Inconsistency in Science

225 Pages·2002·6.359 MB·English

by  Thomas Nickles (auth.), Joke Meheus (eds.)

INCONSISTENCY IN SCIENCE
ORIGINS
Studies in the sources of scientific creativity
Volume 2
Managing Editor:
Fernand Hallyn, University of Ghent, Belgium
Editorial Board:
Gillian Beer, Cambridge University, U.K.
James J. Bono, State University ofN ew York, Buffalo, U.S.A.
Marc de Mey, University of Ghent, Belgium
Thomas Da Costa Kaufman, Princeton University, U.S.A.
Peter Galison, Harvard University, U.S.A.
Paolo Galluzzi, Istituto e Museo di Storia delle Science, Firenze, Italy
Rom Harre, Oxford University, U.K.
Peter Machamer, University of Pittsburgh, U.S.A.
Arthur I. Miller, University College London, U.K.
William Shea, University of Strasbourg, France
Gerard Simon, University of Lille III, France
Geert Vanpaemel, University ofL euven, Belgium
Peter Weingart, University ofB ielefeld, Germany
SCOPE
The aim of the series is to present historical and theoretical studies on the sources of
scientific creativity. The series provides a platform for various transdisciplinary
viewpoints.
Indeed, on the one hand, the origins of scientific creativity should be studied in the
light of its relations with sources of creativity in other disciplines (literary, artistic),
in order to illuminate the particular scientific element in the genesis of scientific in
novation.
On the other hand, the complexity of the topic necessitates a variety of approaches,
where logic, cognitive studies, poetics, rhetoric, history of ideas and other disciplines
meet in a common interrogation.
In short, the series welcomes studies which integrate philosophy and history of
science in a broad, diversified field of research, where there is room for a great va
riety of perspectives with different methodological and conceptual references and
where isolationism as well as reductionism are avoided.
Inconsistency in Science
Edited by
JOKEMEHEUS
Ghent University, Ghent, Belgium
....
"
Springer-Science+Business Media, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-90-481-6023-5 ISBN 978-94-017-0085-6 (eBook)
DOl 10.1007/978-94-017-0085-6
Printed on acid-free paper
All Rights Reserved
© 2002 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 2002.
Softcover reprint of the hardcover 1s t edition 2002
No part of this work may be reproduced, stored in a retrieval system, or transmitted
in any form or by any means, electronic, mechanical, photocopying, microfilming, recording
or otherwise, without written permission from the Publisher, with the exception
of any material supplied specifically for the purpose of being entered
and executed on a computer system, for exclusive use by the purchaser of the work.
CONTENTS
Preface Vll
From Copernicus to Ptolemy: Inconsistency and Method
Thomas Nickles
Inconsistent Reasoning toward Consistent Theories 35
Arthur 1. Miller
Inconsistencies in the History of Mathematics 43
Jean Paul Van Bendegem
Mathematical Change and Inconsistency 59
Otavio Bueno
Approximate Truth 81
Bryson Brown
Inconsistency in Science: A Partial Perspective 105
Newton da Costa and Steven French
Inconsistency and the Empirical Sciences 119
Graham Priest
v
VI CONTENTS
In Defence of a Programme for Handling Inconsistencies 129
Diderik Batens
How to Reason Sensibly yet Naturally from Inconsistencies 151
Joke Meheus
Why the Logic of Explanation is Inconsistency-adaptive 165
Erik Weber and Kristof De Clercq
A Paradox in Newtonian Gravitation Theory II 185
John D. Norton
Inconsistency, Generic Modeling, and Conceptual Change in Science 197
Nancy J. Nersessian
INDEX 213
PREFACE
Within traditional philosophy of science, the role of inconsistencies has largely been
ignored. At best, inconsistencies were seen as a hindrance for good scientific
reasoning. The reason for this is not difficult to understand. Until very recently,
rationality has been identified with reasoning according to Classical Logic. And, as
is well known, Classical Logic does not allow one to reason sensibly in the presence
of inconsistencies.
Today, it is generally recognised that almost all scientific theories at some point
in their development were either internally inconsistent or incompatible with other
accepted findings (empirical or theoretical). A growing number of scholars
moreover recognises that inconsistencies need not be disastrous for good reasoning.
Three developments were central for this change in attitude. First, there is the
shift in attention from finished products to discovery processes. Whereas finished
theories usually seem to satisfy the consistency requirement, developing theories
typically do not. Next, there is the availability of case studies on episodes in the
history of the sciences that involved inconsistencies. Finally, there is the study of
paraconsistent logics' that started some fifty years ago. This study not only
challenged the view that Classical Logic would be the appropriate tool for reasoning
in all contexts, but also resulted in a variety of systems that are adequate for
reasoning in inconsistent contexts.
The prevalence of inconsistencies in the sciences raises a large number of
interesting questions. How should 'logical anarchy' be avoided? Should one resort
to a paraconsistent logic or to non-logical criteria? What about the acceptance of
inconsistent theories? Are we ever justified to accept an inconsistent theory, and if
so, can this acceptance be more than provisional? How does inconsistency affect our
notion of truth? Should inconsistent theories at best be considered as 'containing
some truth' or can they be considered as true in the same strong sense as consistent
theories? Do inconsistencies exist in the world out there or only in the theories we
, A logic is called paraconsistent iffit does not validate Ex Fa/so Quodlibet (A, -A f-- B).
Vll
Vlll PREFACE
humans design about that world? The obvious importance of these questions
certainly warrants to devote a series of studies to the theme.
The incentive for this book was the First World Congress on Paraconsistency
(Ghent University, Belgium, 30 July - 2 August 1997). At this congress, a workshop
on The Role of Inconsistencies in the History and Philosophy of Science was
organized. This was not the first meeting devoted to the theme. However, the Ghent
workshop was at least for two reasons unique. Never before had a meeting on this
subject been attended by specialists from all over the world. And even more
importantly, never before had philosophers of science and historians of science met
with logicians and computer scientists to discuss this intriguing theme. A selection
of papers presented at this workshop is included in the present volume. In order to
do justice to the variety of approaches, this selection has been extended with a
number of invited papers.
The book opens with two contributions from the philosophy of science, "From
Copernicus to Ptolemy: Inconsistency and Method" by Thomas Nickles and
"Inconsistent Reasoning toward Consistent Theories" by Arthur Miller. Nickles
compares the standard theory-centred conception of science with newer pragmatic
and model-based accounts of scientific inquiry regarding their methodological
treatment of inconsistencies. Miller investigates different sources of inconsistencies,
and draws some conclusions from this with respect to scientific progress. These are
followed by two studies in the philosophy of mathematics, "Inconsistencies in the
history of mathematics: the case of infinitesimals" by Jean Paul Van Bendegem and
"Mathematical Change and Inconsistency: A Partial Structures Approach" by Otavio
Bueno. Van Bendegem explores an alternative approach for limit analysis that
solves the inconsistencies connected with infinitesimals; the case is further used to
defend a contingent view on mathematical progress. Starting from da Costa's and
French's partial structures approach, Bueno presents a framework for mathematical
change that assigns a positive role to inconsistencies. He applies the framework to
the development of set theory.
Next, there are several analyses of inconsistencies in the empirical sciences that
are based on a specific paraconsistent approach, "Approximate Truth: A
Paraconsistent Account" by Bryson Brown, "Inconsistency in Science: A Partial
Perspective" by Newton da Costa and Steven French, "Inconsistency and the
Empirical Sciences" by Graham Priest, "In Defence of a Programme for Handling
Inconsistencies" by Diderik Batens, "How to Reason Sensibly yet Naturally from
Inconsistencies" by Joke Meheus and "Why the Logic of Explanation is
Inconsistency-adaptive" by Erik Weber and Kristof De Clercq. The first three of
these defend each a different realistic view on inconsistent theories. Brown presents
an account of approximate truth that is based on a specific non-adjunctive approach
to paraconsistency, and that aims at explaining the success of past and current
(possibly inconsistent) theories. da Costa and French offer a model-theoretic account
in which theories are regarded as partial structures. On this account, inconsistent
theories (just like consistent ones) can be considered as partially true and accepted as
such. Priest advocates the view that reality itself is inconsistent and that
contradictions are observable. In line with this, he defends the idea that inconsistent
theories can be considered as true in the strong sense of the word. The last three
PREFACE IX
papers in this group explore the philosophical foundations and some applications of
inconsistency-adaptive logics. Batens spells out the philosophical programme
underlying this family of logics; one of his central arguments is that handling
inconsistent theories requires a logic that stays as close as possible to Classical
Logic. Meheus argues that reasoning from inconsistencies requires an extremely rich
inconsistency-adaptive logic, and presents a system that meets this requirement.
Weber and De Clercq argue that inconsistency-adaptive logics are much better
suited than Classical Logic to define the different types of explanation.
The volume closes with two case studies, "A Paradox in Newtonian Gravitation
theory II" by John Norton and "Inconsistency, Generic Modeling, and Conceptual
Change in Science" by Nancy Nersessian. Norton provides a rigorous yet
transparent demonstration of the inconsistency of Newtonian Cosmology, and
defends the view that physical theorists handled this inconsistency by a content
driven approach rather than a logic driven approach. Nersessian analyses Maxwell's
construction of the laws of electrodynamics, and shows how generic modeling
enabled him to tolerate several inconsistencies in his derivation.
Acknowledgments
The workshop The Role of Inconsistencies in the History and Philosophy of Science
was organized by the international research community "Science and Culture" and
was sponsored by the Fund of Scientific Research - Flanders. The editor is a
Postdoctoral Fellow of the same Fund.
The editor wants to thank the members of the organising committee of the First
World Congress on Paraconsistency for their help in organising the workshop and
Isabel D'Hanis for her help in preparing the manuscript.
Joke Meheus
THOMAS NICKLES
FROM COPERNICUS TO PTOLEMY:
INCONSISTENCY AND METHOD*
Abstract: In recent years several philosophers and other science studies experts have adopted a somewhat
more Ptolemaic than Copernican view of theories, models, and scientific research, namely, the "semantic"
conception of theories and their applications. On the old, "Copernican" view, theories are deductively
integrated, interpreted logical calculi, in standard symbolic logic, and science is a theory-centered
enterprise that aims for a comprehensive, single picture of the universe. Accordingly, consistency
becomes a hard constraint, a sine qua non of useful, rational inquiry. Proponents of the semantic
conception are somewhat more "Ptolemaic" in treating theories as collections of models and in placing
the solution of local problems in restricted domains ahead of grand, spectator theories of the universe.
They focus as much on the process of inquiry as upon the logical structure of its products. Remarkably, in
scientific practice we find inconsistencies and near-inconsistencies of various kinds apparently popping
up everywhere, suggesting that one cannot lay a tight grid of standard logic over scientific practice.
However, deflating unitary theories into collections of models makes inconsistency harder to define and
locate precisely-but also less serious. Consistency often becomes a soft, negotiable constraint--one
constraint among others. In practice, inconsistency rarely leads to complete disaster, for there are various
ways to tame it. I urge paraconsistency and inconsistency-tolerant logicians to pay attention to real
scientific examples of scientists' responses to inconsistency and quasi-inconsistency, e.g., conceptual
incongruities such as conceptual "blowups" and pragmatic inconsistencies such as the simultaneous use
of mutually inconsistent models.
1. INTRODUCTION
Methodological treatments of (in)consistency in the empirical sciences usually take
for granted a theory-centered conception of inquiry according to which theories are
the primary units of and for analysis. Theories are supposed to provide correct
(realist) representations of the universe or at least unified engines of prediction and
explanation for a universal domain of phenomena. Since the 1960s, however, this
Copernican paradigm (as we may call it) has been challenged by numerous studies
of historical and contemporary scientific practice, especially experimental practice.
Some science studies experts now favor something closer to a Ptolemaic paradigm,
according to which the theories (if any) of a scientific field are tools in a toolbox
alongside various other tools for solving the variety of problems that arise in that
field. Such a view is more characteristic of those who take a pragmatic, problem
solving approach to scientific work than of those who take a universal-truth-seeking,
* Acknowledgement. I thank the U.S. National Science Foundation for support on projects concerning
heuristic appraisal and knowledge pollution. Thanks also to Joke Meheus for helpful suggestions. She
is not responsible for infelicities that remain.
J. Meheus (ed.), Inconsistency in Science, 1-33.
© 2002 Kluwer Academic Publishers.