Science and Hypothesis: The Complete Text

✍ Scribed by Henri Poincaré; Mélanie Frappier; David J. Stump; Mélanie Frappier; Andrea Smith; David J. Stump

• Publisher: Bloomsbury Academic
• Year: 2018
• Tongue: English
• Leaves: 209
• Category: Library

✦ Synopsis

Science and Hypothesis is a classic text in history and philosophy of science. Widely popular since its original publication in 1902, this first new translation of the work in over a century features unpublished material missing from earlier editions.
Addressing errors introduced by Greenstreet and Halsted in their early 20th-century translations, it incorporates all the changes, corrections and additions Poincaré made over the years. Taking care to update the writing for a modern audience, Poincaré’s ideas and arguments on the role of hypotheses in mathematics and in science become clearer and closer to his original meaning, while David J. Stump’s introduction gives fresh insights into Poincaré’s philosophy of science. By approaching Science and Hypothesis from a contemporary perspective, it presents a better understanding of Poincare’s hierarchy of the sciences, with arithmetic as the foundation, geometry as the science of space, then mechanics and the rest of physics.
For philosophers of science and scientists working on problems of space, time and relativity, this is a much needed translation of a ground-breaking work which demonstrates why Poincaré is still relevant today.
Poincaré saw the recognition of the role of hypotheses in science as an important alternative to both rationalism and empiricism. In Science and Hypothesis, his aim is to show that both in mathematics and in the physical sciences, scientists rely on hypotheses that are neither necessary first principles, as the rationalists claim, nor learned from experience, as the empiricist claim. These hypotheses fall into distinct classes, but he is most famous for his thesis of the conventionality of metric geometry. Poincaré discusses the sciences in a sequence, starting with arithmetic. Mathematical induction is essential in arithmetic, because only by using it can we make assertions about all numbers. Poincaré considers mathematical induction to be a genuine synthetic a priori judgment. He next considers magnitude, which requires arithmetic, but goes further. Likewise, geometry extends our knowledge still further, but requires the theory of magnitude to make measurements, and arithmetic to combine numbers. Poincaré then considers classical mechanics, which again extends our knowledge while relying on the mathematics that came before it. Finally, he considers theories of physics, where we have genuine empirical results, but based on the mathematics, hypotheses and conventions that came before. Thus the sciences are laid out like expanding concentric circles, with new content being added to the base at each level.

✦ Table of Contents

Cover page
Halftitle page
Series page
Title page
Copyright page
Contents
Foreword
Acknowledgments
Original Sources of the Material in Science and Hypothesis
Author’s Preface to the Halsted Translation
Introduction
Part One Number and Magnitude
1 On the Nature of Mathematical Reasoning
I
II
III
IV
V
VI
VII
2 Mathematical Magnitude and Experience
Definition of incommensurables
The physical continuum
Creation of the mathematical continuum
Measurable magnitude
Various remarks
The multidimensional physical continuum
The multidimensional mathematical continuum
Part Two Space
3 Non-Euclidian Geometries
Lobachevskiian geometry
Riemann’s geometry
Surfaces with a constant curvature
Interpretation of non-Euclidean geometries
Implicit axioms
The fourth geometry6
Lie’s theorem
Riemann’s geometries
Hilbert’s geometries8
On the nature of axioms
4 Space and Geometry
Geometrical space and representative space
Visual space
Tactile space and motor space
Characteristics of representative space
Changes of state and changes of position
Conditions of compensation
Solid bodies and geometry
The law of homogeneity
The non-Euclidean world6
The four-dimensional world
Conclusions
5 Experience and Geometry
1
2
3 Geometry and astronomy
4
5
6
7
SUPPLEMENT
8
Ancestral experience6
Part Three Force
6 Classical Mechanics
The principle of inertia
The law of acceleration
Anthropomorphic mechanics
The “School of the Thread”
7 Relative and Absolute Motion
The principle of relative motion
Newton’s argument
8 Energy and Thermodynamics
Energetics
Thermodynamics
General Conclusions for Part Th ree
Part Four Nature
9 Hypotheses in Physics
The role of experiment and generalization
The unity of nature
The role of hypotheses
Origin of mathematical physics
10 Theories of Modern Physics
The meaning of physical theories
Physics and mechanism
The current state of physics
11 Probability Calculus
I: Classification of problems of probability
II: Probability in mathematics
III: Probability in the physical sciences
IV: Red and black
V: Probabilistic causation
VI: Theory of errors
VII: Conclusions
12 Optics and Electricity
Fresnel’s theory
Maxwell’s theory
The mechanical explanation of physical phenomena
13 Electrodynamics
I Ampère’s theory
II Helmholtz’s theory
III Difficulties raised by these theories
IV Maxwell’s theory
V Rowland’s experiments
VI Lorentz’s theory
14 The End of Matter
Index