The 17th Century Western Mathematics, Natural Philosophy Background

Taking the development of mathematics in western rational tradition as the basic thread and springboard, reviewing the influence of rebound of the view of the nature in Greece and religionary reform, combining the characteristics of the "science of quantum" of western mathematics in 17th century, the article not only provides abundant blurry continuum of quantity directly and defends for the "rationality of arithmetic" indirectly but also expatiated that the philosophy of the nature whose characteristics are the quantification of the nature and the mechanization of the universe has a great influence over 17th century's "mathematics of arithmetic" , especially over the birth and the development of analytic geometry and calculus. The article goes along Cartesian train of thoughts, clarifies that while the new mathematics whose commissary is calculus is the new byproduct of "retrieving phenomena" in the western traditional logos, the philosophy of the nature after Revival of Learning which was greatly influenced by the western logos of tradition has already formed a new effective way of "retrieving phenomena" in west logos from the quantification of the prospect of the world to the mathematication of the philosophy of the nature.Some famous historians of science such as Boter and A. Koyre emphasized that the outstanding characteristic of neoteric mathematics is "mathematication" in their series of classical books such as The Base of Neoteric Physics as Metaphysics, Study of Galileo, from the Close World to the Infinite Universe. Professor Wu Guosheng of Philosophy Department, Peking University also concentrated on this issue in his books such as The Error in Noumenon of the Nature, The Retreat of the Nature, Concept of Time. They discussed the issue from aspects of new prospect of the universe and the nature, characteristics of physics (philosophy of the nature), etc. The same thing of these scholars on this issue is that they all concentrated on the theoretic surface. As a result, we can't see the influence of scientific "mathematization" on the development of mathematics itself.The article takes mathematization as the characteristic of neoteric science by starting from the background of 17th century's philosophy of the nature and reviewing three aspects. These three aspects are the mathematization of the prospect of the nature which is based on the tradition of Pythagoras, the mechanization of the prospect of the universe which is based on the tradition of Christianism, and the deducting of the system physics which is based on the tradition of Euclid. At the same time, the point that must be clarified is that the establishment of the new view of the nature and the booming of the philosophy of the nature offered the necessary qualification of mathematization. After analyzing the process of mathematization, several conclusions are summed up as follows.First, while the subjects investigated of 17th century's mathematics include the mixture of the structure of sequence, the structure of algebra and the fuzzy quantum in the structure topology. And it is nothing other than the new philosophy of the nature whose characteristics are the quantification of substance and the mechanization of the movement that defends the existence and the property of this quantumSecond, the quantification of substance and the mechanization of the movement which are emphasized by the new philosophy of the nature offers a intuitionistic continuun which takes the extension of the space-time for the birth of calculous. It is nothing else than the division, the summing and the ratio of the intuitionistic continuun that become the basic manner in whichNewton and Leibnitz established their universal differential coefficient and integral arithmetic.Third, it is this "moment" of the segment of space-time which based on the the philosophy of the nature and describing the mechanical movement that symbolize the transform from the view of integralization in classical atomism of mathematics to the view of integralization of modern re...