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)

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.

Study at a glance

Abstract

The article focuses on the exploration of the under-researched area of the philosophy of mathematics, as presented by Valerian Nikolaevich Muravyov (1885–1930). The arti­cle focuses on concepts related to set theory, Pythagoreanism, and mathematical mysti­cism, with a particular emphasis on Muravyov’s concept of dialectical construction of plurality. Muravyov developed this concept based on the ideas of Pythagoreans, Neo­platonists, Leibniz, and Cantor. The article explores questions about the nature of num­bers and their relationship to the dialectics of the one and the many within Muravyov’s work. For Muravyov, numbers are not just abstractions or bare schemes assumed by rea­son. Instead, they are the basis of both thinking and being, and they represent unity as a set that includes all subsets. This leads to paradoxical conclusions about the identity of elements within a set and the set itself. The article also discusses the influence of Georg Cantor’s set theory on Muravyov’s philosophy, including his desire to create a new logical system to resolve paradoxes within naive set theory. It emphasizes that Mu­ravyov’s work represents an important contribution to Russian philosophy of mathe­matics and analyzes a number of archive materials from the philosopher. The chapter “The Arithmetical Grounds” from his work “Formation of Plurality” is published for the first time in this article.