Epistemology and Psychology of Functions
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'.
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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. II. Series: 3. Functions. I. Piaget, Jean, 1896Etudes d'epistemologie genetique ; 23. 77-6792 BF723.C5E613 155.4'13 ISBN-13: 978-90-277-1242-4 DOl: 10.1007/978-94-010-9321-7
e-ISBN-13: 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 an
