In the paper two types of the theory of abstraction are examined. One of them is based on the method of inclusion and exclusion of the abstractions. The other one - on the method of ascending from the abstract to the concrete. Both of the theories have constituted the ground for constructing of two logics: formal and dialectical. Neither one nor the other have an independant meaning in itself novadays.

An attempt is made in this paper to analyze the specificity of the present-day controversy on universals. In conclusion, the author indicates that dialectical materialism does not deny abstractions, including abstractions of high levels, and positively appraises nominalistic analyses as a means for substantiating abstract and hypothetical knowledge, as a means for disclosing constructive substance in unconstructive theories.

According to the basic idea of the theory of semantic categories the huge variety of expressions could be reduced to three basic classes, called basic semantic categories: names, statements, and functors. On this basis abstract objects or universale can be reduced also to three basic typest abstract objects-terms, abstract objects-statements, and abstract objects-operators. The so-called auxilliary signs, in particular brackets in formalized languages, fulfil a certain, structural function and, on this ground, can be numbered to the type of abstract objects-operators with a specific semantic index.

As the answer to the question clearly depends on its precise meaning, the paper aims at presenting some explications of the problem and the conclusions entailed by each of them. If mathematical entity is taken in a narrow sense, the answer turns out to be negative; on some broader conceptions, it is positive. Though irreducible to a numerical structure, a scientific domain is identifiable with some set theoretic entity.