{"ID":2873774,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.06055","arxiv_id":"2509.06055","title":"Fixed-Point Theorems and the Ethics of Radical Transparency: A Logic-First Treatment","abstract":"This paper establishes a formal framework, grounded in mathematical logic and order theory, to analyze the inherent limitations of radical transparency. We demonstrate that self-referential disclosure policies inevitably encounter fixed-point phenomena and diagonalization barriers, imposing fundamental trade-offs between openness and stability. Key results include: (i) an impossibility theorem showing no sufficiently expressive system can define a total, consistent transparency predicate for its own statements; (ii) a categorical fixed-point argument (Lawvere) for the inevitability of self-referential equilibria; (iii) order-theoretic design theorems (Knaster-Tarski) proving extremal fixed points exist and that the least fixed point minimizes a formal ethical risk functional; (iv) a construction for consistent partial transparency using Kripkean truth; (v) an analysis of self-endorsement hazards via Löb's Theorem; (vi) a recursion-theoretic exploitation theorem (Kleene) formalizing Goodhart's Law under full disclosure; (vii) an exploration of non-classical logics for circumventing classical paradoxes; and (viii) a modal $μ$-calculus formulation for safety invariants under iterative disclosure. Our analysis provides a mathematical foundation for transparency design, proving that optimal policies are necessarily partial and must balance accountability against strategic gaming and paradox. We conclude with equilibrium analysis and lattice-theoretic optimality conditions, offering a principled calculus for ethical disclosure in complex systems.","short_abstract":"This paper establishes a formal framework, grounded in mathematical logic and order theory, to analyze the inherent limitations of radical transparency. We demonstrate that self-referential disclosure policies inevitably encounter fixed-point phenomena and diagonalization barriers, imposing fundamental trade-offs betwe...","url_abs":"https://arxiv.org/abs/2509.06055","url_pdf":"https://arxiv.org/pdf/2509.06055v1","authors":"[\"Faruk Alpay\",\"Hamdi Alakkad\"]","published":"2025-09-07T13:45:53Z","proceeding":"math.LO","tasks":"[\"math.LO\",\"cs.GT\"]","methods":"[\"LoRA\"]","has_code":false}