245 XXIV. THE POSTULATE OF EQUIVALENCE 250 XXV. THE INCLUSION OF GRAVITATION IN THE MODEL OF SPACE-TIME 261 XXVI. TENSORS AND THE LAWS OF NATURE 266 XXVII. THE PRINCIPLE OF GENERAL COVARIANCE, OR THE GENERAL PRINCIPLE OF RELATIVITY 276 XXVIII. THE DISCOVERY OF THE EINSTEINIAN LAW OF GRAVITATION 281 XXIX. THE GENERAL LAWS OF MOTION 286 XXX. THE VERIFICATION OF EINSTEIN’S LAW 290 XXXI. THE SEPARATION OF SPACE-TIME INTO SPACE AND TIME IN A GRAVITATIONAL FIELD 293 XXXII. THE PRINCIPLES OF CONSERVATION 305 XXXIII. OTHER ASPECTS OF THE GRAVITATIONAL EQUATIONS 310 XXXIV. THE FINITENESS OF THE UNIVERSE 313 XXXV. THE IMPORTANCE OF SPACE-TIME, AND THE PRINCIPLE OF ACTION 347 XXXVI. THE MYSTERY OF MATTER 356 XXXVII. THE THEORIES OF WEYL AND EDDINGTON 360 PART IV THE METHODOLOGY OF SCIENCE XXXVIII. THE METHODOLOGY OF SCIENCE 373 XXXIX. THE CO-ORDINATION OF PHYSICAL FACTS ACCOMPLISHED BY RELATIVITY 474 XL. THE GENERAL SIGNIFICANCE OF THE THEORY OF RELATIVITY 481 APPENDICES I. THE SPACE AND TIME GRAPHS 509 II. THE CURVATURES OF SPACE-TIME 524 III. THE GRAVITATIONAL EQUATIONS 527 IV. SPACE, GRAVITATION AND SPACE-TIME 531 [Pg ix] FOREWORD “And now, in our time, there has been unloosed a cataclysm which has swept away space, time and matter, hitherto regarded as the firmest pillars of natural science, but only to make place for a view of things of wider scope, and entailing a deeper vision.” H. WEYL (“Space, Time and Matter”). THE theory of relativity represents the greatest advance in our understanding of nature that philosophy has yet witnessed. If our interest is purely philosophical, we may wish to be informed briefly of the nature of Einstein’s conclusions so as to examine their bearing on the prevalent philosophical ideas of our time. Unfortunately for this simplified method of approach, it is scarcely feasible. The conclusions themselves involve highly technical notions and, if explained in a loose, unscientific way, are likely to convey a totally wrong impression. But even assuming that this first difficulty could be overcome, we should find that Einstein’s conclusions were of so revolutionary a nature, entailing the abandonment of our ideas on space, time and matter, that their acceptance might constitute too great a strain on our credulity. Either we would reject the theory altogether as a gigantic hoax, or else we should have to accept it on authority, and in this case conceive it in a very vague and obscure way.