Abstract

Aristotle discovered the law of contradiction more than 2000 years ago. Since then, this law has been regarded as one of the basic principles of logic. Aristotle considered this principle to be 'the most indisputable of all beliefs,' but nearly half a century ago, it began to be criticized. The voice of criticism came from a philosophical logic - paraconsistent logic. This study analyses in depth the specific properties of the positive logic plus approach, non-adjunctive approach, and relevant approach of paraconsistent logic and presents three definitions of the law of contradiction. It also shows that there are two types of the law of contradiction in C-logics and that the law of contradiction with classical negation is valid in them. Furthermore, this study proves that the law of contradiction with classical negation is also valid in a non-adjunctive approach and explains the reason this law cannot be deduced in some relevant logic systems. Based on these, we can clarify what type of the law of contradiction is questioned by paraconsistent logics and thoroughly reveal the exact meaning of 'the law of contradiction is invalid' in paraconsistent logics.