The Importance of Polyvalent Logic for the History of Logic and Logical Pluralism

Abstract

Many-valued logic, later known as polyvalent logic, emerged from Jan Łukasiewicz’s critical reexamination of Aristotle’s principles of non-contradiction and the law of the excluded middle. A philosopher and logician of the Lviv–Warsaw School, Łukasiewicz drew inspiration from Aristotelian texts, which, as Niels Öffenberger has argued, contain conceptual antecedents of many-valued reasoning. Building on these insights, Łukasiewicz developed polyvalent logic within the framework of an indeterministic philosophy, which he regarded as the indispensable ‘metaphysical substratum’ of non-classical logic. By examining the transition from strict bivalence to the notion of objective possibility, together with Łukasiewicz’s original parenthesis-free symbolic notation (Polish notation) and the influence of nineteenth-century mathematical structuralism, this paper analyzes the historical and theoretical factors that facilitated the emergence of polyvalent logic. Particular attention is devoted to Łukasiewicz’s innovative symbolic notation and its role for the analysis of logical objects. Drawing on the existing literature, the study investigates the intellectual and historical circumstances that fostered this development and explores the new perspectives it opened for subsequent advances in logic, ultimately contributing to the emergence of logical pluralism.

Received: 20 February 2026  │  Accepted: 10 June 2026  │  Published: 23 July 2026