Contextualistic-Worldview Philosophy Of Mathematics

With the constant emerging of defects of the paradigms for the philosophy of mathematics behind a variety of concrete approaches and in order to go through these plights, putting forward a new paradigm which is able to be accord with the task of the philosophy of mathematics and adapted for the tendency of the philosophy of mathematical practice is becoming an important agenda. This dissertation tries to put forward a contextualistic-worldview paradigm of the philosophy of mathematics and give a new interpretation of the mathematical ontology question about "the nature and reality of mathematics".This dissertation consists of introduction, five systematic argumentations and conclusion.The introduction gives reasons for why the dissertation selects "paradigm" as a visual angle and "the nature and reality of mathematics" as its topic.Present situation of research is reviewed, problems this dissertation will solve is clarified, basic strategies, contents and hence the significance of this dissertation are illustrated.Chapter One is named "Backgrounds of the Contextualistic-Worldview Paradigm in the Philosophy of Mathematics:Emerging of the Philosophy of Mathematical Practice".There are three research paradigms in the philosophy of mathematics, which are Prescriptive Paradigm, Descriptive Paradigm and Naturalistic Paradigm. Nowadays, these paradigms fail to meet the task of the philosophy of mathematics so that the philosophy of mathematical practice is emerging.This chapter illustrates the earnest requests and necessary conditions for advancing a new paradigm in the philosophy of mathematics, on the basis of critically analyzing three present paradigms and the backgrounds of the philosophy of mathematical practice emerging.Chapter Two is "Contextualistic-Worldview Paradigm in the Philosophy of Mathematics:Theoretic Sources and Core Principles".At first, this Chapter goes back to three theoretic sources of contextualistic-worldview paradigm:contextualistic worldview, contextual realism and contextualistic philosophy of sciences.Secondly, six core principles of this paradigm are illustrated, which are practice principle, dynamic principle,context principle, consistency principle, holism principle and interdiscipline principle.At last, taking naturalistic set theoretic realism for example, it points out the significance of the paradigm viewpoint in the philosophy of mathematics research.Chapter Three, "Contextual ist-Worldview Paradigm's Understanding of the Nature of mathematics:the Nature of Mathematics is Concept", discusses the nature of mathematics by using the principles of contextualistic-worldview paradigm.It firstly gives the meaning of "the nature of mathematics".Secondly, on the basis of mathematical practice, mathematical object-Platonism and mathematical structuralism is critically analyzed.At last, it shows contextualistic-worldview paradigm's interpretation of the nature of mathematics, that is,concept.Chapter Four, "Contextualist-Worldview Paradigm's Understanding of the Reality of mathematics:There is no Abstract Mathematical World", analyzes the reality of mathematics by using the principles of contextualistic-worldview paradigm. Traditional realistic and anti-realistic interpretations of "existence" in mathematics are reviewed.Then, the indispensability argument and fictionalism in mathematics are analyzed. It finally points out the opinions of the contextualistic-worldview paradigm: there is no abstract mathematical world and the relation between mathematics and physical world is representation not description.Chapter Five, "The Methodology of Contextualistic-Worldview Paradigm:Presentation of the Contextual Analysis",illustrates the methodology of contextualistic-worldview paradigm and its functions.Firstly, this chapter clarifies the application basis of contextual analysis with its contents and characters. After that, contextual analyses of the development and the nature of mathematical knowledge are presented.Corresponding contextual interpretations are also argued. Finally, the significance of the contextual analysis in the philosophy of mathematics research is illustrated.Conclusion, "Contextualistic-Worldview Paradigm and the Development of Contemporary Philosophy of Mathematics",summarizes the main work, main idea and conclusion of the dissertation. It points out contextualistic-worldview paradigm has very important significance for contemporary philosophy of mathematics research.