Operational Set Theory: Reconstructing the Genesis of Mathematics and Cognition

This work proposes the Operational Set Theory (OST) — a formal system in which a set is constructed as the result of a cognitive operation on a more fundamental structure called a collection. Unlike classical approaches that postulate a set as a primary ontological given, OST derives the basic properties of sets (such as the idempotency of union) from explicitly specified primitives: object, collection, system of features, fold operator, weight, and significance threshold. The theory treats the existence of an object as an empirical fact determined by its weight (a measure of stability in the flow of experience) exceeding a given threshold. The work focuses on the internal logical coherence and constructive transparency of the proposed system, not aiming to replace axiomatic foundations like ZFC, but offering an alternative, genetic reconstruction of their ontological genesis.