On a Proof of the Inconsistency of The Classical Propositional Calculus and The Intuitionistic Propositional Calculus

The Classical Propositional Calculus CPC (zero-order logic, classical propositional logic), is the most fundamental two-valued logical system. Next, the Intuitionistic Propositional Calculus IPC differs from the CPC among others, that in IPC some laws of CPC are invalid (among others, the law of excluded middle and the law of double strong negation). Another difference is such that in IPC the principle of indirect proof (proof by contradiction) is rejected. In this paper, inconsistency (in the absolute sense i.e. Post’s sense) of the Classical Propositional Calculus is proved. From the inconsistency of CPC it follows immediately that the Intuitionistic Propositional Calculus is inconsistent in the absolute sense (Post’s sense), too.