The Mathematical Factor In Western Philosophy

In each developing stage,western philosophy is more or less related with mathematics in a certain extent.Mathematics is an important source and basis of the philosophical problems as well as it provides rich soil and environment for the development of the Western philosophy.Many philosophers in the history are also accomplished mathematicians.In their view,mathematics and philosophy are part of each other.The research object of mathematics is the world of ideas,which has always been regarded as the embodiment of truth.Although philosophers have doubts on everything,they generally believe that mathematics are always the truth.Therefore,philosophers felt that they need to explain the above judgement,and extract a general philosophy conclusion.Many philosophers regard mathematics as another form of philosophy based on its abstractness and general research objects.Mathematics are inextricably linked to the western philosophy based on its truth and certainty.This paper focuses on the introspection of mathematical methods of many philosophers(such as Pythagoras,Socrates and Platon,Descartes,Leibniz etc.)in the history of the Western Philosophy,form the philosophical knowledge closely related with the mathematics,open the diversified direction of the philosophical study and initiate the introspection of different disciplines.This paper is divided into four parts:The first chapter: the world outlook and methodology originated from the mathematical thinking of the Ancient Greek philosophy.It mainly focus on the topics including Pythagoras applied numbers to stipulate the basic order of everything,Socrates explores definition of virtue in the dialogue,Platon replace hypothesis by rational intuition to form a philosophical interpretation of the rational and intuitive method.The second chapter: the medieval Christian philosopher Augustin Thomas and Anselm Aquinas applied "Cauchy convergence principle" to proof the existence of god.The third chapter: the development of the mathematical world outlook and method of ancient Greek philosophy theory in modern science and philosophy,mainly focusing on the facts that Galileo,Newton,Leibniz,etc.applied the mathematical methods and had a profound impacts on the modern science and philosophy.The fourth chapter: the application of mathematical methods in philosophy led to the rationalist dogmatism,but the modern western philosophy still refine the philosophy analytic tool,the mathematical logic and applied this tool to criticize the traditional metaphysics.Reflection on mathematics is an important source to generate the philosophical thinking.