Analysis And Its Significance Of Frege Arithmetic Real Problem

As a creative logician and mathematician,Frege dedicated his entire life to the demanding work of deriving mathematics from logic and establishing a logistic basis for mathematics.In the effort to conduct this work,he created a new set of artificial language and logical system,and thus laid the foundation of modern Mathematical Logic.He investigated into the question as of what is the most elementary number of mathematics,and came up with numerous profound insights.As a result,He was also regarded as one of the founders of analytical philosophy and language philosophy in the 20th Century.In order to achieve the ultimate goal of reducing mathematics to logic,he gave a definition to the term Number relying exclusively on logic concepts, and built an arithmetic system on this basis.But that work was considered incongruous and unsuccessful with the advent of Russell Paradox.Affected by this, researches about Frege have largely been focused on logic and philosophy fields rather than his key work.This thesis undertakes to explore how Frege conducted his key work and what is the value of his work.In the view of the author,a more reasonable description of Frege's key work is the demonstration that arithmetical truth is analytical.This thesis is divided into three chapters.The first chapter examines Frege's philosophical demonstration of the problem on the truth of arithmetic,and argues that a proper definition of Number is essential.Chapter two deals with Frege's philosophical argument on Number,as well as how he gave a technically proper definition to Number.The last chapter compares thoughts of Frege and Kant,and notes that both of them based their work on the objectiveness of knowledge and confidence of human abilities.Frege claimed that Kant and he had more in common than in divergence,yet the author tends to conclude from comparison analysis that the two had apparently different thoughts.Kant attributed the universal source of knowledge to cognitive subject,Frege cognitive object.In Kant's theory Time was preliminary and was the basis,yet Frege excluded it. Frege used symbols rather than representations as the cognitive mediation,relation rather than entity as the core of his logic system,and thus achieved certain superiority over Kant approaches.Frege didn't carry out philosophy thinking and technical handling in isolation,but combined them effectively.The approaches employed by Frege to construct objects from equal relation of objects are widely used in daily life as well as modern-time mathematic researches.Consequently,the work done by Frege, in terms of both thoughts and approaches,is of significant implication and value even in the present age.