Abstract

The features of development of the subject-matter of mathematics can be viewed from the standpoint of the study of mathematics as objectification in Marx’s sense – as a relatively independently self-reproduced sphere of activity. For an explication of this development it is necessary to define concepts of “world”, “object”, “subject-matter”, “subject-actor”, “reality”, “structure”, “model”, “objectification”, “ontology”. In the process of objectification of the domain of objects of mathematics takes place a transformation of forms of existence and creation of new ontologies, with respect to new types of realities. The development of mathematics as a sphere of human activity necessarily contains subjectification. The results of mathematical activity are fixed as objects and reproduced in the intersubjective, objectivized domain of mathematics, because the subject-actor itself is practically incorporated into the structure of the world as an object. Mathematics as practically realizable objectification of knowledge is modelling of ontologies. The immediate subject-matter of mathematics is the manifold of abstract structures of subject-actor, whereas the mediated object of mathematics is the manifold of object structures of the world.