Theoretical framework demonstrates a tertiary truth value to resolve alternating paradoxes, indicating that classical logical anomalies stem from informational incompleteness.
This paper introduces an alternative axiomatic framework, Xi-Logical Analysis (XLA), designed to evaluate thetruth values of oscillating propositions and non-convergent mathematical objects. By deploying two foundationalaxioms, the system systematically resolves classical anomalies including the Liar’s Paradox, Russell’s Paradox, andthe temporal supertask of Thomson’s Lamp, while offering a scalable architectural model for broader paradoxicaldomains. The first axiom formalizes the existence of a distinct tertiary truth value, Xi, inherent to infinite oscillatorystates. The second axiom establishes structural boundary constraints, mandating explicit informational specificationwhenever a construction interfaces with the non-binary Xi domain. Ultimately, this framework re-frames classicallogical paradoxes not as systemic failures, but as artifacts that are informationally incomplete.
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Maximus Martinez (2026) studied this question.
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