A Resolution of Russell's Paradox
Abstract
Russell's paradox is traditionally taken to show that naive set theory is inconsistent and must be restricted. This paper demonstrates that the paradox arises only from an unstated and unnecessary assumption: that membership must be bivalent (true or false). By introducing a third, non-collapsing membership state — "might" — we show that the original 11 naive rules of set theory remain fully intact, unrestricted composition remains valid, and Russell's paradox dissolves without modifying any rule.
Fields of Study & Subjects
Advanced Algebra and Logic
Logic
Reasoning
and Knowledge
Advanced Topology and Set Theory
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 9 March 2026
- Language
- EN
- Document type
- Preprint