Science has taken over from pre-scientific thought the concepts space,
time, and material object, and has modified them and rendered them more
precise. Its first significant accomplishment was the development of
Euclidean geometry, whose axiomatic formulation must not be allowed to
blind us to its empirical origin.
The subtlety of the concept of space was enhanced by the discovery
that there exist no completely rigid bodies. All bodies are elastically
deformable and alter in volume with chang in temperature. The
structures, whose possible congruences are to be described by Euclidean
geometry, cannnot therefore be represented apart from physical concepts But
since physics after all must make use of geometry in the establishment of
its concepts, the empirical content of geometry can be stated and tested only
in the framework of the whole of physics
In this connection atomistics must also be borne in mind, and its
conception of finite divisibility; for spaces of sbu-atomic extension cannot
be measured up. Atomisics also compels us to give up, in principle, the idea
of sharply statically defined bounding surfaces of solid bodies. Strictly
speaking, there are no precise laws, even in the macro-region, for the
possible configurations of solid bodies touching each other.
In spite of this , no one thought of giving up the concept of space,
for it appeared indispensable in eminently satisfactory whole system of
natural science. Mach, in the nineteenth century, was the only one who
thought seriously of an elimination of the concept of space, in that he
sought to replace it by the notion of the totality of the instantaneous
distances between all material points. (He made this attempt in order to
arrive at a satisfactory understanding of inertia) .