Bivalence, Classical Logic and the Problem of Contingent Statements

Abstract

The main objective of this paper is to argue that the principle of bivalence is right, contrary to the view of some philosophers. To fulfil this objective, the paper examined some arguments raised in Philosophy of Logic about the principle of bivalence starting from Aristotle‟s challenge to the principle of bivalence based on the idea that the principle cannot accommodate contingent statements. The paper examined Lukasiewicz‟s challenge of the principle of bivalence and Lesniewski‟s response to him. The paper evaluated these debates, in Philosophy of Logic, to determine if the principle of bivalence should be rejected. The paper employed the methods of logic. The study showed that the principle of bivalence had been misunderstood by some of the most influential proponents of many-valued logic, for example, Lukasiewicz. It was established that the terms true (or false), in the arguments against bivalence, was used in an epistemic sense and not a logical sense. It was established that contrary to Aristotle‟s and Lukasiewicz‟s assumption, contingent statements were necessarily either true or false; hence, the principle of bivalence could accommodate contingent statements. The paper concluded that the principle of bivalence is not in any way limited; it is the core of logic; Furthermore, there may be no conflict between the principle of bivalence and other systems of logic that are not strictly bivalent, if their justification does not rely on a rejection of the principle of bivalence.

Keywords: Bivalence, Contingent statements, Classical logic, Non-contradiction, Necessity, Ontology