ABSTRACT

Our problem is now a material one, and not a formal one. We propose to investigate the objects which satisfy the axioms of Euclidean geometry. Now, these axioms are not unique. We are confronted with a choice of many possible systems. The problem then divides into many specific problems, each aiming at the particular objects capable of satisfying each separate system of axioms. But the formal relationship of all these systems re-establishes an a priori unity among the diverse objects to which they apply.