On the Inconsistency of Classical Propositional Calculus

• 作者: Lukasz T.Stepien Teodor J.Stepien
• 来源期刊: 数学和系统科学:英文版
• 学科: 数学
• 关键词: Classical propositional calculus consistency in the traditional sense consistency in the absolute sense
• 年，卷（期）: 2020,（1）
• 页码范围: 13-14
• 页数: 2页
• 分类号: O17

摘要

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.