Charles Peirce on the Classification of Dyadic Relations and the Implications for Mathematical Logic

Abstract

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.