Logical and Epistemological Doctrine of Leonid E. Gabrilovich on Mathematical Thinking and Actual Form

The research examines the logical and epistemological studies of Leonid Evgenievich Gabrilovich (1878-1953), a Russian philosopher, logic and engineer, and subsequently a Russian-American thinker. The works of L.E. Gabrilovich still remain practically unknown or little known in Russian philosophy. In the study of the philosophical concept of one of the main works of L.E. Gabrilovich “On Mathematical Thinking and the Concept of the Actual Form” (1914), the study of the theory of “actual forms”, which clarifies the foundations of human thinking, is central to the attention of readers. It is proved that the topics of mathematical formalism, the system of experience, the actual form and the problems of number touched upon by Gabrilovich were logical and epistemological aspects of his philosophy. The research covers the content of a review of this essay by Gabrilovich of the famous German mathematician and logic Leopold Löwenheim, published in 1915. The similarity of the theory of actual forms Gabrilovich’s and the meaning of the Löwenheim theorem is revealed. The analysis of Gabrilovich’s work conducted here covers little-known pages of Russian philosophical thought and should serve to enrich and fill existing lacunae in the study of Russian philosophy of the 20th century. In the process of studying the central work of Gabrilovich, results were obtained, on the basis of which they came to the conclusion that the Russian thinker sought to build a complete system of the science of philosophy. In his emigration, Gabrilovich turned to the legacy of such Russian philosophers as Vladimir Solovyov and Nikolai Berdyaev, which was surprisingly combined with mathematical thinking and the concept of actual forms. The study outlines the prospects for studying this and other works of Gabrilovich in the context of neo-Kantianism and the philosophy of mathematics. The original theory of “actual forms” proposed by Gabrilovich can be considered the result of a philosophical understanding of the foundations of mathematics, which was characteristic precisely for logical and epistemological philosophical searches.