Structure and Approximation in Physical Theories

254 Pages·1981·6.94 MB·English

by  A. Hartkämper

Structure and
Approximation in
Physical Theories
Structure and
Approximation in
Physical Theories
Edited by
A. Hartkiimper
and
H.-J. Schmidt
University of Osnabriic1c
Osnabriic1c. FRG
PLENUM PRESS • NEW YORK AND LONDON
Library of Congress Cataloging in Publication Data
Colloquim on Structure and Approximation in Physical Theories (1980 : Osna
briick, Germany)
Structure and approximation in physical theories.
·Proceedings of a Colloquium on Structure and Approximation in Physical
Theories, held at Osnabriick, FRG, in June 1980" - T.p. verso.
Bibliography: p.
Includes index.
1. Physics-Methodology-Congresses. 2. Approximation theory-Congresses. I.
Hartkiimper, A. II. Schmidt, H.-J. (Heinz-Jiirgen), 1948- . III. Title.
QC5.56.C66 1980 530'.028 81-15846
AACR2
ISBN-13:978-1-4684-4111-6 e-ISBN-13:978-1-4684-4109-3
DOl: 10.1007/978-1-4684-4109-3
Proceedings of a colloquium on Structure and Approximation
in Physical Theories held at Osnabriick, FRG, in June 1980
© 1981 Plenum Press, New York
Softcover reprint of the hardcover 1s t edition 1981
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PREFACE
The present volume contains 14 contributions presented at a
colloquium on "Structure and Approximation in Physical Theories"
held at Osnabruck in June 1980. The articles are presented in the
revised form written after the colloquium and hence also take
account of the results of the discussion at the colloquium.
It is a striking feature that the problem of approximation
in physical theories has only recently found some attention in the
philosophy of science, although the working physicist is con
stantly confronted with those questions. No interesting theory of
exact science exactly fits its experimental data; almost every
relation between different theories is an approximate one. There
fore an adequate reconstruction of physical theories must take
into account and conceptualize the moment of approximation. The
majority of the articles in this book is centered around this
subject.
There are at least two elaborate, 'structuralistic' approaches
to the formalization of physical theories in which the aspect of
approximation has been incorporated: the approach due to P. Suppes,
J. Sneed, W. Stegmuller ("S-approach") and the approach of G. Lud
wig and his co-workers ("L-approach"). The articles in this book
correspondingly fall into three classes: presentation, elaboration
and critique of the L-approach [Hartkamper/Schmidt, Ludwig, Neumann,
Werner, Schmidt, Mayr, Kamiah, Majer, Grafe] or of the S-approach
[Moulines, Balzer, Cooke], and articles referring to both approaches
or concerned with related matters [Scheibe, Pfarr, Castrigiano].
Of course, this is only a rough classification and each article
must be appraised in its own right.
It is appropriate to indicate among the topics touched on in
this book are the following:
1. Discussion of different kinds of imprecision and its mathe
matical representation by uniform structures [Ludwig, Moulines,
Balzer, Mayr, Schmidt].
2. Physical examples of approximation: Kepler-Newton approxi
mation [Moulines, Mayr], approximate quantum dynamics [Werner]
and approximate causality [Neumann].
v
vi PREFACE
3. Philosophical reflections on the concept of approximation
[Majer, Grafe, Balzer].
4. Comparison of the formal apparatuses of the S- and L-approach
[Scheibe].
5. Axiomatizations of special physical theories: Geometry and the
theory of grinding plates [Castrigiano], Special relativity
[Pfarr], Classical particle mechanics [Cooke].
ACKNOWLEDGEMENT
The editors gratefully acknowledge the sponsorship of the Deutsche
Forschungsgemeinschaft concerning the colloquium, the efforts of the
authors, the cooperation of Plenum Publishing Corp. in publishing
these proceedings and the kind assistance of Dr. R. Cooke and
Dipl.-Phys. R. Werner concerning the editing and the final
linguistic form of the manuscripts. Last not least we would like
to thank Frau P. Ellrich and Frau A. Schmidt for retyping the
manuscripts.
A. Hartkamper
H.-J. Schmidt
May 1981
University of Osnabruck
CONTENTS
A Short Account of the L-program 1
A. Hartk~mper and H.-J. Schmidt
Imprecision in Physics 7
G. Ludwig
Causality in Statistical Theories as an Example
for Idealization of Physical Laws • . • • 21
H. Neumann
Approximate Embeddings in Statistical Mechanics . . . • • 27
R. Werner
Stable Axioms in Physical Theories 39
H.-J. Schmidt
Approximative Reduction by Completion of
Empirical Uniformities • • . • 55
D. Mayr
G. Ludwig's Positivistic Reconstruction of
Theoretical Concepts .••••• 71
A. KamIah
Abstraction, Idealization and Approximation • . • • . . • 91
C.U. Majer
Differences in Individuation and Vagueness 113
W. Grafe
A General Scheme for Intertheoretic
Approximation 123
U. Moulines
Sneed's Theory Concept and Vagueness 147
W. Balzer
vii
viii CONTENTS
Mystical Realism 165
R.M. Cooke
A Comparison of Two Recent Views on Theories 197
E. Scheibe
What Do We Know from Light-Experiments about
the Principle of Relativity and the
Light Principle? ...•....••• 217
J. Pfarr
Geometrical Structures and the Grinding
Process for Three Plates . . . . 237
D.P.L. Castrigiano
Participants 249
Index 253
A SHORT ACCOUNT OF THE L-PROGRAM
A. Hartkamper and H.-J. Schmidt
Fachbereich Physik der Universitat
Postfach 4469/ 4500 Osnabruck
Federal Republic of Germany
I.
As pointed out in the preface, this volume will be concerned
for the greater part with the structure of physical theories and
the role of approximation with respect to two programs of theory
reconstruction: the "S-program" (P. Suppes, J. Sneed, W. Stegmuller)
and the "L-program" (G. Ludwig). The reader who is not acquainted
with the S-program can consult some introductory literature [1,2,3]
whereas Ludwig's work [4-11] has not yet been published in English.
Therefore a short account of the L-program might be useful for the
non-German reader to understand those articles which deal with
this program. It should be mentioned that some articles in this
book (esp. Kamlah, Scheibe,Majer) give a more detailed introduc
tion to certain aspects of the L-program and may round off our
account. (Articles will be cited by the author's name in brackets.)
The authors have been requested to use the standardized translation
of Ludwig's technical terms which will be established in this
account. Exceptions to this standard terminology as well as some
remarks on the notation used in this volume4) will be indicated
in the footnotes.
II.
When discussing the L-program one should bear in mind that Ludwig's
approach to the basic structures of a physical theory has not been
set up in the context of the contemporary discussion in philosophy
of science and methodology. It has rather been created as a frame
work to cope with physical problems, e.g. the interpretation of
quantum mechanics and the relation between macrophySics and micro-
2 A. HARTKAMPER AND H.-J. SCHMIDT
physics. The contribution of working physicists to philosophy of
science has a long tradition: we only mention the work of v. Helm
holtz, N. Bohr and Bridgman. It is therefore not surprising, that
the L-approach cannot easily be classified within the current
" ... isms" considered in philosophy of science. It is more ap
propriate to lay emphasis on the physical motivations when giving
an account of this approach.
To the layman, physics appears as a complex human enterprise
consisting of different actions and interactions of physicists:
constructing and operating apparatuses (preparing and measuring),
symbolic manipulations (mathematical deductions, numerical calcu
lations) and communication. According to what physicists themselves
say, the reason of this enterprise is to construct and to apply
physical theories (PT'~). Leaving aside the question of the ulti
mate goal of the whole buisiness, we may ask: what is a PT, or,
less pretentiously, how does a PT work? According to the L-con
ception of theories a PT "pictures", or represents, certain
elements of reality via corresponding elements in a mathematical
theory. In Ludwig's terms: there is a correspondence (--) between
a mathematical theory MT and a domain of reality [Wirklichkeitsbe
reich] W described by the particular PT. The correspondence (--)
is not an exact mapping <-> but a blurred one, speaking metaphori
cally. An element of MT corresponds to different physical situations,
and vice versa. These explanations, abbreviated as PT = W (--) MT,
can be viewed as a (provisional) definition only if the components
W, (--),MT of the definiens could be determined independently of
PT. This entails regarding MT as a formal theory without "built-in"
physical interpretation. This is for instance done in the work
of N. Bourbaki, on which Ludwig rests his appr~a~h. But the objects
of W the PT is talking about, e.g. the fields E,B in electrodynamics,
are typically defined within PT. This poses a problem, sometimes
called the "problem of theoretical terms", which seems to be a
point of bi-furcation, or rather multi-furcation, for the different
approaches towards understanding physical theories (cf. Kamlah,
Cooke). Ludwig's solution goes as follows: He restricts the domain
of reality W to a basic domain of applications [Grundbereich] G,
such that (1) G (--) MT may be defined independently of PT and (2)
W may be reconstructed in terms of G (--) MT. This policy could be
described as some kind of "cautious realism": a term of a PT is
not supposed to picture an element of W unless it is reconstructed
from G, of course using the "laws" of PT. This implicit appeal of
Ludwig to precaution becomes significant if one recalls some
premature realistic interpretations of e.g. certain terms in quan
tum theory like "the collapse of the wave function". This prominent
"collapse" disappears if it is traced back to the basic domain G
of quantum theory (consisting of macroscopic apparatuses).
At this point, several questions arise.
(1) What distinguishes G from W?
(2) How can we exclude that the reconstruction of W suffers