SIDELIGHTS ON RELATIVITY

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This view of axioms, advocated by modern axiomatics, purges mathematics
of all extraneous elements, and thus dispels the mystic obscurity
which formerly surrounded the principles of mathematics.

But a presentation of its principles thus clarified makes it also
evident that mathematics as such cannot predicate anything about
perceptual objects or real objects. In axiomatic geometry the words
"point," "straight line," etc., stand only for empty conceptual
schemata. That which gives them substance is not relevant to
mathematics.

Yet on the other hand it is certain that mathematics generally,
and particularly geometry, owes its existence to the need which
was felt of learning something about the relations of real things
to one another. The very word geometry, which, of course, means
earth-measuring, proves this. For earth-measuring has to do with
the possibilities of the disposition of certain natural objects