t vogue for c o n stru c tin g very' precise m odels to fit th e d a ta o f specified p a ra d ig m s (e.g. C la rk a n d C h a se , 1972) is n o t seen as very p ro ­ ductive. T h is exercise tells us m ore a b o u t th e tasks th a n the people w ho perfo rm th em . A t th e risk o f c o n d em n in g m y ow n efforts (cf. E vans, 1977b), I m u st say th a t th e c o n stru c tio n o f precise m odels is p re m a tu re , w h e n w e d o n o t h a v e a c le ar, g e n era l p ic tu re o f the o rg a n isatio n a n d fun ctio n o f cognitive system s. M o d el b u ild in g m ay even be c o u n te r-p ro d u c tiv e , in th a t th e elegance o f th e e x p la n a tio n d istra c ts us from th e all too severe lim ita tio n s o f th a t w hich is bein g explained. In essence, th e psychology o f re aso n in g involves th e stu d y o f processes d e riv e d from th e sam e cognitive system s th a t u n d e rlie the results o f o th e r cognitive re sea rc h . T h e co n cern w ith logic a n d ra tio n alism h a s c re a te d a n illu so ry iso latio n o f th e field. It is now tim e to perceive a n d p u rsu e re aso n in g re se a rc h in its c o rre c t con tex t, an d to recognise th a t th e o bjectives, m e th o d s, a n d in d ee d fu n d a -

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m e n ta l d iffic u lties, a re n o t p e c u lia r to th e field, b u t a re s h a re d by all p sy c h o lo g ists w h o seek to u n d e r s ta n d c o g n itio n .

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Name index

A dam s, M . J ., 66 A llport, D. A., 45, 48, 233 A nderson, J . R ., 14, 16-21, 23, 45, 68 Atw ood, G ., 20 A ustin, G. A., 30, 207

B acharach, V. A., 41 B addeley, A. D., 244-5, 247-8 Begg, I., 8S -5, 91 Bever, T . G ., 40 Bourne, L. E., 135, 137 Bower, G. H ., 14, 17 Bracewell, R. J ., 180, 182-3 B raine, M . D. S., 145, 148, 219, 222-3 Bree, D. S., 166, 169, 176 Brooks, L. R., 2 0 -2 , 60-1 Brooks, P. G ., 31, 40, 204, 206, 244-6, 248-9, 251-2 B runer, J . S., 30, 207 B ryant, P. E ., 65 Bucci, W ., 94-5 Byrne, R., 237

C am pbell, A. C ., 30 C a rp en ter, P. A., 26, 30, 39-42, 44, 47 C a rr, T . H ., 41 C arroll, J . M ., 40 C atlin, J ., 40 C eraso, J ., 89 C h a p m a n , J . P., 8 3 -6 , 88, 90-1 C h a p m a n , L. J ., 8 3 -6 , 88, 90-1 C h a p m a n , R. H ., 9 3 -4 C hase, W . G ., 26, 34, 36-44, 4 6 -7 , 250 C hom sky, N ., 12-14, 28-9, 54, 218, 222 C hristie, D. F. M ., 22 C lark, E. V ., 13-14, 33, 256

C lark, H . H ., 13-14, 26, 33-4, 36-44, 46-7, 54-61, 66-9, 202-3, 250, 256 C ohen, G., 62, 243 C ohen, M ., 29 C ooper, L. A., 15, 40, 46-7 C oppens, G., 169 C osterm ans, J ., 33 D avey, M ., 161, 182 D enny, P. J ., 8 3 -5 , 91 D e Soto, L. B., 5 2 -3 , 56-8, 6 0 -1 , 232 D ickstein, L. S., 86, 90-2, 94, 100—2, 104-5 D oherty, M . E ., 30 D onaldson, M ., 30, 220 E iferm ann, R. R ., 30 E nnis, R. H ., 222 E rikson, J . R., 94, 100 E v a n s ,J . St. B. T ., 6, 79-81, 124-34, 138, 140-2, 145-7, 149-50, 152, 155, 163-7, 170-80, 182-3, 185-6, 190, 192-3, 195-6, 198-200, 203-4, 207, 219-20, 225-6, 229-31, 234-8, 240, 242-6, 248-9, 252-3, 256 F alconer, W . A., 180, 182-3 Falm agne, R. J . , 4, 79 F eather, N. T ., 109 Fellows, B. J . , 60, 235-6 Filby, N ., 42 F illenbaum , S., 29, 151-4 Fischhoflf, B., 217 Flavell, J . H ., 221 Frase, L. T ., 99-101, 109 French, P. L., 67 Frick, F., 107, 109

273

274

N am e index

G a lan ter, E., 12 G alto n , F., 15 Geiss, M . C ., 151-2 Gilhooly, K . J . , 180, 182-3 G lushko, R. J . , 40, 46-7 G olding, E., 160-2, 243, 250-1 G oldm an-E isler, F., 29 G oldstein, S., 109 G oodnow , J . J ., 30, 207 G oodw in, R. Q ., 167, 169-71 G örden, R. L., 108 G ough, P. B , 26, 29 G reene, J . M ., 30, 32-3, 4 1 -2 , 47 G riggs, R. A., 64, 95-7 H andel, S., 52, 232 H arris, R. J . , 5, 151 H arriso n , C ., 161, 182 H ayes-R oth, F., 19 H enle, M ., 5, 79-80, 85, 92-5, 105, 108-9, 111, 124-5, 126-30, 144, 153, 155, 212, 215-16, 217, 219, 223, 226, 228 H idi, S. E., 180, 182-3 H iggins, E. T ., 59, 63, 6 7 -8 H ill, 130 H itch, G . J ., 244-5, 247-8 H ovland, C . I., 30 H u n te r, I. M . L., 51, 57-8 H u p et, M ., 33 H u tten lo ch er, J . , 53, 5 6 -7 , 5 9 -60, 62, 67-9 Inhelder, B., 220 Ja n is, I. L ., 107, 109 Jo h n so n , D. M ., 90 Jo h n so n -L a ird , P. N ., 13, 19, 29-31, 33, 51-3, 5 7 -9 , 68, 86, 93, 100, 102-5, 129, 137-8, 142, 147, 159-62, 165-7, 169-70, 180-3, 193, 197, 214, 222, 225 Jo n e s, N. K ., 40 Jo n e s, S., 26, 31, 39, 58-9 J u s t, M . A., 26, 31, 39-42, 44, 47 K a h n em a n , D ., 217-18, 229 K atz, A. N .} 243 K aufm an, B., 59 K aufm ann, H ., 109 Kellv, G . A., 3 Kelly, H ., 238 K ieras, D ., 20

K in tsch , W ., 13, 14 K la h r, D ., 65 K o d ro iT J. K ., 130 K osslyn, S. M ., 16-18 K ubovy, M ., 229 L ang, S., 58 Lee, W ., 4, 217 LefTord, A ., 109 L egrenzi, M . S., 181, 225 L egrenzi, P., 153-4, 181, 225 L eirer, V. O ., 89, 109-12 L em m on, E. J . , 115 L ichtenstein, S., 217-18 L ondon, M ., 52, 232 L unzer, G. A., 161, 182-3 L ynch, J . S., 163-4, 166, 170-1, 176-9 M c K e an , K . O ., 28 M anktelow , K . I., 147, 164, 180, 182-3, 199, 203-4, 208, 226 M arcu s, S. L., 135, 137, 144-5, 147-8, 154-5 M ayer, R. E., 4, 79 M eh ler, J ., 29 M etzler, J ., 15 M ichael, L. M ., 108 M iller, F. D., 236-7 M iller, G . A., 12, 13, 28-30 M illigan, L ., 59 M onaco, G . E., 5, 151 M organ, J . J . B., 107-8, 110 M o rto n , J . T ., 107-8, 110 M o sen th al, P., 61 M o sh m an , D ., 169 M oyer, R. S., 64 M y n a tt, C. R., 30 N eilsen, G ., 44 N eim ark, E. D ., 9 3 -4 N eisser, U ., 43, 241-2 Newell, A ., 69-70, 213-16, 223, 237 N ew stead, S. E., 124, 138, 141-2, 147, 149-50, 198-200, 203 N isb ett, R. E. Y., 235-8, 256 O ’B rien, T . C ., 130 O lson, D. R., 42 O sherson, D ., 222 O ste rm an , L. J . , 97 Paivio, A., 16-17, 19-20, 47, 61, 241-3, 249, 252

N am e index Paris, S. G ., 142, 199 Perchoncck, E ., 29 Perky, C . W ., 15 Pezzoli, J . A., 99-100 Phillips, W . A., 22 Piaget, J ., 65, 105, 130, 182, 2 2 0-1, 233 Pierson, L., 58 Pollard, P., 90, 131-4, 152, 175, 178-9, 183, 185-7, 196, 200, 220, 225-7, 229-32, 243-4 P om eranz, J . R ., 16-17 Popper, K ., 3, 42, 157, 230 Potts, G. R., 63-4, 6 6 -7 , 69, 95-7 P ribram , K . H ., 12 Provitera, A., 89 Pylyshyn, Z. W ., 16-20, 22, 60, 68 Q u in to n , G., 60 Reich, S. S., 243 R evlin, R ., 4, 79, 89, 109-12 Revlis, R ., 8 6 -9 , 105, 109, 111 R ichardson, J . T . E., 20 Riley, L. A., 65 Rips, L. J ., 135, 137, 144—5, 147-8, 154-5 Roberge, J . J ., 100, 130-1, 193-5, 197, 199, 201-2 Rollins, H ., 39 Ross, L., 235, 256 R oth, E. M ., 161 Ryle, G., 236 S althouse, T . A ., 20 Sass, E., 62-3, 69, 243 Savin, A. B., 29 Scholz, K . W ., 63-4, 6 6 -7 , 69 Schw artz, S. P., 18 Segal, S. J . , 15 Sells, S. B., 73, 79, 8 2 -4 , 91 Seym our, P. H . K ., 43, 45-6, 250 Shanck, R. C ., 13 S hapiro, B. J ., 130 Shapiro, D ., 160, 162, 180, 181-3, 226 Shaughnessy, E ., 39 S haver, P., 58-63, 69 S h ep ard , R. N., 15 Shoben, E. J ., 40 Sim on, H . A., 69-70, 213-16, 223, 237 Sim pson, M . E., 90 Skinner, B. F., 4

275

Slobin, D. I., 29 Slovic, P., 217 Sm alley, N . J . , 169-70 Sm edslund, J ., 79 Sm ith, E., 44 S m ith, E. R., 236 Sm oke, K. L., 30 S pringston, F. J ., 202-3 S tau d en m ay er, H .. 129, 135-7, 153 S teedm an, M ., 100, 102, 105 Stevenson, R., 29 S uppes, P., 130 T a g a rt, J ., 137-8 T a n e n h a u s, M . K ., 40 T a p lin , J . E., 129, 135-6, 203 T rab a sso , T ., 26, 34, 39, 63, 65 T rid g ell, J . M ., 193 T versky, A., 217-18, 229 T w eney, R. D ., 30, 238 V a n D uyne, H . J ., 62-3, 69, 243 V an D uvne, P. C ., 165, 180, 182-7, 197, 201-2 V ygotsky, L. S., 248 W allace, J . G., 65 W an n em ach er, J . T ., 42 W ason, P. C ., 6, 25-8, 3 0 -2 , 34, 38-9, 4 7 -8 , 80, 86, 93, 119-20, 124, 126, 129, 138, 142, 147, 150-1, 157, 159-67, 169-75, 180-5, 187-8, 193, 197-8, 204, 206, 214-15, 220-2, 2 2 5-6, 228, 232, 234-5, 237-43, 249, 251, 255 W 'atson, J . B., 15 W'eiss, Wr., 30 W hitfield, J . W ., 30 W ilkins, M . C ., 106-7, 110-12, 180, 224 W illiam s, R. C ., 61 W ilson, E. G ., 65 W'ilson, T . D., 235-8 W inograd, T ., 13 W ohlw ill, J . F., 221 W oodw orth, R. S., 73, 79, 82, 91 Y oung, R., 39 Z ajonc, R. B., 109, 23£ Zwicky, A. M ., 151-2

Subject index

associational theory, 99-100, 186-7, 200-1, 229 atm osphere effect, 82-93, 9 8 -9 , 228 behaviourism , 4, 15 belief bias, 107-11, 2 0 2-3, 226-7; tru th status in the W ason selection task, 184-7 c h ild ren ’s reasoning, 62, 65-6, 94-5, 130, 142, 221 com petence: linguistic, 13; logical, 218-23, 232-3, 252, 255; ste also logical com ponent concept identification, 30, 207 conditional inferences, 120-2, 128-34, 146 content an d context effects: in syllogistic reasoning, 105-11; in conditional reasoning, 151-5; in the W ason selection task, 180-7; in disjunctive reasoning, 201-4; see also facilitation by realism ; belief bias; linguistic factors; in te rp reta tio n a l com ponent conversion of statem ents: in syllogistic reasoning, 82-101, 109-10; in conditional reasoning, 143; see also equivalence in te rp reta tio n decision m aking, 4, 216-18 directionality of reasoning: in transitive inference, 52-4, 58-9; in conditional reasoning, 130, 145-51, 161, 191, 195 disjunctive inferences, 122-3, 193-7 d u al coding, 19—22, 45-7, 6 1 -9 , 242, 244, 250; see also im agery

276

d u al process theory: W ason a n d Evans, 126, 173, 234-41; revised version, 240-1; b ro a d e r im plications an d evidence, 241-52 equivalence in te rp reta tio n , 129, 133, 135-7, 143, 153-4 E vans tw o-factor theory, 8 9 -90, 125-7, 133-4, 141, 155-6, 176, 192, 240-1, 253-4; see also logical com ponent; in te rp reta tio n a l com ponent; nonlogical tendencies facilitation by realism , 106, 180-4, 201-2, 224-6; see also content an d context effects falsification o f theories or hypotheses, 3, 42, 157-9, 160-2, 166 figural bias, 99-105, 230 h em ispheric specialisation, 6 2 -3 , 242-3, 250-1 H enle hypothesis, 5, 79-81, 85, 92-3, 111-12, 125, 129-30, 153, 155, 215-16, 228; see also rationalism heuristic biases, 217-18, 229-30 im agery: conceptual issues, 15-23; in transitive inference, 5 1 -4 , 56-63, 68-9; in conditional reasoning, 2489; see also du al coding individual differences, 134—5 inductive reasoning, 1, 238-9 inform ation processing m odels: of sentence verification, 34-47; of transitive inference, 5 1-6; of

Subject index syllogistic reasoning, 8 7 -9 , 100-5, 253; see a lso insight m odels insight m odels, 165-70 interference tasks, 20-2, 60-2, 244-8 in te rp reta tio n a l com ponent/factors, 125, 127, 144-51, 155, 179, 189-96, 202, 207-8; see also linguistic factors; content an d context effects introspection, 15-19, 60-1, 80, 160-1, 235-9; see a lso protocol analysis linear represen tatio n s, 6 3 -8 linguistic factors, 126, 137-8, 145-55, 223-4; see also in te rp reta tio n a l com ponent; content a n d context effects linguistic theory o f transitive inference, 54-9, 63, 67-9 logic: concept of, 1-3; linear syllogism s, 49-50; classical syllogism s, 73-7; propositional logic, 115-23 logical com ponent (of perform ance), 112, 125-7, 131-4, 141, 231-2; see also in te rp reta tio n a l com ponent; E vans tw o-factor theory m atching bias, 139-42, 147, 163-6, 170-3, 197-200, 206, 228-9 m em ory for inference, 64, 95-8 negative conclusion bias, 131-5, 146, 152, 196, 230 negatives: in verification tasks, 25-47; sem antic aspects, 30-4; in conditional reasoning, 130-5, 138-42; in W ason selection task, 162-7; in disjunctive inference, 190-201; negative equatives, 59; see also m atching bias; negative conclusion bias non-logical tendencies, 79-81, 112, 125-7, 133-4, 228-30, 255; see also a tm osphere effect; m atc h in g bias; negative conclusion bias; figural bias; belief bias; E van s tw o-factor theory

277

operatio n al theory o f transitive inference, 51, 56-8 p arallel processes, 125, 241-4 passives, 28-9, 32-4, 41-2 P iagetian theory, 105, 220-1 p rag m atic inference, 5, 151-3 p robabilistic inference: in syllogistic reasoning, 84-5; statistical ju d g m e n t, 217-18 p robabilistic m odels, see stochastic m odels problem solving, 213-16 propositional represen tatio n s, 12-15, 34-42, 54-5, 60; vs im ages, 16-19, 45-7 protocol analysis, 80, 167-73, 273-9; see a lso introspection ratio n alisatio n , 171, 173, 235-6 rationalism , 3-6 , 79-81, 112, 135, 188, 212-13, 233, 252-3; see a lso H enle hypothesis response biases, see non-logical tendencies self-contradiction, 160-2, 198-9 sem antic m em ory, 5, 25-6, 224, 226, 229 stochastic m odels, 94, 174—9 T H O G problem , 124, 2 0 5-8, 228, 232 train in g o r th erap y experim ents, 90, 160-2, 186-7 tran sfo rm atio n al g ra m m ar, 12, 28-9; see a lso negatives; passives tru th tables: logical, 119-22, 190; psychological, 123, 137-44, 146, 158— 60, 197-201; inferred, 135-7 verification bias, 150, 163-6; insight m odels w orking m em ory, 244, 248

see also