A Temporal Consistency Rule for Set Formation: Resolving Russell's Paradox via Evaluation Semantics

This short paper examines Russell’s paradox from the perspective of semantic and temporal consistency in set formation. Rather than proposing new axioms or rejecting classical set theory, it identifies a missing but necessary rule governing when membership evaluations are valid. Many standard examples of sets (e.g., “the set of all living cats”) are implicitly time-dependent, yet classical formulations treat set membership as eternally fixed. Russell’s paradox arises when self-referential membership is evaluated without any rule constraining temporal relevance or admissibility of evaluation. We propose a minimal consistency requirement:membership in a set must be evaluated relative to a well-defined context, and elements may be excluded if their inclusion violates the rules defining that context. This rule is temporal in nature but does not require explicit time variables; it formalizes an assumption already used informally in mathematics and logic. With this addition, Russell’s paradox is shown to be an artifact of incomplete semantic specification rather than an inherent contradiction of naive set formation. The result preserves existing frameworks while clarifying a foundational ambiguity.