Against the concept of an infinite spatial world and in favor of a finite spatial world, this much can be said:

(1) From the point of view of the theory of relativity, it is much simpler to conceive of a finite spatial world than a quasi-Euclidian world bounded by infinite space.

(2) Mach’s supposition that inertia depends on the reciprocal action of bodies is approximated in the equations of the theory of relativity; from these equations it follows that inertia depends, partly at least, on the reciprocal action of masses. Mach’s supposition is therefore well founded, for it is hardly appropriate to suppose that inertia depends partly on reciprocal action and partly on the independent properties of space. But Mach’s supposition calls for a finite spatial world, not a quasi-Euclidian infinite world. In short, from the epistemological point of view it is better to have the mechanical properties of space wholly determined by matter, and this obtains only if the world is spatially finite.

(3) An infinite world is possible only if the average density of its matter is lost. Such a supposition is logically possible, to be sure, but it is less probable than the supposition that the world’s matter has an average finite density.