The crisis of meaning in the decidability-procedure of propositional calculus: a philosopher’s contribution to the debate “is logic empirical?”

Abstract

The question: “Is logic Empirical” is an ongoing debate among logicians in recent times. Generally, the debate has taken two dimensions that can be regarded as different schools of thought. Whereas one of the schools responds affirmatively to this question, the other school toes the opposite direction. This paper also responds to this question, but focuses on propositional logic, which forms a basic part of the curriculum of logic as taught in many universities in Nigeria. This paper adopted a Reconstructionist approach that replaced alethic semantics with binary semantics and also assigned different meanings to the logical operators of Propositional Logic other than the ones found in many logic text-books used in Nigerian universities. The result of this bold but radical venture is that decidability in propositional Calculus preserves a mathematical meaning which is somewhat contrary to the empirical meaning preserved by many authors of logic-texts in Nigeria,. On the strength of this discovery, the paper submits that there is indeed a crisis of meaning in propositional calculus as the practice of testing for the validity of syntactic expressions, presumed to be symbolic representations of real arguments, is paradoxical to the principle of consistency.

Keywords: Decidability, Propositional Calculus, Truth-Table