RELATIVITY...EXCERPT

Relativity: The General and Special Theory, “Part I. The Special Theory of Relativity; Physical Meaning of Geometrical Propositions,” by Albert Einstein (Forgotten Books: 1920, 2012), p.1-4 “Geometry sets out from certain conceptions such as ‘plane,’ ‘point,’ and ‘straight line,’ with which we are able to associate more or less definite ideas, and [form] certain simple propositions (axioms) which, in virtue of these ideas, we are inclined to accept as ‘true,’ Then, on the basis of a logical process, the justification of which we feel ourselves compelled to admit, all remaining propositions are shown to follow from those axioms, i.e. they are proven. A proposition is then correct (‘true’) when it has been derived in the recognized manner from the axioms. The question of the ‘truth’ of the individual geometrical proposition is thus reduced to the truth of the axioms. Now it has long been known that the last question is not only unanswerable by the methods of geometry, but that it is in itself entirely without meaning… The concept ‘true’ does not tally with the assertions of pure geometry, because by the word ‘true’ we are eventually in the habit of designating always the correspondence with a ‘real’ object; geometry, however, is not concerned with the relation of the ideas involved in it to objects of experience, but only with the logical connection of these ideas among themselves…. “Geometrical ideas correspond to more or less exact objects in nature, and these last are undoubtedly the exclusive cause of the genesis of these ideas. Geometry ought to refrain from such a course, in order to give to its structure the largest possible unity… “If, in pursuance of our habit of thought, we now supplement the propositions of Euclidean geometry by the single proposition that two points on a practically rigid body always correspond to the same distance (line-interval), independently of any changes in position to which we subject the body, the propositions of Euclidean geometry then resolve themselves into propositions on the possible relative position of practically rigid bodies. Geometry which has been supplemented in this way is then treated as a branch of physics. We can now legitimately ask as to the ‘truth’ of geometrical propositions interpreted in this way, since we are justified in asking whether these propositions are satisfied for those real things we have associated with the geometrical ideas… “Of course the conviction of the ‘truth’ of geometrical propositions in this sense is founded exclusively on rather incomplete experience. For the present, we shall assume the ‘truth’ of the geometrical propositions, then at a later stage (in the general theory of relativity) we shall see that this ‘truth’ is limited, and we shall consider the extent of its limitation.”