The one returns to itself: “The dialectical construction of multiplicity” and the mathematical mysticism of V.N. Muravyov. Appendix. V.N. Muravyov. The dialectical construction of multiplicity (ed. and comments by A.M. Kuksyuk)
Philosophy Journal December 2, 2025 Alexey Kuksyuk
Numbers, for philosopher Valerian Muravyov, are not mere abstractions but the foundation of both thought and reality, uniting the one and the many. Drawing on Pythagoreans, Neoplatonists, Leibniz, and Cantor, he developed a dialectical concept of plurality in which a number is a set containing all its subsets, leading to paradoxes about identity. The article examines Muravyov's attempt to create a new logical system to resolve paradoxes in naive set theory and publishes his chapter 'The Arithmetical Grounds' for the first time. His work is presented as an important contribution to Russian philosophy of mathematics.