 The main technical and philosophical innovation of the neo-logicists is their use of abstraction principles in order to secure the existence of such things as numbers, understood, with Frege, as logical objects. One favored kind of abstraction principle typically effects the reification of equivalence classes of an equivalence  relation.[1]  One of Frege’s favorite examples involved the equivalence relation of parallelism among lines. The relevant abstraction would be that of the direction of a line. Thus, two lines l1 and l2 have the same direction just in case they are parallel: 