The study is devoted to the philosophical and mathematical concepts in N. V. Bugaev’s
philosophy. The goal is to identify the features of the structuring of mathematical knowledge in his philosophical views. The relevance of this study is determined by the fact that, unfortunately,
the philosophical views of N. V. Bugaev still remain insufficiently studied. The article analyzes
the main works of the thinker on the philosophy of mathematics. It is shown that the ideas
presented in these works allow us to talk about a separate direction in the history of Russian
philosophy, based on arithmology and evolutionary monadology. To the main characteristics
of the philosophical views of N. V. Bugaev include the complementarity of the material and
spiritual, the antinomy of the discontinuous and the continuous, attention to aesthetic and
ethical issues, and the rationale for considering mathematics in a philosophical context. Based
on a study of the classification of sciences and the structure of mathematical knowledge in
N. V. Bugaev’s philosophy shows that the division into continuous and discontinuous analysis
refers only to the analysis of functions, all mathematics is divided into a block that is based on
continuity (mathematical analysis and geometry) and a block, the main one of which is discrete
analysis (synthesis), discrete block includes: arithmology, probability theory and number theory.
Keywords
arithmology, philosophy of mathematics, history of Russian philosophy
Literature
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