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.