•  2
    Post-non-classical philosophy: postmodern “deconstruction” and rational reconstruction of the history of science
    Liberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitarnyj Zhurnalrossiiskii Gumanitarnyi Zhurnal 9 (1): 16. 2020.
  • “The society of self-realization”: specificity and formation conditions
    Liberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitarnyj Zhurnalrossiiskii Gumanitarnyi Zhurnal 8 (3): 184. 2019.
  • Regularities in the development of scientific knowledge
    Liberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitarnyj Zhurnalrossiiskii Gumanitarnyi Zhurnal 7 (4): 245. 2018.
  •  4
    The concept of implicit knowledge in the context of rational reconstruction of the history of mathematics
    Liberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitarnyj Zhurnalrossiiskii Gumanitarnyi Zhurnal 7 (1): 3. 2018.
    In the article, questions from the field of philosophy of mathematics are studied. The author is driven by the need to achieve a balance between the philosophy of science and the history of science in formation of concepts of the science development. In this regard, the author justifies the reliance on the methodology of implicit knowledge, combined with the epistemology principle of criticism in studying the development of mathematics as the most expedient and effective. The author expresses th…Read more
  •  3
    Understanding in mathematical science
    Liberal Arts in Russia 6 (1): 33-39. 2017.
    In the article, the phenomenon of understanding in mathematics is studied. This topic is relevant in contemporary philosophy of science, in which the classic dichotomy of ‘understanding-explanation‘, characteristic of classical science, undergoes serious transformations. One reason for this transformation is a quantitative increase in the flow of information in modern science. It is clear that in such a situation you want to hold a serious understanding of this information in the context of mode…Read more
  •  14
    The nature of the topological intuition
    Liberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitaryj Zhurnalrossiiskii Gumanitarnyi Zhurnal 5 (1): 14. 2016.
    The article is devoted to the nature of the topological intuition and disclosure of the specifics of topological heuristics in the framework of philosophical theory of knowledge. As we know, intuition is a one of the support categories of the theory of knowledge, the driving force of scientific research. Great importance is mathematical intuition for the solution of non-standard problems, for which there is no algorithm for such a solution. In such cases, the mathematician addresses the so-calle…Read more
  • Mathematical symbolization: Specificity and implementation
    Liberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitaryj Zhurnalrossiiskii Gumanitarnyi Zhurnal 3 (4): 237. 2014.
  •  25
    Historical dynamics of implicit and intuitive elements of mathematical knowledge
    Liberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitaryj Zhurnalrossiiskii Gumanitarnyi Zhurnal 1 (1): 30. 2012.
    The article deals with historical dynamics of implicit and intuitive elements of mathematical knowledge. The author describes historical dynamics of implicit and intuitive elements and discloses a historical and evolutionary mechanism of building up mathematical knowledge. Each requirement to increase the level of theoretical rigor in mathematics is historically realized as a three-stage process. The first stage considers some general conditions of valid mathematical knowledge recognized by the …Read more
  •  2
    Intuition and heuristics in mathematics
    Liberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitaryj Zhurnalrossiiskii Gumanitarnyi Zhurnal 2 (3): 237. 2013.
  •  3
    Mathematical symbolization: Specificity and implementation
    Liberal Arts in Russia 3 (4): 237--245. 2014.
    In this article the philosophy of mathematics issues related to the procedure of mathematical symbolization are studied on the basis of phenomenon of implicit knowledge. The specificity of mathematical symbolization and conditions of its implementation, defines the role of mathematical symbolization in the development of mathematics. The author believes that the results can justify the thesis that the basis of mathematical symbolization is a priori epistemological ‘foundation‘. The author believ…Read more
  •  13
    Intuition and heuristics in mathematics
    Liberal Arts in Russia 2 (3): 237--251. 2013.
    The article is devoted to philosophy of mathematics. Mathematical heuristics, being a complex of methods for solving the non-standard problems of mathematics (such problems which have no known algorithms to be solved), is the main subject of the research. As a specific mechanism for thinking, generating elements of guesswork needed as the basis of mathematical heuristics, the author considers intuition. In the work, the author uses Descartes’s, Poincaré’s, Hadamard’s and Piaget’s findings. Base…Read more