Mathematization as a form of integration of scientific knowledge

Mathematization of science, acting on almost all spheres of society, has great social significance as a phenomenon of human culture. The modern stage of mathematization is closely connected with computerization, informatization, with the development of new technologies that are already being determined and will determine the development of society in the 21st century even more. The problem of mathematization in a certain sense is a specific problem of our century. In the past, occupying philosophical and scientific thought, surprising with its “incomprehensible” efficiency and often baffling quite large minds, it was recognized as a problem only, probably, by the scientific community, but not by society as a whole. Now, as a result of the widespread use of computers, intensive computerization and informatization of life, the attitude to mathematization underwent a radical change.

In the late 20th century, something unknown to the past was discovered and this time is not characteristic of individual scientists, and not even their community, but the entire community about I simply have a sense of the influence of mathematization on all spheres of a person’s life. Today, reality acquires, and in many areas has already acquired, a new mathematized (computerized, computerized) dimension. In this situation, understanding the universal role of mathematization presupposes a modern one. A deeper analysis of its essence, nature and foundations, and based on them - understanding the prospects for mathematization in the foreseeable future.

The problems of mathematization cannot be abstract, belonging to any one science, be it atematics, or physics, or some other science. The fundamental problem of mathematization, in our opinion, is the problem of understanding and interpreting mathematization as one of the forms of human activity, its meaning and character, dynamics and structure. Not the concept of mathematization from the point of view of a particular science, no matter how developed and mathematized it is, but mathematization in its broad socio-historical and humanistic definition is the true problem of general cultural significance. The most important key problems of human development somehow turned out to be interconnected with the achievements and capabilities of mathematical science and its applications. Hence the keen interest in the problem of mathematization, its present and future.

In the conditions of the modern stage of the scientific and technological revolution, which posed the problem of the systematic and systematic application of mathematics and computer technology in the development of the productive forces of society, interest in mathematization is growing even more. It is caused by changes in the nature of labor, the increasing role of management and automation processes, and the widespread use of computers.

Mathematization acquires special significance in connection with the study of complex system objects, the main method of cognition of which is mathematical modeling, which is not a private technocratic recipe for a narrow circle of specialists, but a universal methodology, the main tool for mathematizing scientific and technological progress. Mathematization is now a complex scientific and technological process, a sociocultural phenomenon that includes the most important aspects of the creation, development, “designing” of mathematical structures and models with their subsequent transformation in order to introduce them into computer systems and influence them on the life of society. An analysis of the essence of mathematization allows us to conclude that mathematization is now becoming a powerful factor in the development of modern sciences, not only mechanics and physics traditional for mathematics, but also new scientific disciplines and areas of scientific knowledge. Mathematization of modern science in the future will be the most important factor in its integration, the desire for a unified science of the future, which K. Marx spoke about. The means of realizing this are modern mathematical methods using abstract theoretical constructions and computer programs.

The results of the study of the computerized form of mathematization showed the need to reckon with a person not as a disciplined automaton, clothed its internal content in a linguistic form, but as a person. Already flexible expert systems, being based on a reasonable combination of “reflective” capabilities of computers and cognitive abilities of a person, are a prototype of human-machine systems designed to connect the mathematization of science with the process of its humanization in the future.

Thus, the prospects for mathematization are largely determined by the development of its computer form, embodying in a filmed form those subject meanings of human activity that are relevant in modern society.

In the future, a person should be ready for a possible meeting with such objects, for the disclosure of the inherent measures of which he needs to further develop himself. Therefore, the famous thesis of Protagoras "Man is the measure of all things" should be understood in the context of self-development of "man as a person, in all its infinity." Then really a person will be the measure of all things. In this case, neither a person nor the world can be measured either by finite scales or by final measures, for the real wealth is no longer things, not results in themselves, but the development of all human forces as such and the interaction of the developing person with the surrounding reality. In the context of such an understanding of the ancient thesis, it can be said that in the future, the computer form of mathematization will be replaced by a new form that will include not only all sciences as a whole, but through them all nature, according to the person himself with his true values and ideals. This form of mathematization will thus be human-directed, humanistic. The guarantor of the humanization of modern science through its mathematization is the development of the latter in the context of the cultural and historical movement of human society. Consequently, the analysis of mathematization should be carried out in the dialectical unity of its sociocultural and methodological contexts. The true basis for further progress in the mathematization of science is the socio cognitive nature of the subject-practical activity of a public subject in the development of the quantitative and structural aspects of objective reality. Under the influence of computerization, the classical ideal of mathematical science will be "removed" and replaced by the ideal of a unified science of man, integrated with the ideals of natural science and humanitarian knowledge. The implementation of this process will be carried out at the stage of transition from a computerized form of mathematization to a more progressive one, associated with new thinking, essentially aimed at developing the essential forces of man.

New thinking, coupled with a global vision of modern scientific problems, with reaching a universally human level of historically unified science, penetrates into mathematical knowledge, into the processes of mathematization of science. An adequate understanding of this is possible from the standpoint of dialectical logic, a dialectical-materialistic activity concept that can direct research along a systemic channel that takes into account all the modes of global mathematization as a form of human activity.