The Discussion On Implication

Implication" is a universally used, rather important notion in logic, especially in modern logic. Only you roundly understand and master the problem of implication and its related questions, can you truly learn modern logic well. Therefore, it is important to study it.This article, basing on two sides: theoretic changing and the development of history, discusses the problem of implication. Firstly, it studies the definition of implication and its classification, basing on this, deeply analyzes the relations between implication and the connective "if, then" universally used in our ordinary life. Then the article points out that implication is logical abstract to the connective "If, then" used in the natural language. However, because of different understanding and mastering to it, implication may have different classification, it can't be given a right definition. We must master it by all kinds of concrete implications.According to different criterion, implication has different categories. This article mainly discusses its classification from two sides: Ancient Greece and Medieval's and metalogic's.Basing on this, this article deeply analyzes the relations between implication and the connective "If, then" used in ordinary logical thinking, and points out that material implication is scientific abstract generation to the ordinary language "If, then". Their sameness lies in: when a conditional's protasis is true and its consequent is false, material implication equation is false. At the same time, the article also deeply analyzes their differences.This article discusses the track of the development of implication theory, generalizes B.Russell's idea about implication,simply induces such implication theories as C.I.Lewis' "strict implication" W.Ackermann's "relevant implication" and so on, and analyzes the relations among these theories, emphasizes that material implication's basic status in mathematical logic.Finally, this article expounds disturbing problem "implication paradox" in the theory of implication, analyzes its causes which arise this paradox, and points out the meaning of implication paradox. On the one hand, Implication paradox provides semantics grounding for two conditional inference principles; on the other hand, the discovery of implication paradox arouses logicians' discussion to the implication theory and makes them put forward many new implication theories such as: strict implication -, relevant implication and etc., and promotes the development of the implication theory and makes implication theory step down mysterious palace, and gradually penetrates into many other concrete sciences.