Other titles of interest CUSWORTH, D. C. Biochemical Screening in Relation to Mental Retardation KIRMAN, B. Mental Retardation BARANYAY, E. P. The Mentally Handicapped Adolescent HELMORE, G. A. Piaget: A Practical Consideration BOWYER, R. The Lowenfeld World Technique FRANCIS-WILLIAMS, J. Rorschach with Children FROMMER, E. A. Voyage through Childhood into the Adult World HERRMANN, E. R. & CAMPBELL, S. F. Piaget - Dictionary of Terms KAHN, J. H. Human Growth and the Development of Personality, 2nd Edition GRAZIANO, A. M. Child without Tomorrow STROUD, J. Services for Children and their Families: Aspects of Child Care for Social Workers The terms of our inspection copy service apply to all the above books. Full details of all books listed will gladly be sent upon request. A Students' Guide to Piaget BY D.G.BOYLE, B.sc.PhD Lecturer in Psychology in the University of Leeds PERGAMON PRESS OXFORD NEW YORK TORONTO SYDNEY PARIS FRANKFURT U.K. Pergamon Press Ltd., Headington Hill Hall, Oxford OX3 OBW, England U.S.A. Pergamon Press Inc., Maxwell House, Fairview Park, Elmsford, New York 10523, U.S.A. CANADA Pergamon of Canada Ltd., P.O. Box 9600, Don Mills M3C 2T9, Ontario, Canada AUSTRALIA Pergamon Press (Aust.) Pty. Ltd., 19a Boundary Street, Rushcutters Bay, N.S.W. 2011, Australia FRANCE Pergamon Press SARL, 24 rue des Ecoles, 75240 Paris, Cedex 05, France WEST GERMANY Pergamon Press GmbH, 6242 Kronberg/Taunus, Pferdstrasse 1, Frankfurt-am-Main, West Germany Copyright © D. G. Boyle 1969 All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers First edition 1969 Reprinted 1970 Reprinted 1976 Library of Congress Catalog Card No. 77-94056 Printed in Great Britain by Biddies Ltd., Guildford, Surrey ISBN 0 08 006406 X (Fc) ISBN 0 08 006407 8 (He) Preface NATHAN ISAACS, in Some Aspects of Piaget's Work, remarks that we need an "Intelligent Students' Guide to Piaget". The fact that the adjective "intelligent" does not appear in my title does not, of course, mean that this book is intended for unintelligent students. It was simply that my book was well advanced before I came across Mr. Isaacs's suggestion. However, it encourages me to learn that a distinguished Piagetian scholar feels, as I do, that a book making Piaget's ideas more accessible to non- specialists may be welcome. I have not attempted to give a systematic exposition of the whole of Piaget's work. That is not necessary, as Flavell has recently done this in The Developmental Psychology of Jean Piaget; indeed, had Flavell not written his book I should have been greatly handicapped in writing mine (readers familiar with this field will also discover the influence of Baldwin's Theories of Child Development). However, Flavell explicitly assumes a know ledge of epistemology on the part of his readers,-whereas I believe that it is precisely a lack of acquaintance with epistemological ideas that prevents students from appreciating Piaget's work. For this reason I have emphasized Piaget's epistemological work. Inasmuch as my primary aim has been to give a brief exposition for psychology students, I have not attempted to discuss all aspects of Piaget's multifarious epistemological interests. Whilst Piagetian specialists may feel that the picture has been over simplified, it has seemed to me right, in the interests of clarity of exposition, to restrict the treatment to the minimum necessary to provide a clear framework for psychologists. For this reason I have made no attempt to relate Piaget's epistemology to the views of other European and British philosophers. vii Vlll Preface In writing this book I have been greatly aided by discussions with my colleagues in the Psychology Department of Leeds University, and I must express particular gratitude to Professor Meredith, who first encouraged me to write this book. With respecc to Chapter 9, I was much assisted by the kindness of Dr. K. Lovell, who sent me a copy of a chapter that he is contributing to a forthcoming book. For preparing the typescript for publica tion my thanks go to Mrs. Margaret Greaves, and the Misses Noreen Giddens and Margaret Morrison. I owe an incalculable debt to my wife, who not only gave me great encouragement to continue writing when my enthusiasm was flagging, but also read every chapter in manuscript and made many valuable suggestions for improving the clarity of exposition. I am indebted to the following authors and publishers for per mission to quote from their works: To Professor Jean Piaget and the Manchester University Press for a quotation from Logic and Psychology. (Chapter 2.) To J. M. Dent & Sons Limited, publishers of Jerome K.Jerome, for a passage from Idle Thoughts of an Idle Fellow. (Chapter 4.) To Professor Morris Kline and the Oxford University Press (New York) for a quotation from Mathematics in Western Culture. (Chapter 4.) To Dr. R. S. Peters and George Allen & Unwin Limited, for a quotation from Ethics and Education. (Chapter 10.) D.G.B. List of Symbols Used \/ square root > greater than + plus — minus = equals => logical implication (e.g. p^q; p implies q) V disjunction (e.g. p\/ q; either p or q) conjunction (e.g.p.q; both/? and q) - negation (e.g.p; not-/?) / incompatibilty [e.g. {pZDq)l{p*q); "p implies q" is incompatible with the truth of/? and the falsity of q] IX CHAPTER 1 The Problems to be Solved THIS book is intended as a guide for students to the work of one of the most influential thinkers in contemporary psychology, and so it is as well that we should start with the major problem that confronts students when they first encounter Piaget's work. The students find little difficulty in following what he has done, but they seldom understand why he has done it. If one does not understand the why of Piaget's work, one cannot grasp the rela tionship between the facts that Piaget gives and the theory that he derives from them. This book is intended to answer the question "Why?" Piaget is attempting to answer some very important questions in the branch of philosophy called "epistem ology". In this chapter we shall try to show what he means by this. First we must explain what epistemology is about. Put very briefly, epistemology is a study of the limits of knowledge. It addresses itself to such questions as "In what sense can we say that we know anything?" A study of what we know about the intellect, for example, is the province of psychology: consideration of how we are to describe that knowledge is epistemology. Until the eighteenth century, psychology and philosophy were not clearly distinguished, and many of the questions to which major philosophers of the past attempted to give answers were questions that we should today regard as problems for psycholo gists. One of these questions was whether the mind at birth is a blank sheet, or tabula rasa, on which experience—and experience alone—writes, or whether the mind has an existence, and laws, of its own. These two viewpoints are known to psychologists as 3 4 A Students9 Guide to Piaget the "empiricist" and "nativist" views .respectively. Questions of this sort are not resolvable by empirical evidence, but we can conceive of ways in which empirical evidence would be relevant: for instance, if the overwhelming majority of experimental facts could be more satisfactorily explained in terms of one rather than the other viewpoint, then the one yielding the more satisfactory explanations would be more acceptable to scientists. Since this is not so, the point of view that we adopt depends largely on our philosophical outlook which, whether we are aware of it or not, is influenced by the arguments of the great philosophers of the past. There are other questions to which empirical evidence seems even less relevant. One of the most important of these questions concerns the nature of mathematical entities such as infinite numbers, or the square root of — 1. At one time in the history of mathematics these ideas were not part of the science, so how did they come into being? Did Cantor "discover" infinite numbers in a vision, as he claimed? Was \/—1 "discovered" or was it "invented"? If it was invented, what does "invention" mean in this context? These questions are the province of mathematical epistemology, and they have exercised the greatest minds of Western civilization since the days of Plato and Aristotle. The reason for this great interest is that mathematical knowledge (and, in par ticular, geometry) comprises a body of deductions from self- evident axioms and is therefore indisputably true: at the same time these deductions are more than mere tautologies, and mathe matical study really does tell us things that we did not know before. For example, starting from the axioms of Euclidean geo metry (which are self-evidently true), we can deduce that the angle inscribed in a semicircle is a right angle (which is undeni ably true but by no means self-evident). Geometry thus poses a paradox. The theorems constitute new knowledge, yet this knowledge consists of deductions from self- evident truths such as "the whole is greater than any of its parts" and "any two points may be connected by a straight line". In what sense, then, is mathematical knowledge "new"? The major part of Piaget's work may be interpreted as an attempt to The Problems to be Solved 5 answer questions of this sort. Piaget takes the view that a fruitful approach to understanding the problems of knowledge is by way of a study of the genesis of intellectual structures in man, hence genetic epistemology. He originally intended to spend approxi mately 5 years studying the development of intelligence in the child, but in fact devoted 40 years to the problem. In the rest of this chapter we shall attempt to state the problems of mathematical epistemology as philosophers have seen them, and summarize the various types of answer that they have given.* Then we shall indicate the nature of Piaget's answer, developing this theme in succeeding chapters before attempting an evalua tion of Piaget's contribution to psychology. Let us start by considering a triangle. There is one sure thing that we can say about a triangle, namely that the sum of its internal angles equals two right angles. If one tries to demonstrate this by drawing a triangle and deriving the proof, one finds that the triangle that has been drawn has other properties: for example it may be equilateral or isosceles or right-angle. Even if one is careful to draw a scalene triangle, the particular triangle that one has drawn will have specific properties that other triangles have not. Of what triangle are we talking when we say that the sum of the angles equals two right angles ? Clearly we are talking about triangles in general, but we have performed our reasoning about one particular triangle. Rene Descartes (1596-1650) argued that our minds work in such a way that they form general propositions from a knowledge of particular cases. Whilst this suggestion is highly plausible, it is open to the objection that our propositions about triangles seem indisputably true, whereas if they were formed from reasoning about individual triangles, it is conceivable that one day we should come across a triangle whose angles did not sum to two right angles. Two solutions to the difficulty were offered by the British Empiricists John Locke (1632-1704) and George Berkeley (1685-1753). Locke suggested that our geometrical reasoning is * The rest of this chapter is based on Part One of Mathematical Epistemology and Psychology by E. W. Beth and J. Piaget (see the bibliography for details.) 6 A Students' Guide to Piaget performed upon a general triangle, which is neither right-angled, nor equilateral, nor isosceles, nor scalene. Formulations of this sort have seldom proved as helpful in clarifying thinking as their formulators intended, and Berkeley proposed an alternative solution. Berkeley's solution was to propose that, when we demon strate a theorem about a particular triangle we make no mention in the proof of the specific properties of that particular triangle. Hence we are entitled to generalize from particulars to the general case. Two questions are involved in this discussion, the first being "Why do we need to perform our reasoning upon a particular example, rather than deduce theorems directly from axioms without an intermediate step?" Descartes's proposal about how the mind works is an answer to this question. It does not satis factorily answer the second question, which is "How can an argument about a particular triangle yield a general conclusion?" Locke's suggestion that we reason about a "general triangle" is an answer to this second question, as is Berkeley's proposal that, in the proof of a theorem, we mention only the features of general relevance. The third member of the trio of British Empiricists, David Hume (1711-76), commented on the psychological aspect of the problem. He observed that when we reason about a particular triangle we are led to think about other triangles that differ from the one in front of us. If, say, we have formulated a general con clusion about a triangle that is equilateral, the thought of an isosceles triangle may cause us to realize that our conclusion is not as general as we first thought, and we may revise our conclu sion. Then thinking of a scalene triangle may make us realize that our revised conclusion applies only to equilateral and isosce les triangles. In this way we progressively refine our conclusion until we have arrived at a satisfactory formulation. Hume is describing a dialectical argument, and his suggestion is a reply to the first question rather than the second because it is not clear that we could ever be certain of our conclusions, however long we continued our dialectical reasoning, for it is always conceivable