
25Historical dynamics of implicit and intuitive elements of mathematical knowledgeLiberal 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 threestage process. The first stage considers some general conditions of valid mathematical knowledge recognized by the …Read more

14The nature of the topological intuitionLiberal 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 nonstandard problems, for which there is no algorithm for such a solution. In such cases, the mathematician addresses the socalle…Read more

13Intuition and heuristics in mathematicsLiberal Arts in Russia 2 (3): 237251. 2013.The article is devoted to philosophy of mathematics. Mathematical heuristics, being a complex of methods for solving the nonstandard 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, PoincarÃ©’s, Hadamard’s and Piaget’s findings. Base…Read more

4The concept of implicit knowledge in the context of rational reconstruction of the history of mathematicsLiberal 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

3Mathematical symbolization: Specificity and implementationLiberal Arts in Russia 3 (4): 237245. 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

3Understanding in mathematical scienceLiberal Arts in Russia 6 (1): 3339. 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 ‘understandingexplanation‘, 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

2Postnonclassical philosophy: postmodern “deconstruction” and rational reconstruction of the history of scienceLiberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitarnyj Zhurnalrossiiskii Gumanitarnyi Zhurnal 9 (1): 16. 2020.

2Intuition and heuristics in mathematicsLiberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitaryj Zhurnalrossiiskii Gumanitarnyi Zhurnal 2 (3): 237. 2013.

Mathematical symbolization: Specificity and implementationLiberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitaryj Zhurnalrossiiskii Gumanitarnyi Zhurnal 3 (4): 237. 2014.

Regularities in the development of scientific knowledgeLiberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitarnyj Zhurnalrossiiskii Gumanitarnyi Zhurnal 7 (4): 245. 2018.

“The society of selfrealization”: specificity and formation conditionsLiberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitarnyj Zhurnalrossiiskii Gumanitarnyi Zhurnal 8 (3): 184. 2019.