Ebook: Interactions: Mathematics, Physics and Philosophy, 1860–1930

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

---

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

---

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

Content:
Front Matter....Pages I-XIV
Kant, Helmholtz and the Determinacy of Physical Notes....Pages 1-44
A Mechanical Image: Heinrich Hertz's Principles of Mechanics....Pages 45-64
From Classical to Relativistic Mechanics: Electromagnetic Models of the Electron....Pages 65-134
Enriques: Popularising Science and the Problems of Geometry....Pages 135-154
Hilbert's Axiomatic Approach to the Foundations of Science—A Failed Research Program?....Pages 155-184
The Space between Helmholtz and Einstein: Moritz Schlick on Spatial Intuition and the Foundations of Geometry....Pages 185-206
Mathematical Structure, “World Structure,” and the Philosophical Turning-Point in Modern Physics....Pages 207-230
Einstein's Allies and Enemies: Debating Relativity in Germany, 1916–1920....Pages 231-280
The Changing Concept of Matter in H.Weyl's Thought, 1918–1930....Pages 281-306
Why Does the Standard Measure Work in Statistical Mechanics?....Pages 307-320
Back Matter....Pages 321-326

---

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

Content:
Front Matter....Pages I-XIV
Kant, Helmholtz and the Determinacy of Physical Notes....Pages 1-44
A Mechanical Image: Heinrich Hertz's Principles of Mechanics....Pages 45-64
From Classical to Relativistic Mechanics: Electromagnetic Models of the Electron....Pages 65-134
Enriques: Popularising Science and the Problems of Geometry....Pages 135-154
Hilbert's Axiomatic Approach to the Foundations of Science—A Failed Research Program?....Pages 155-184
The Space between Helmholtz and Einstein: Moritz Schlick on Spatial Intuition and the Foundations of Geometry....Pages 185-206
Mathematical Structure, “World Structure,” and the Philosophical Turning-Point in Modern Physics....Pages 207-230
Einstein's Allies and Enemies: Debating Relativity in Germany, 1916–1920....Pages 231-280
The Changing Concept of Matter in H.Weyl's Thought, 1918–1930....Pages 281-306
Why Does the Standard Measure Work in Statistical Mechanics?....Pages 307-320
Back Matter....Pages 321-326
....