↑ Quine has argued that the set-theoretical implementations of the concept of the ordered pair is a paradigm for the clarification of philosophical ideas (see "Word and Object", section 53).The general notion of such definitions or implementations are discussed in Thomas Forster "Reasoning about theoretical entities".
↑ Wiener's paper "A Simplification of the logic of relations" is reprinted, together with a valuable commentary on pages 224ff in van Heijenoort, Jean (1967), From Frege to Gödel: A Source Book in Mathematical Logic, 1979-1931, Harvard University Press, Cambridge MA, ISBN 0-674-32449-8 (pbk.). van Heijenoort states the simplification this way: "By giving a definition of the ordered pair of two elements in terms of class operations, the note reduced the theory of relations to that of classes".
↑ cf introduction to Wiener's paper in van Heijenoort 1967:224
↑ cf introduction to Wiener's paper in van Heijenoort 1967:224. van Heijenoort observes that the resulting set that represents the ordered pair "has a type higher by 2 than the elements (when they are of the same type)"; he offers references that show how, under certain circumstances, the type can be reduced to 1 or 0.
