Mathematics, Physics and Philosophy, 1860-1930

Vincent F. Hendricks
jesper lützen
klaus frovin jørgensen
stig andur pedersen

Dordrect: Springer, Octoberr 2006

 ISBN 14020 5194-8 (hardback)
ISBN 14020 5195-6 (ebook)

Buy from Amazon: US

Table  of Contents


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 neo-Kantianism in its hey-day, from 1840-1940? 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 neo-Kantianism, 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 first-rate philosopher-historians probe insightfully into key conceptual questions of pre-quantum 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



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 neo-Kantian trends.

Table of Contents


DAVID E. ROWE / Einstein’s Allies and Enemies: Debating Relativity in
Germany, 1916-1920.

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 Turning-point 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

JESPER LÜTZEN / A Mechanical Image: Heinrich Hertz’s Principles of

JEREMY GRAY / Enriques: Popularising Science and the Problems of Geometry.

Models of the Electron and the Transition from Classical to Relativistic

ULRICH MAJER / Hilbert’s Axiomatic Approach to the Foundations of
Science—a Failed Research Program?