ABSTRACT
Geometry becomes a sort of physics—as its name suggests. Its axioms, taken together, constitute a synthetic proposition, which can in principle be tested, and which makes some significant claim about the world. Granted an interpretation, the question of which geometry is true is simply an empirical one; and, it is often maintained further, only physicists and not philosophers can contribute to its solution. A physicist can always avoid having to reject a set of axioms as false by refusing the interpretation under which they turn out to be false. There may be another interpretation, equally acceptable, under which the axioms turn out to be true. In general, it is possible to secure an interpretation under which a certain set of axioms—say the Euclidean axioms—will come out true, but this interpretation may be purchased at the price of having to have a more complicated physical theory than otherwise.
