On the Inconsistency of Classical Propositional Calculus

The classical propositional calculus (often called also as “zero-order logic”), is the most fundamental two-valued logical system. It is necessary to construct the classical calculus of quantifiers (often called also as “classical calculus of predicates” or “first-order logic”), which is necessary to construct the classical functional calculus. This last one is being used for formalization of the Arithmetic System. At the beginning of this paper, we introduce a notation and we repeat certain well-known notions (among others, the notions of operation of consequence, a system, consistency in the traditional sense, consistency in the absolute sense) and certain well-known theorems. Next, we establish that classical propositional calculus is an inconsistent theory.