Significance of Mathematization of Philosophical Problems from the Angle of Broadspectrum Philosophy

Abstract

Whether philosophy can realize mathematization has long been controversial. As the mathematics develops a nonquantative branch- structural mathematics, however, mathematization of philosophy has a turnaround. Broadspectrum philosophy which makes use of structural mathematics has established a generally applicable as well as precise mathematical model for many philosophical problems, giving a positive answer to whether the philosophy can be mathematized. Mathematizaiton of philosophy allows more accurate and clear distinction of people’s expression in meaning, gives ideas the visible characteristics, makes philosophy an analyzable discipline, and realizes routinization of philosophical methods. Hegel was well versed in mathematics but opposed “Extreme Mathematic Attitude”, since he thought recognizing all the objects from the mathematic standpoint of “Quantity or Quantitative Relationship” would ignore the qualitative difference among the objects.［1］P239 Hegel’s opinion was based on the traditional mathematic which takes the Quantitative Relationship as the foundation. Holding the same evidence as Hegel's, most philosophers nowadays still suspect that the philosophy can be mathematized. When the modern mathematics has developed a new nonquantative branch, the Structural Mathematics, the philosophy mathematization, however, meets a turning point. Opposed to Quantitative Mathematics, the Structural Mathematics focuses on research of mathematic relationship and structure on the basis of abstract set theory. Since the structural mathematics doesn't rely on quantity and quantitative relationship, it can be combined in research of philosophy which usually doesn’t possess quantitative characteristics. Establishment of Broadspectrum Philosophy is a successful attempt. With full application of set theory, symbolic logic, modern algebra, transformation group theory and graph theory, Broadspectrum Philosophy constructs a generally applicable as well as precise mathematical mode for many philosophical problems, bringing a fundamental change to the philosophy. This paper attempts to make some preliminary analysis on the significance of establishment of Broadspectrum Philosophy.