"Philosophical Mathematics" is a science that studies the deep-seated and macro-relationship between nature, society and life, and it is a new mathematics that is fundamentally different from traditional mathematics. The essential feature that distinguishes it from traditional mathematics lies in the organic combination of philosophical thinking and mathematical thinking, dialectical logic and formal logic, qualitative research and quantitative research, and traditional culture and modern science. Therefore, we can overcome the limitations brought by formal logic to traditional mathematics, and make mathematical thinking enter all research fields that traditional mathematical thinking is difficult to enter, including superstructure, humanities and social sciences, traditional Chinese medicine and so on.

The quantitative study of identity and opposition is the core of philosophical mathematics. The concepts of leading attribute clarity, correlation deviation and central variable clarity are introduced, which lays the foundation for this paper. The quantities involved in these concepts are generally unmeasurable and can be grasped through thinking, so they are fuzzy, which is no different from fuzzy mathematics. The difference is that fuzzy mathematics is only examined from one aspect, while philosophical mathematics is examined from two opposing and unified aspects. This has led to a qualitative leap in mathematical thinking, from simple quantity to the organic combination of qualitative and quantitative, with positive and negative symbols for qualitative and absolute values for quantitative. The identity and opposition between things are also revealed through symbols. On this basis, we can further calculate the degree of approval and opposition, so as to achieve a qualitative leap in philosophical thinking, from simple qualitative development to the organic combination of qualitative and quantitative. The theoretical framework of philosophical mathematics is based on four basic concepts: meta-system, clarity of dominant attributes, correlation deviation and clarity of central variables. Its basic theories include basic attribute theory, correlation deviation theory, central variable theory, dialectical relationship theory and meta-system theory. Among them, the first four theories are the foundation and the meta-system theory is the core. Its main content is to explore the origin of various characteristics of natural system, social system and symbol system. For example, how human society came into being, why all kinds of creatures in nature are relatively stable, what are the roots of social contradictions and so on. , all belong to its research category.