反证法与归谬法的现代分析

Modern Analysis of Law of Indirect Proof and Reductio

本文以现代命题逻辑为分析工具,证明了:在正命题逻辑系统的基础上,反证法的证明能力强于归谬法,它们之间相差一个双重否定律;归谬律与不矛盾律加上充分条件否定后件律相等价;反证律与不矛盾律、排中律、充分条件否定后件律加上选言推理否定肯定律相等价。

By way of modern propositional logic, this paper proves three issues: Firstly, In positive propositional logical system, the indirect proof is more efficient than reductio, and the difference between them is that the former has the law of double negation. Secondly, reductio is equivalent to the law of non-contradiction with negative consequent of sufficient conditional additionally. At last, the law of indirect proof is equivalent to the combination of law of non-contradiction; excluded middle; negative consequent of sufficient conditional and negative affirmation form of disjunctive reasoning.