 The foregoing considerations are rather abstract. To see more clearly what is at stake, let us focus on a specific example. Geach (1967) mentions that rational numbers are defined set-theoretically to be equivalence classes of integers determined by a certain equivalence relation defined on “fractions,” i.e., ordered pairs of integers (1/2 is \(\langle 1,2\rangle\), 2/4 is \(\langle 2,4\rangle\), etc.). He suggests that we can instead construe our theory of rational numbers to be about the fractions themselves, taking the \(I\)-predicable of our theory to be the following equivalence relation, \(E\):