Relativity is the study of matter in motion, and the basis of a theory of relativity can be either physical, mathematical, or logical. It is physical if some of the elementary objects and relations are concepts derived from the external world and if certain of their properties are assumed as physically obvious. If, however, the elementary objects, etc. are defined as mathematical symbols and relations, and if the subsequent theorems are mathematical deductions from these definitions, then the theory may be described as mathematical. Lastly, the basis of a theory is logical if certain terms are undefined—and clearly stated as such—and if the theory is then developed strictly deductively from an explicit set of axioms and definitions. Analogous examples taken from geometry are the Euclidean, algebraic, and projective theories. The first, as developed by Euclid, has a physical basis, while the second is mathematical, a point being defined as an ordered set of numbers (co-ordinates) and a line as the class of points satisfying a linear equation. The third is logical, the undefined elements being point and line (an undefined class of points) and the axioms being those of incidence, extension, etc. Usually a physical theory comes first, to be followed by a mathematical and then by a logical theory, this last being so constructed that it includes previous theories when its undefined elements are replaced on the one hand by the conceptual physical objects and on the other hand by the symbolic mathematical objects. The construction of such a logical theory is not merely a matter of academic interest, for it can be regarded as an analysis of the previous theories. It tests, for example, the consistency and independence of their basic assumptions and definitions. It also indicates how a theory can be modified, with as little change as possible, so as to include some feature previously excluded. This can be particularly useful in the case of a physical theory which has been constructed to correspond as closely as possible to the external world, for such a theory may need continual modification to keep in step with observational data. For this reason the axioms of a logical theory should be not only consistent and independent but also simple, i.e. indivisible.