The Study Of Dummett's Intuitionism Logic

In the second half of the nineteenth century,Cantor created the Collection Theory,and then mathematicians in this period began to propose a mathematical framework on the base of the Collection Theory,so that they could create a more perfect mathematical theory.However,Russell,a famous British mathematician,proposed the "Russell paradox",which thoroughly disclosed the problems of Cantor's Collection Theory.As a result,it triggered modern mathematical crisis and led to the three schools of mathematics,Modern logic,Formalism and Intuitionism,they all to explore the mathematical basic problems.Objectively speaking,the discussion of the basis of mathematics,in fact,is equal to the logic basis of mathematics.Frege thinks that mathematics follow logic,and logic is the basis of mathematics.Mathematics and logic can be combined into one.Mathematical formula,the rule of reasoning and the validity of the accurate representation can all be achieved through logical reasoning.The binary logic because of its perfect,strict and absolute was treated as a sufficient demonstration of mathematics.But Brouwer found that as the foundation of mathematics,some of the rules of the logic,such as the Law of Excluded Middle,were not rigorous.Therefore,he thinks it is necessary to establish a set of non-logical effects,which loyal to themselves only and not obey the external axioms of mathematics,and that is Intuitionism.To sum up,intuitionistic mathematics is based on the relation between mathematics and logic,and then Brouwer proposed a constructive ideas.This idea amend certain principles of the classical logic and inference rules.The view of "to be is to be constructed" began to accepted by people.It stressed that the mathematical content is not an objective existence,but the result of our mental structure.It claims that truth is decided by our mind,it is a state that we have confirmed to the object or proposition.That is to say,the logic really is true,it means we can find methods and means to confirm proposition or object.As the successor of the Brouwer,Heyting further developed the view of intuitionistic mathematics and created an intuitionistic symbolic logic system for Brouwer's foundational program in mathematic.The system keep the export generated propositional transform confirmed rather than truth.Its appearance,to a large extent,affected the development of mathematics,which has been the attention of many mathematicians.For example,Kolmogorov?Godel?Kressel?Kripke?etc are made some contributions in this respect.Among these,Dummett's research is very worthy of attention.Dummett is an excellent representative of the 20th century analytic philosophy faction,he put the debate between realism and anti-realism summarized as Intuitionism and Platonism,and further expounds the importance of the intuitionis logic in semantic respects.This paper aims to through development process of Intuitionism,and study Dummett's"Elements of Intuitionism" expression of Intuitionism logic view.The research regards his logical views as a case for depicting intuitionist logic view,so that people could have a better understanding of contemporary non classical logic.