  Charles Peirce develops a scheme for classifying different kinds of monadic,
dyadic and triadic relations. His account of these different classes of
relations figures prominently in the development of his algebraic and
diagrammatic systems of mathematical logic. Our aim in this essay is to
reconstruct and examine central features of the classificatory system that he
develops. Given the complexity of the system, we will focus our attention on
the classification and explanation of of degenerate and genuine dyadic
relations, and we will take up the discussion of triadic relations elsewhere.
One of our reasons for wanting to explore this account of relations is to
better understand how it informed the later development of relations as they
figure in the history of mathematical logic. The earlier work of Peirce on
dyadic relations influenced the development of the account of dyadic logical
relations in works of Ernst Schroder, Leopold Lowenheim, Thoralf Skolem and
Alfred Tarski. As such, our primary aim in this essay is to trace the early
development of these ideas about the formal relation of the dyad for the sake
of better understanding how it might have influenced these later developments.
