Intuitionism In Mathematics

Intuitionism is a trend of thought and doctrine that emphasizes the role of intuition or intuition in cognition.Think of intuition as a more basic and reliable way of understanding the world than abstract reason.With the continuous development of traditional mathematics,mathematical scientists and philosophers have gradually realized that traditional mathematics has limitations on the interpretation of potential infinity,mathematical induction,especially the law of the middle row.In the context of traditional mathematics research,intuitionism in mathematics can reasonably and effectively explain the rigor of traditional mathematics.It has an irreplaceable important position in traditional mathematics.Intuitionism in mathematics has important research significance to traditional mathematics in both mathematical science and mathematical philosophy.Intuitionism,logicalism,and formalism are collectively called the three major schools of mathematics,and intuitionism,which is one of the three major schools of mathematics,takes its mental structure as the most typical feature.This article analyzes and demonstrates intuitionism from two aspects of mathematical philosophy and mathematical science.First,I studied intuitionism in the development of mathematics,specifically analyzed the initiation of intuitionism in mathematics,and analyzed the rise of two major schools of logicism and formalism.Through the confrontation between intuitionism and the two major schools,it is further concluded that the mental structure of intuitionism has played a huge role in promoting traditional mathematics.Secondly,intuitionism analyzes the influence of logicalism and formalism in traditional mathematics,and then draws the most essential characteristic of intuitionism: the structure of the mind.Two phases of the development of intuitionistic mental structure were then introduced: the pre-intuitionistic phase that allowed the inductive logical connectives to appear,and the new intuitionistic phase that explained the constructive interpretation of the intuitionistic logical connectives.The author studies the characteristics of the mental structure in the two stages of intuitionism,and further draws the important role played by the intuitionist logic in the two stages,and thenanalyzes the processing logic and characteristics of the two stages of intuitionist logic.Once again,it focuses on the inspiration of intuitionistic mathematics to mathematical quality education.It explains that intuitionism in mathematics has a profound influence on traditional mathematics,especially its most classic feature: the structure of the mind has been more and more mathematical scientists and mathematical philosophers.Applied.Finally,the intuitionism is researched by comprehensive method and analytical method.At the same time,reasonable reasoning and deductive reasoning are also carried out.In the two-stage argumentation process of intuitionistic mental+construction,the comprehensive argumentation method of comprehensive method and analytical method is adopted from top to bottom and bottom to top,which makes the argumentation of many important issues easy to understand.Intuitionism in mathematics can effectively make up for traditional mathematics.Make mathematics more than just traditional logic and formal symbols.The emergence of intuitionism is an inevitable product of the development of mathematics and a manifestation of respect for science.