The Philosophy of Space & Time"An important landmark in the developmant of the empiricist conception of geometry, this book is still one of the clearest and most valuable expositions of the crisis in physical science and mathematics occasioned by the advent of the non-Euclidean geometries. With unusual depth and clarity, it covers the problem of the foundations of geometry, the theory of time, the theory and consequences of Einstein's relativity including: relations between theory and observations, coordinate definitions, relations between topological and metrical properties of space, the psychological problem of the possibility of a visual intuition of non-Euclidean structures, and many other important topics in modern science and philosophy." --Back cover. |
Contents
The axiom of the parallels and nonEuclidean geometry | 1 |
Riemannian geometry | 7 |
6 | 24 |
Copyright | |
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Common terms and phrases
according action by contact arbitrary assertion axioms axis causal chain characterized circle classical theory concept consider coordinate system coordinative definition corresponds curvature curved defined definition of congruence definition of simultaneity determined dimensionality dimensions direction distance Doppler effect empirical epistemological equal equation equivalent Euclidean geometry Euclidean space exists experience expression fact formulation four-dimensional function genidentity given gravitational field inertial system infinitesimal domains interpretation intersection interval kinematic length light ray light-geometry logical Lorentz contraction Lorentz transformation mass points mathematical means measuring instruments measuring rods metrical field motion moving segment non-Euclidean geometry objective observer parallel parameter space perceptions philosophical physical plane possible problem properties relations relativistic relativity of simultaneity rest rest-length result rigid bodies rigid rods rotation satisfied space-time manifold spatial special theory sphere spherical statement straight line surface tensor theorem theory of relativity theory of space three-dimensional topological universal forces velocity of light visualization world-line