On Dummett’s Thought Of Intuitionistic Logic

Michael Dummett is a famous British philosopher who has made remarkable contributions to logic,philosophy of language and metaphysics.Dummett systematically studied intuitionistic logic,which became the important foundation of his philosophy.Brouwer’s constructive thought and Heyting’s formalization of intuitionistic logic provide theoretical background for Dummett’s thought of intuitionistic logic.Dummett rejected classical logic and argued that the meaning of mathematical statements should be explained by intuitionism.Because the meaning of a mathematical statement lies in its use,when we learn the meaning of expressions in a mathematical theoretical language,we learn how to use the statements in that language.On this basis,the central concept of meaning theory is the concept of proof.A decidable mathematical statement is true because we have actually constructed a proof that the statement is true.Dummett gives intuitionistic explanation to logical constants and thinks that intuitionistic logic should adopt constructive proof method.Dummett rejects law of excluded middle,he thinks proposition A∨﹁A parting on intuition is invalid.He used Beth semantics to establish the formal system of intuitionistic logic,systematically introduced the natural deduction system N and the sequent calculus system L,and proved the equivalence relationship between different systems by proving theorems.There are no axioms in system N,only rules of inference,but it is permissible to introduce any formula as a hypothesis at any stage of inference.Dummett introduced an extended concept of sequent in system L,and emphatically demonstrated the cut-elimination theorem.Dummett’s intuitionistic logic thought has produced two aspects of influence: one is to promote the development of intuitionistic logic formalization,on the other hand,it provides philosophical justification for intuitionist logic.