Interactions: Mathematics, Physics and Philosophy, 1860-1930 (Boston Studies in the Philosophy and History of Science, 251)

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 Kant, Helmholtz And The Determinacy Of Physical Notes -- A Mechanical Image: Heinrich Hertz's Principles Of Mechanics -- From Classical To Relativistic Mechanics: Electromagnetic Models Of The Electron -- Enriques: Popularising Science And The Problems Of Geometry -- Hilbert's Axiomatic Approach To The Foundations Of Science—a Failed Research Program? -- The Space Between Helmholtz And Einstein: Moritz Schlick On Spatial Intuition And The Foundations Of Geometry -- Mathematical Structure, “world Structure,” And The Philosophical Turning-point In Modern Physics -- Einstein's Allies And Enemies: Debating Relativity In Germany, 1916–1920 -- The Changing Concept Of Matter In H.weyl's Thought, 1918–1930 -- Why Does The Standard Measure Work In Statistical Mechanics?. Edited By Vincent F. Hendricks ... [et Al.]. Includes Bibliographical References And Index. 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 "The present volume is unique in assembling a broad spectrum of positions on the history of science by some of its leading representatives. Readers will find it illuminating to learn how prominent authors judge the current status and the future perspectives of their field. Students will find this volume helpful as a guide in a fragmented field that continues to be dominated by idiosyncratic expertise and that still lacks a methodical canon."--Résumé de l'éditeur The main theme of this anthology is the unique interaction between mathematics, physics and philosophy during the beginning of the 20th century. In this book, ten renowned philosopher-historians probe insightfully into key conceptual questions of pre-quantum mathematical physics. The result is a diverse yet thematically focused compilation of first class papers on mathematics, physics and philosophy, and a source-book on the interaction between them. "The present volume is unique in assembling a broad spectrum of positions on the history of science by some of its leading representatives. Readers will find it illuminating to learn how prominent authors judge the current status and the future perspectives of their field. Students will find this volume helpful as a guide in a fragmented field that continues to be dominated by idiosyncratic expertise and that still lacks a methodical canon."--Jacket