4 - A Report on an Axiomatization of Einstein's Theory of Space-Time

Summary

A clarification of the fundamental concepts of the theory of relativity will only be possible if the tenets of the theory are presented in axiomatic form. The axioms contain the fundamental facts whose existence justifies the theory; in principle, they are empirical assertions capable of experimental verification. In addition to these are the definitions through which the theory's conceptual content is constructed. These, in contrast to the axioms, are arbitrary forms of thought, capable of neither empirical confirmation nor refutation. Their arbitrariness is only constrained by certain well-understood logical demands that are required for a scientifically appropriate system. They must be univocal; but moreover they must lead to a scientific system characterized by certain properties of simplicity. Whether they fulfill these demands is not solely a matter of form, but depends upon the validity of the axioms; the preferred properties of the conceptual system derive from the facts laid down in the axioms. The results of the systematic derivation of all the theorems of the theory from the definitions and axioms, viz., “ordine geometrico,” are twofold: on the one hand the discovery of those facts without which the theory could not exist and whose validity completely proves the theory, and the other hand the discovery of its logical structure which gives the theory its legitimate place as a scientific theory.

The axioms fall into two classes: light axioms (I–V) and matter axioms (VI–X).