An introduction to mathematics, by A. N. Whitehead.

244 INTRODUCTION TO MATHEMATICS
fact which ties together our various sensations. Accordingly, the space perceptions
are in a sense the common part of our sensations. Again it happens that the abstract
properties of space form a large part of whatever is of spatial interest. It is not too
much to say that to every property of space
there corresponds an abstract mathematical
statement. To take the most unfavourable
instance, a curve may have a special beauty
of shape: but to this shape there will correspond some abstract mathematical properties which go with this shape and no
others.
Thus to sum up: (1) the properties of
space which are investigated in geometry,
like those of number, are properties belonging to things as things, and without special
reference to any particular mode of apprehension; (2) Space-perception accompanies
our sensations, perhaps all of them, certainly
many; but it does not seem to be a necessary
quality of things that they should all exist
in one space or in any space.