The Philosophical Analysis Of Mathematical Explanation

The traditional view in philosophy of mathematics shows that the explaining is the focus of this subject. However, the study of mathematical explanation is still in a dispersed and peripheral phase for a long time. This article attempts to analysis of philosophy on the problem of mathematical explanation, with it stand out from mathematical practice. And through the researching on the system about the mathematical explanation’s origin, connotation, philosophical account and philosophic significance, we can demonstrated mathematical explanation as a new research field in the philosophy of mathematics, plays an important value in the expansion for philosophy of mathematics.This article consists of introduction, four systematic argumentations and conclusion.The introduction gives reasons for why the article selects "mathematical explanation" as its topic. Present situation of research is reviewed, problems this article will solve is clarified, basic strategies, contents and hence the significance of this article are illustrated.Chapter One is "The motivation of mathematical explanation". It expounds the motivation of mathematical explanation in the mathematics and philosophy. In mathematics, mathematical explanation comes from excavation of reason. In philosophy, mathematical explanation is a new field of mathematical realism and anti-realism, also it is a new form of indispensability arguments for mathematical realism. So, mathematical explanation has turn into an unavoidable topic in the contemporary philosophy of mathematics.Chapter Two is "The connotation of mathematical explanation". It discussed the connotation of mathematical explanation, introduced the two different categories of mathematical explanation. That was explanation in mathematics and mathematical explanation in science. The former mainly refers to explanatory proof and non-explanatory proof, the latter refers to that mathematics play a part in account natural phenomena and scientific phenomena. Through the analysis, there has no consensus for the standards of explanatory proof, at the same time, whether mathematics is really play role explanation in science has also not reached a consensus.Chapter Three is "Contemporary philosophical accounts of mathematical explanation". It analysis two accounts model of the mathematical explanation, that was Steiner’s local model and Kitcher’s holistic model. The local model is a model from study mathematical explanation in mathematics. And the local model is a model from effect of mathematics in scientific explanation. The article explained the two models and there predicament respectively.Chapter Four is "The philosophical significance of mathematical explanation". That mainly reflected in the relation of mathematical practice and philosophy of mathematics, also in the argument of mathematical realism and mathematical anti-realism, and in test theories of scientific explanation.In conclusion, summarizes the main work, It points out the innovation and deficiency, and make prospects for the mathematical explanation of further research.