Aleksei Losev on number, mathematics and music

The article is devoted to the analysis and development of A.F. Losev’s philosophy of number. A review of existing research on this issue is provided. Definitions of arrhythmology, eidetic and hyletic numbers are given according to the early works of the philosopher of the 1920s. The roots of the term “hyletics” in E. Husserl and the change in its meaning in Losev are noted. The subject of the philosophy of number as a separate discipline is considered. The difference between number and numbering, between hyletic and real number is revealed. Examples are given of the irreducibility of numbers and the non-commutativity of operations with numbers, which can only be interpreted through a dialectical approach to mathematics. The early Losev’s philosophy of mathematics is considered in the light of Gödel's theorem formulated later. An introductory sketch of possible non-classical mathematics (a paradigm similar to quantum physics) based on correlation calculus is given. The difference between functional and correlation dependence is considered. The reductionism that is characteristic of modern mathematics is criticized. In this regard, a new view of the ancient cosmology of the Pythagoreans and Platonists and the resulting conclusions about the nature of space and time are interpreted. The final part of the study characterizes the connection between A.F. Losev’s philosophy of music with the understanding of time in the general cosmological worldview.