[2509.06055] Fixed-Point Theorems and the Ethics of Radical Transparency: A Logic-First Treatment

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arXiv:2509.06055 (math)

[Submitted on 7 Sep 2025]

Title:Fixed-Point Theorems and the Ethics of Radical Transparency: A Logic-First Treatment

Authors:Faruk Alpay, Hamdi Alakkad<br>View a PDF of the paper titled Fixed-Point Theorems and the Ethics of Radical Transparency: A Logic-First Treatment, by Faruk Alpay and 1 other authors

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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 $\mu$-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.

Comments:<br>29 pages

Subjects:

Logic (math.LO); Computer Science and Game Theory (cs.GT)

MSC classes:<br>03B70, 03F40, 91A80

ACM classes:<br>F.4.1; I.2.0; F.3.1; K.4.1

Cite as:<br>arXiv:2509.06055 [math.LO]

(or<br>arXiv:2509.06055v1 [math.LO] for this version)

https://doi.org/10.48550/arXiv.2509.06055

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arXiv-issued DOI via DataCite

Submission history<br>From: Hamdi Alakkad [view email]<br>[v1]<br>Sun, 7 Sep 2025 13:45:53 UTC (42 KB)

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