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Bfm:978-94-010-9321-7/1.Pdf STUDIES IN GENETIC EPISTEMOLOGY XXIII EPISTEMOLOGY AND PSYCHOLOGY OF FUNCTIONS SYNTHESE LIBRARY MONOGRAPHS ON EPISTEMOLOGY, LOGIC, METHODOLOGY, PHILOSOPHY OF SCIENCE, SOCIOLOGY OF SCIENCE AND OF KNOWLEDGE, AND ON THE MATHEMATICAL METHODS OF SOCIAL AND BEHAVIORAL SCIENCES Managing Editor: JAAKKO HINTIKKA, Academy of Finland and Stanford University Editors: ROBER T S. COHEN, Boston University DONALD DAVIDSON, University of Chicago GABRIEL NUCHELMANS, University of Leyden WESLEY C. SALMON, University of Arizona VOLUME 83 STUDIES IN GENETIC EPISTEMOLOGY Published under the direction of JEAN PIAGET Professor of the Faculte des Sciences at Geneva XXIII EPISTEMOLOGY AND PSYCHOLOGY OF FUNCTIONS By JEAN PIAGET, JEAN-BLAISE GRIZE, ALINA SZEMINSKA, AND VINH BANG With the Collaboration of Catherine Fot, Marianne Meylan-Backs, Francine Orsini Andrula Papert-Christophides, Elsa Schmid-Kitzikis and Hermine Sinclair D. REIDEL PUBLISHING COMPANY DORDRECHT-HOLLAND/BOSTON-U .S.A. Libnuy of Congress Cataloging in Publication Data Epistemology and psychology of functions. (Studies in genetic epistemology; 23) (Synthese library; v. 83) Translation of Epistemologie et psychologie de la fonction. Includes bibliographical references and indexes. I. Cognition in children. 2. Knowledge, Theory of. 3. Functions. I. Piaget, Jean, 1896- II. Series: Etudes d'epistemologie genetique ; 23. BF723.C5E613 155.4'13 77-6792 ISBN-13: 978-90-277-1242-4 e-ISBN-13: 978-94-010-9321-7 DOl: 10.1007/978-94-010-9321-7 ETUDES D'EPlSTEMOLOGIE GENETIQUE X Xlii EPlSTEMOLOGIE ET PSYCHOLOGIE DE LA FONCTION First published by Presses Universitaires de France, 1968 Translated from the French by F. Xavier Castellanos and Vivian D. Anderson Published by D. Reidel Publishing Company, P.O. Box 17, Dordrecht, Holland Sold and distributed in the U.S.A., Canada, and Mexico by D. Reidel Publishing Company, Inc. Lincoln Building, 160 Old Derby Street, Hingham, Mass. 02043, U.S.A. All Rights Reserved Copyright © 1977 by D. Reidel Publishing Company, Dordrecht, Holland Softcover reprint of the hardcover 1st edition 1977 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any informational storage and retrieval system. without written permission from the copyright owner PREFACE Years ago, prompted by Grize, Apostel and Papert, we undertook the study of functions, but until now we did not properly understand the relations between functions and operations, and their increasing interactions at the level of 'constituted functions'. By contrast, certain recent studies on 'constitutive functions', or preoperatory functional schemes, have convinced us of the existence of a sort of logic of functions (springing from the schemes of actions) which is prior to the logic of operations (drawn from the general and reversible coordinations between actions). This preoperatory 'logic' accounts for the very general, and until now unexplained, primacy of order relations between 4 and 7 years of age, which is natural since functions are ordered dependences and result from oriented 'applications'. And while this 'logic' ends up in a positive manner in formalizable structures, it has gaps or limitations. Psychologically, we are interested in understanding the system­ atic errors due to this primacy of order, such ·as the undifferentiation of 'longer' and 'farther', or the non-conservations caused by ordinal estimations (of levels, etc.), as opposed to extensive or metric evaluations. In a sense which is psychologically very real, this preoperatory logic of constitutive functions represents only the first half of operatory logic, if this can be said, and it is reversibility which allows the construction of the other half by completing the initial one-way structures. Furthermore, with respect to schemes of action, as opposed to general and operatory coordinations, functions constitute the common source of oper­ ations and of causality and it is also in regard to this second point of view that the studies contained in this volume present certain new data. The first part of this work, authored by J. Piaget in collaboration with C. Fot, M. Meylan-Backs, F. Orsini, A. Papert-Christophides, E. Schmid-Kitzikis, H. Sinclair and A. Szeminska, bears above all on constitutive or preoperatory functions and on their gradual transformations into constituted functions, linked to operations. 641 subjects from 3 to 12-13 years of age were tested on this point. Part II is from the pen of Vinh Bang and relates 5 experiments which he conducted over a period of years on the quantification of constituted func- VI PREFACE tions, and specially on proportionality (based on 353 subjects from 6 to 14 years of age). Part III comprises two theoretical studies. In the first, J .-B. Grize reviews the history of the logical structure of functions, including the different levels considered in the preceding chapters. In the second, J. Piaget draws the 'General Conclusions' from these studies. INTRODUCTION Reading a book by Piaget is like entering a system. To a large extent he and his collaborators (but particularly he) are builders of an impressively struc­ tured whole - an experimentally based and controlled set of truth judge­ ments about knowing and knowledge. It seems almost irrelevant to choose just a single book out of his enormous oeuvre. Always one meets a number of fundamental concepts which have arisen through many decades of experi­ mental work with hundreds of collaborators, and from very productive thinking. Without doubt, for more than forty years Piaget has been (and still is) the spearhead and the creating and integrative power behind several generations of famous co-workers in 'the circle of Geneva'. It is impossible to mention all these women and men who were and are explicitly and implicitly present at the fabrication of so many writings. In the highly interesting autobiography of his scientific development, Piaget himself thankfully acknowledges the help of psychologists Barbel Inhelder, Alina Szeminska, Vinh Bang, Bresson, Greco, and Fraisse, the psycholinguist Sinclair, the mathematicians Henriques and Beth, the physicists Garcia and Halbwachs, the cyberneticians Papert and Cellerier, the methodologist in biology Nowinski, the logicians Apostel, Grize, Wermus, "and so many more". And here we are at the heart of the Centre International d'Epistemologie Genetique, where the studies in genetic epistemology originate and come about under the direction of Piaget. This particular book from 1968 was the twenty-third to be published since 1956. With the permanent aid of the Rockefeller Foundation since the beginning, and with that of the Fond National Suisse de Recherches Scientifiques since 1964, a production of approximately two volumes per year up till now (1977) has been maintained. I hardly need to say that this all surpasses the frontiers of psychology in the usual sense. Piaget was and his successors are directing the Faculte de psychologie et sciences de l'education of the University of Geneva. From about 1920, as chef des travaux at the Institut Jean-Jacques Rousseau under his predecessor Claparecte, Piaget began his very original studies in experi­ mental child psychology and especially the cognitive development from VIII INTRODUCTION childhood to adolescence, in which observations of his own two children played a major role. But significantly (I will come back to the underlying meaning of this) at an earlier date he started as a young man to study 'natural sciences' and wrote a doctoral thesis about the varieties of snail species living under different ecological conditions in Swiss lakes at different altitudes. At the same time he was attracted to and studied traditional philosophy (which, in the course of his scientific development, he surpassed - see his very thoughtful book Sagesse et illusions de la philosophie, 1966). This led in his early years, at the Universities of Geneva and Neuchatel, to teaching not only child psychology but also the philosophy of science and the development of ideas as reflected in the history of science. Even courses in human sociology for students (remember the studies on biological ecology) were amongst his tasks. With these and other starting points in his scientific career, stemming from the 'irrational' roots of his personality (with vital early questions about the essence of life and truth and securities), it is understandable that his very productive experimental and synthetic mind engendered a sizable problem convergency rather early. He wished to discover a kind of 'psychological embryology' of intelligence (using biological preformation) in which the relations between the acting and thinking subject and the objects of his experience, and between the subject and other subjects, had to be seen as a special case of the relation between the biological 'organism' and its surroundings. The difference being in the first case exchange of informajion and in the second case exchange of material. Piaget occupied himself temporarily with the development of social cooperation between individuals and groups, with social exchange of satis­ factions, with valuation, with motivational aspects, with the growth of normative thinking in morals and justice, but his main line was cognitive development in a more strictly mathematical, geometrical and physical sense and its continuation in the development and the stages of intellectual thinking in science, and the epistemological
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