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We can imagine innumerable laws which would serve the same

purpose, without our being able to state a reason why one of them

is to be preferred to the others; for any one of these laws would

be founded just as little on more general theoretical principles

as is the law of Newton.

XXXI.

THE POSSIBILITY OF A "FINITE" AND YET "UNBOUNDED" UNIVERSE

But speculations on the structure of the universe also move in

quite another direction. The development of non-Euclidean

geometry led to the recognition of the fact, that we can cast

doubt on the infiniteness of our space without coming into

conflict with the laws of thought or with experience (Riemann,

Helmholtz). These questions have already been treated in detail

and with unsurpassable lucidity by Helmholtz and Poincare,

whereas I can only touch on them briefly here.