Science and Convention. Essays on Henri Poincaré's Philosophy of Science and the Conventionalist Tradition

243 Pages·1982·11.23 MB·English

by  Jerzy Giedymin and Mario Bunge (Auth.)

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The Philosophy of Technology
ALCOCK, J.
Parapsychology: Science or Magic?
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Relativity: The Theory and its Philosophy
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The Mind-Body Problem
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The Logical Foundations of Mathematics
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Mathematics as a Cultural System
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Science and Convention
Essays on Henri Po/ncaré's Philosophy of Science
and The Conventionalist Tradition
by
JERZY GIEDYMIN
University of Sussex, Brighton
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First edition 1982
Library of Congress Catalog Card no: 81-81334
British Library Cataloguing in Publication Data
Giedymin, Jerzy
Science and convention. - (Foundations &
philosophy of science & technology)
1. Science - Philosophy
I. Title
501 Q175
ISBN 0-08-025790-9
Printed in Great Britain by A. Wheaton & Co. Ltd., Exeter
To the memory
of my parents
Preface
ESSAYS in this volume are concerned with Henri Poincaré's philoso-
phy of science—physics in particular—and with the conventionalist
tradition in philosophy which he revived and reshaped at the turn of
the century, simultaneously with, but independently of, Pierre
Duhem. My aim was to make explicit the main ideas of that
philosophy (Essays 1 and 5), to trace at least some of its historical
background (Essays 1, 2 and 3) and to follow some of its later
developments (Essays 2 and 4). Since the ideas in question are, for
the most part, epistemological in nature and are discussed here in
their historical context, the essays may perhaps be characterised as
belonging to comparative epistemology.
The main reason for writing these essays was this. On the basis of
my research I came to the conclusion that the philosophy of Poin-
caré and of his fellow-conventionalists had been perceived in too
narrow a fashion, misunderstood and, consequently, under-
estimated. It is my belief that in Poincaré's philosophical writings
one of the leading traditions in 19th century mathematics found its
epistemological and ontological expression, viz. the tradition,
represented in the writings of Galois, Poncelet, Plücker, Cayley,
Hermite, Darboux, Klein and many others, for which the concepts
of transformations, groups and invariants were fundamental and
characteristic. It penetrated not only many branches of pure
mathematics but also kinematics, analytic dynamics, optics and elec-
trodynamics. It provided the foundation for the mathematical shape
of much of the new 20th century physics of relativity and of the
quanta. As regards Poincaré's own research, discontinuous groups
were essential for the theory of automorphic functions (of one
complex variable) which he discovered, stimulated by Hermite's
work on modular functions; Lie's theory of transformation groups
was the basis for his analysis of the foundations of geometry
vii
viii Preface
and—as Hadamard put it (1914, 1921, p. 220)—"in his guiding the
nascent theory of relativity". Not surprisingly, the general ideas of
transformations, groups and their structures as well as of a theory of
invariants with respect to a group, which may be identified with the
relativity theory of the group, became fundamental for Poincaré's
epistemology (Essays 1, 2 and 5).
However, the outlined perception of Poincaré's philosophy is not
the one shared by the majority of his commentators, nor is it
reflected in the name "conventionalism" (geometrical or physical)
now usually attached to it. For some reason, those whose
pronouncements were to set the trend over roughly sixty years in
defining and assessing Poincaré's contribution to the philosophy of
physics, have restricted their attention to only one of its two inter-
related features, viz. the one expressed in the claims such as that the
axioms of geometry are conventions, that the choice of one of
metric geometries is (empirically) arbitrary, that scientists often
elevate empirical generalisations to the status of conventional prin-
ciples, that some hypotheses (indifferent ones) are conventions freely
invented by the mind, etc. This feature, undoubtedly important,
became henceforth enshrined in the name conventionalism, never
used by Poincaré himself. So, for example, as early as April 1922
Albert Einstein is reported as saying—at a discussion in Paris where
he attended a reception in his honour—that there existed two
opposite views concerning physical theories between which he felt
unable to decide: Kant's apriorism and Poincarés conventionalism.
Both were in agreement on the point that to construct science we
need arbitrary concepts; but according to Kant these were given in α
priori intuition whereas according to Poincaré they were conventions
(Bulletin de Ια Société Française de Philosophie, Juillet 1922; reported in
Nature, August 18, 1923, p. 253). Through a kind of "harmony of
illusions" (to use L. Fleck's terms) this line of exegesis became firmly
established in the German-speaking countries where, in all prob-
ability, the term "conventionalism" was coined. Roughly between
1918 and 1960 it permeated the logical empiricist perception of
Poincaré's philosophy through the writings of Schlick, Reichenbach
and Frank. It also dominated the view of the critics of logical
empiricism under the influence of Popper, Frank and Holton, the
Preface ix
first of whom saw instrumentalism (theories are nothing but
mathematical contrivances) as an essential part of conventionalism.
And yet, any attentive reader of Science and Hypothesis—not to
mention other writings of Poincaré, especially the (1898) paper—
should have noticed the other side of Poincaré's philosophy, the side
concerned with the cognitive role of groups and their invariants in
mathematics and physics. This can be illustrated by the following
claims: the object of geometry is to study a particular group; in our
minds the latent idea of a number of groups pre-exists (these are
groups with which Lie's theory is concerned); from all possible
groups we choose one to which to refer natural phenomena; there is
no absolute space, there is no absolute time, we have no direct intuition
of the simultaneity of distant events; the principle of relative motion is
impressed upon us because the commonest experiments confirm it
and because the consideration of the contrary hypothesis is singularly
repugnant to the mind, etc. The concept of invariance (invariantism)
or of relativity would be much more appropriate than "con-
ventionalism", to refer to this feature of Poincaré's epistemology.
If now one inquires how the two aspects of Poincaré's epis-
temology, viz. conventionalism and invariantism came to be asso-
ciated, then my answer is roughly this:
Poincaré's main epistemological problem was the question how
objective knowledge and continuous progress were possible in spite
of apparently disruptive changes in mathematics and in science. It is
in his solution of this epistemological problem that he combined the
ideas of convention and conventionality with the ideas of invariance,
groups, transformations, etc.
From such developments as the discovery of non-Euclidean
geometries and of higher spaces, from the criticism of the assump-
tions of absolute space and time in Newtonian mechanics and from
the philosophy of the physics of the principles, Poincaré drew the
conclusion that many elements of science which had appeared as
ultimate truths about the world turned out, on closer analysis, to be
conventional contrivances: though undoubtedly serving a purpose,
they were substitutable by different conventions without change in
the cognitive content of relevant theories. Consequently, not all
problems and disputes in the history of science which had appeared
χ Preface
as substantive and empirical were indeed such. What one did not see
properly was that these disputes resulted from the existence of
observationally equivalent (or, at least, experimentally indistinguish-
able) theories based on different conventions. Having discovered the
non-empirical nature of some of the time-honoured problems con-
cerned, for example, with the nature of space, time, light, etc., some
philosophers, viz. nominalists, have concluded that "anything goes",
that science is purely conventional. In fact it is such only if one
adopts the nominalist attitude, otherwise it is not. However, in order
to avoid the Scylla of naïve empiricism and the Charybdis of
nominalism, one has to be clear about what constitutes the cognitive
content of scientific theories and in effect where the limits of know-
ledge are. One way of doing this is to adopt the view, known as
instrumentalism, according to which only the observational but not
the abstract part of a scientific theory contributes to the cognitive
(descriptive) content. This is Ramsey's view and, perhaps, Duhem's,
but—despite all appearances—not Poincaré's. For, according to
Poincaré, mathematics is not concerned with the production of
purely formal games. It is a study of structures and mappings which,
in its progress, reveals previously unsuspected connections between
remote areas. Mathematical intuition plays the same active role in
theoretical physics except that it is constrained there by the
requirement of numerical (experimental) adequacy. The content of a
theory consists, therefore, of its numerical predictions and of the
form of its equations. The latter may be understood in terms of the
group admitted (in Lie's sense) by the equations, and its invariants.
Theoretical changes which do not alter either numerical predictions
or the form of the theory are inessential. Even essential changes,
however, need not be disruptive. Comparability is preserved if, for
example, the groups of two apparently rival theories are shown to be
subgroups of a third group; such is the case of classical and rela-
tivistic mechanics since the Galileo-Newtonian and Lorentzian
groups are sub-groups of the affine group, as has been shown by F.
Klein. In general, Poincaré's epistemology emphasises the relational
nature of knowledge, whether in mathematics or in physics, and the
unknowability of objects as such, i.e. apart from their relations to
others. It is not equivalent to instrumentalism and might best be
Preface xi
called structural realism. Since it combines elements of empiricism
and rationalism it is a semi-rationalist view.
The outlined interpretation of Poincaré's epistemology has the
advantage that it does justice to a lot of textual evidence ignored in
the traditional interpretation which is in terms of conventionalism to
the exclusion of invariantism or structuralism. Moreover, it has
immediate implications for the debate over the discovery of special
relativity and Poincaré's role in it. Some of the claims made in that
debate, for example that owing to his alleged inductivism Poincaré
was unable to conceive of a general relativity theory ("general", not
in the sense of "general covariance" but in the sense of general
principles applicable to more than one specific area of physics), must
be seen at once as untenable, to say the least. Poincaré's epis-
temology was certainly much more rationalistic than the Machist
epistemology of Einstein around 1905. In fact Einstein embraced a
semi-rationalist philosophy, similar to Poincaré's, only in his later,
post-Machist period. Since the most general concept of relativity
theory, in the sense of an invariant theory of most comprehensive
groups, was the basic element of the mathematical and philosophical
tradition of which Poincaré was a creative member, he was naturally
predisposed to apply such mathematical ideas in dealing with the
problems in theoretical physics that arose from Michelson-Morley's
and related experiments. On the question of Poincaré's role in the
discovery of relativity theory, my position (Essay 5) differs both from
the established view and Whittaker's controversial claims; it is as
follows: the priority for the non-mathematical (experimental) for-
mulation of the (special) relativity principle as well as for the state-
ment of the limiting and constant velocity of light, are credited to
Poincaré; the formulation of the relativity principle in terms of the
Lorentz transformations and its mathematical elaboration are
claimed to be a case of simultaneous and independent discovery by
Poincaré and Einstein, with the latter seeing more clearly the physi-
cal implications and Poincaré being superior in the mathematics of
the theory (invariants of the Lorentz group, basic ideas of the
four-vector formalism, etc.).
In the light of what has been said already about the customary
narrow interpretation of Poincaré's epistemology, it is not surprising
x/7 Preface
that its historical background had been seen in a similarly restrictive
fashion. Though Maxwell's and Lorentz's theories have figured
prominently in the discussions of its origins, little else is usually
mentioned and even the role of those two theories is often described
in a slanted way. So, for example, Duhem, who was perhaps one of
the first to emphasise the role of Maxwell's theory for the genesis of
Poincaré's philosophy, saw this role exclusively in the alleged effect
of Maxwell's instrumentalist view of (mechanical) models. Poincaré's
analysis of the formal analogies between the equations of optics and
electricity (in Poincaré's 1895) and his emphasis on their epistemolo-
gical importance escaped Duhem's attention. Again, in recent con-
tributions to the debate over the discovery of relativity theory, the
impact of Lorentz's theory on Poincaré's world-view has been
claimed (e.g. by Miller) with little regard for those features of
Poincaré's philosophy which are clearly incompatible with Lorentz's
realist interpretation of the ether hypothesis and the electromagnetic
world view. I felt, therefore, that it was important to draw atten-
tion—however unsystematically and tentatively—to those elements
of Poincaré's historical background which, though relevant to his
philosophy, had been largely ignored. This applies, above all, to the
philosophy of the physics of the principles (Lagrange, Poisson,
Fourier, Cauchy in France) whose British representative, Hamilton,
I also link—hypothetically (perhaps through Larmor and Whit-
taker)—with Ramsey (Essay 2). Similarly, though Poincaré wrote
only à propos of Joseph Larmor's physical theories, he did pursue in
detail Larmor's programme of analysing formal similarities between
alternative theories of optics and electricity with important con-
sequences for his epistemology (Essays 2 and 5). Gabriel Koenigs's
kinematics, based on the theory of transformations, is in itself
historically interesting (one of his definitions reads: "Absolute velo-
city is the geometrical sum of relative velocity and the velocity of
entrainment", where "absolute" and "relative" have "a purely con-
ventional sense", 1897, p. 82). Poincaré saw in "Koenigs's theorem",
to which he refers repeatedly, the justification of the conventionalist
thesis of the multiplicity of theoretical explanations for any set of
observational data in mechanics (Essay 5). To my knowledge, this has
never been discussed by critics.