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

TL;DR

This paper analyzes Charles Peirce's classification of relations, focusing on dyadic and degenerate relations, and explores how his ideas influenced later developments in mathematical logic by logicians like Tarski and Löwenheim.

Contribution

It reconstructs Peirce's classification system of relations and examines its impact on the evolution of formal logical relations in the history of mathematical logic.

Findings

Peirce's classification influenced later logicians' work on dyadic relations.

Focus on degenerate and genuine dyadic relations clarifies Peirce's system.

Historical analysis links Peirce's ideas to modern logical frameworks.

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.