Reductionism and Newtonian mechanics are still the most powerful ways of thinking in today's natural science education. However, the success of modem physics and modem system theories, which includes more than ten integrated science and technology theories, suggest a new way of thinking about and explaning the natural world. In this paper we investigate the beginning and development of unified concepts of system from the western history of natural science and analyze the different and complementary relationships between Newtonian mechanics and modem systemics in detail. This investigation includes basic concepts, basic rules, basic theories and logic of thinking which are the general requirements for constructing a theory or philosophical thinking system. According to the evidences shown in almost every branch of natural science which has been investigated by modern system theories, the material systems have an almost infinite number of orderly rrangement states (levels) and self-organized abilities just as the living creature, and the mechanism of self-organization and evolution for these systems are related to the feedback iterations of causes and effects among different levels. This is the key point for the understanding about the beginning of the universe and of the material and living world. This might also be the most important part of the evolutionaI mechanism of these systems in space-time. According to our investigation in dielectric thin films systems (which are typically the open systems) [31, 32] and in "Yi Jing" [33], we propose that the evolutional mechanism should include seven circulative processes: (1) catastrophe process, (2) latent process, (3) expanding process,(4) change in genetic process, (5) maturational process, (6) climax process and (7) unstable process.