Science and an African Logic

283 Pages·2001·18.605 MB·English

by  Helen Verran

Science and an African Logic
Science and
an African Logic
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Helen Verran taught at Obafemi Awolowo University in Ile-Ife, Nigeria,
between 1979 and 1986. She is currently senior lecturer in the Department of
History and Philosophy of Science at the University of Melbourne.
Chapter 6 was originally published as Helen Watson, "Learning to Apply
Numbers to Nature: A Comparison of English Speaking and Yoruba Speaking
Children Learning to Quantify," Educational Studies in Mathematics 18 (1987):
339-57. © 1987 by D. Reidel Publishing Company; reprinted with kind per
mission of Kluwer Academic Publishers. Chapter 9 was originally published as
Helen Watson, "Investigating the Social Foundations of Mathematics: Natural
Number in Culturally Diverse Forms of Life," Social Studies of Science 20
(1990): 283-312.
The University of Chicago Press, Chicago 60637
The University of Chicago Press, Ltd., London
© 2001 by The University of Chicago
All rights reserved. Published 2001
Printed in the United States of America
10 09 08 07 06 05 04 03 02 01 1 2 3 4 5
ISBN: 0-226-85389-6 (cloth)
ISBN: 0-226-85391-8 (paper)
Library of Congress Cataloging-in-Publication Data
Verran, Helen.
Science and an African logic I Helen Verran.
p. em.
Includes bibliographical references and index.
ISBN 0-226-85389-6 (cloth : alk. paper)- ISBN 0-226-85391-8 (pbk. :
alk. paper)
1. Yoruba (African people)-Science. 2. Yoruba (African people)-Mathe
matics. 3. Philosophy, Yoruba. 4. Ethnoscience-Nigeria. 5. Logic
Nigeria. 6. Ethnomathematics-Nigeria. I. Title.
DT515.45.Y67 V47 2001
160'.89'96333-dc21
2001027752
@ The paper used in this publication meets the minimum requirements of
the American National Standard for Information Sciences-Permanence
of Paper for Printed Materials, ANSI Z39.48-1992.
Acknowledgments
VII
Part One: Introduction
Chapter One: Disconcertment
Chapter Two: Toward Generative Critique 21
Part Two: Numbering
Chapter Three: A Comparative Study of Yo ruba and
English Number Systems 51
Chapter Four: Decomposing Displays of Numbers 71
Chapter Five: Toward Telling the Social Lives
of Numbers 92
Part Three: Generalizing
Chapter Six: Learning to Apply Numbers to Nature 123
Chapter Seven: Decomposing Generalizing as "Finding
Abstract Objects" 143
Chapter Eight: Toward Generalization as Transition 156
v
vi Contents
Part Four: CE.'rtainty
Chapter Nine: Two Consistent Logics of Numbering 177
Chapter Ten: Decomposing Predicating-Designating
as Representing 206
Chapter Eleven: Embodied Certainty and
Predicating-Designating 220
Notes 239
References 265
Index 275
1/f/Jy
students in Ife are first to be acknowledged. The book is theirs
YV (
as much as mine.
The research committee of Obafemi Awolowo University, Ile-Ife, pro
vided financial support in two grants, which enabled this work. Colleagues
in the Institute of Education provided encouragement and support. I
specifically acknowledge contributions from friends Akin Aboderin, Joe
Beddu-Ado, Barry Hallen, Segun Osoba, 'Diran Taiwo, Agbo' Folarin,
Margaret Folarin, Karin Barber, Caroline Dennis, Morris Paul, Doreen
Paul, Glenda Dare, the late Buki' Osibodu, and Pa Laosebikan. Joseph
and Grace Odere ran my home along with their own and gave me time
to think.
At Deakin University in Australia, I owe thanks to my colleagues in
science studies and in the Faculty of Education, and to the Koori, Yo lngu,
and Yapa Aboriginal students who continued the work of my Yoruba
students in alerting me to the issues. The History and Philosophy of Sci
ence Department at the University of Melbourne has provided support
for the project over ten years. My graduate students contributed a great
deal: Carol Steiner, Diane Mulcahy, Martin Gibbs, Cass Wrigley, Rey Ti
quia, Jonathan Wearne, Margaret Ayre, Helen Smith, Chris Shepherd,
Geraldine Cheney, and especially Katayoun Sadghi Rad Hassall.
The first draft of the book was completed in 1997 during a year's study
leave in the Philosophy Department, Smith College. I acknowledge the
support and resources that were placed at my disposal. To Kathryn Pyne
Addelson, who arranged my stay, I am grateful, both for that and for her
philosophy.
There is a group of people who have remained staunchly supportive
through the long years of my struggle to think this through: Karin Barber,
vii
viii Acknowledgments
David Turnbull, Anni Dugdale, Rosemary Robins, Bruno Latour, Donna
Haraway, Lucy Suchman, John Law, Murrray Code, and Lorraine Code.
I drew a great deal from their continued interest.
Finally my family. Husbands, Gabriel and Max; son, Daniel; daughter,
Ruth; foster son, Jack; sister, Kaye; and granddaughter, Cecilia, have all
had their lives made more difficult by the project of this book and have
all made a unique contribution to it.
Chaptl'r Onl': Disconcl'rtml'nt
Could African numbers be different from the numbers of science? My experi
ences of struggling to teach science to Ya ruba school teachers in Nigeria led
me to ask that strange question. This first introductory chapter describes some
of those experiences.
Chaptl'r Two: Toward Gl'nl'rativl' Critiqul'
Having elaborated the difference between Yoruba and scientific numbers, I
was disconcerted to recognize that I had explained away the experiences that
led to my odd question. I had seen real differences in numbers being managed
but to tell of that I needed to find a new way to tell the realness of generalizing
logic.