Science and Hypothesis
Henri Poincaré
for Contemporary Readers
First published 1902 (French) · Lucid Classics edition 2026 · 183 pages
Original and Lucid edition, side by side
Greenstreet translation, 1905
The very possibility of mathematical science seems an insoluble contradiction. If this science is only deductive in appearance, from whence is derived that perfect rigour which is challenged by none? If, on the contrary, all the propositions which it enunciates may be derived in order by the rules of formal logic, how is it that mathematics is not reduced to a gigantic tautology? The syllogism can teach us nothing essentially new, and if everything must spring from the principle of identity, then everything should be capable of being reduced to that principle. Are we then to admit that the enunciations of all the theorems with which so many volumes are filled, are only indirect ways of saying that A is A?
Lucid Classics
The very possibility of a mathematical science looks like a flat contradiction. If the science is only deductive in appearance, where does its perfect rigor, which no one challenges, come from? If, on the other hand, every proposition it states can be derived in turn by the rules of formal logic, why is mathematics not reduced to one gigantic tautology? The syllogism teaches us nothing essentially new. If everything must spring from the principle of identity, then everything ought to be reducible to that principle. Must we then admit that the statements of all the theorems that fill so many volumes are only roundabout ways of saying that A is A?
Contents
- Author's Preface
- On the Nature of Mathematical Reasoning
- Mathematical Magnitude and Experiment
- Non-Euclidean Geometries
- Space and Geometry
- Experiment and Geometry
- Classical Mechanics
- Relative and Absolute Motion
- Energy and Thermodynamics
- Hypotheses in Physics
- The Theories of Modern Physics
- The Calculus of Probabilities
- Optics and Electricity
- Electrodynamics