On the incomprehensible effectiveness of mathematics. Searching for the mathematical object

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Transliteration of original Title: 
O «nepostizhimoy effektivnosti» matematiki, ili v poiskakh matematicheskogo ob"ekta
Author(s): 
Andrey Makarov
Samara State University
Alexander Shestakov
Samara State University of Architecture and Civil Engineering
Issue number: 
No. 3 (Vol. 49)
Pages: 
216-224
Abstract: 

Review represents a new edition of the Moscow seminar on philosophy of mathematics works. The book deals with two interrelated problems: the problem of "the incomprehensible effectiveness" of mathematics and the problem of the ontological status of mathematical objects. The conditions of applicability of mathematical theories in the natural, social and human sciences. Ideas and themes proposed by the authors of articles aimed to reveal perspective analysis of the subject, which allows to detect its previously implicit sides. This approach makes possible to put different questions related to the foundations of mathematics and provide an additional impetus to research in this area.

Keywords: 
a mathematical reality, the ontological status of mathematical objects, the interpretation of a mathematical theory, the ontologization of scientific theories, physical and mathematical models, the effectiveness of mathematics