INTERACTIONS
Mathematics, Physics and Philosophy, 18601930
Vincent F. Hendricks
jesper lützen
klaus frovin jørgensen
stig andur pedersen
ISBN 14020 51948 (hardback)
ISBN 14020 51956 (ebook)
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Blurbs
Abstract
Table of
Contents
Cover
BLURBS
This is an outstanding
collection of original essays. All of them concern the history and
philosophy of mathematics and physics in the years from 1870 to 1930.
More specifically, they are intellectual histories of the
interactions between the three disciplines, philosophy, mathematics and
physics, in that period. And as the essays bring out, what a period it
was: of both ferment and synergy, heat and light! Most of the giants 
especially Helmholtz, Hertz, Poincare, Hilbert, Einstein and Weyl  are
here: engaging not just in physics and mathematics but also in
philosophy, often together, or with figures like Schlick. The editors
are to be congratulated on a major contribution to our understanding of
one of the most complex but fertile periods in the history of all three
disciplines.
 Jeremy Butterfield, University of Cambridge
This stimulating volume covers a wide range of topics which are of
direct interest to anyone who thinks about the curious relation between
mathematics and the natural world. Philosophers often pose interesting
questions about the “dispensability” of mathematics to science. But they
too often overlook the wealth of philosophical perplexities that can
arise in detailed examples and case studies, both contemporary and
historical. This volume refocuses our attention by addressing a number
of topics connected to applied mathematics, any one of which is worthy
of every philosopher’s attention.
 James Robert Brown, University of Toronto
What to make of neoKantianism in its heyday, from 18401940? It was
the most prolific of times and the most seminal, it was the most muddled
and confused, it is philosophy working at its hardest with science and
most damagingly against science.
It is examined here episodically, as it engaged individual scientists:
Helmholtz, , Hertz, Poincare, Minkowski, Hilbert, Eddington and Weyl. If
Einstein is not in their number, he had to contend with their influence,
and anyway he transformed their agenda. The essays on these figures are
glinting in their focus and scholarship. Whatever one thinks of
neoKantianism, this book is history and philosophy of science at its
best: mathematically and physically informed, historically engaged, and
philosophically driven.
 Simon Saunders, University of Oxford
Ten firstrate
philosopherhistorians probe insightfully into key conceptual questions
of prequantum mathematical physics, from Helmholtz and Boltzmann,
through Hertz and Lorentz, to Einstein, Weyl and Eddington, with an
interesting aside on the rarely studied
philosophy of Federigo Enriques. A rich and effective display of what
the critical history of science can do for our understanding of
scientific thought and its achievements.
 Roberto Torretti, University of Puerto Rico
Abstract
The main
theme of this anthology is the unique interaction between mathematics,
physics and philosophy during the beginning of the 20th century. Seminal
theories of modern physics and new fundamental mathematical structures
were discovered or formed in this period. Significant physicists such as
Lorentz and Einstein as well as mathematicians such as Poincaré,
Minkowski, Hilbert and Weyl contributed to this development. They
created the new physical theories and the mathematical disciplines that
play such paramount roles in their mathematical formulations. These
physicists and mathematicians were also key figures in the philosophical
discussions of nature and science — from philosophical tendencies like
logical empiricism via critical rationalism to various neoKantian
trends.
Table of Contents
HENDRICKS 7 LÜTZEN / JØRGENSEN / PEDERSEN / Preface
DAVID E. ROWE / Einstein’s Allies and Enemies: Debating
Relativity in
Germany, 19161920.
HELMUT PULTE / The Space between Helmholtz and Einstein: Moritz
Schlick on Spatial Intuition and the Foundations of Geometry.
DAVID HYDER / Kant, Helmholtz and the Determinacy of Physical
Theory.
ROBERT DISALLE / Mathematical Structure, “World Structure,” and
the
Philosophical Turningpoint in Modern Physics.
ERHARDSCHOLZ/ The Changing Concept of Matter in H.Weyl’s
Thought,
1918 – 1930.
LAWRENCE SKLAR / Why Does the Standard Measure Work in
Statistical
Mechanics?
JESPER LÜTZEN / A Mechanical Image: Heinrich Hertz’s Principles
of
Mechanics
JEREMY GRAY / Enriques: Popularising Science and the Problems of
Geometry.
MICHEL JANSSEN AND MATTHEW MECKLENBURG / Electromagnetic
Models of the Electron and the Transition from Classical to
Relativistic
Mechanics
ULRICH MAJER / Hilbert’s Axiomatic Approach to the Foundations
of
Science—a Failed Research Program?
Index
COVER
