Saved in:
| Hovedforfatter: | |
|---|---|
| Format: | Recurso digital |
| Sprog: | engelsk |
| Udgivet: |
Zenodo
2025
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| Fag: | |
| Online adgang: | https://doi.org/10.5281/zenodo.15192061 |
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Indholdsfortegnelse:
- <p>We propose and prove the Batesonian Completeness Conjecture, which states that<br>any mathematically well-formed conjecture—expressible within first-order logic, ZFC,<br>or higher-order type theory—can be resolved within a unified framework based on Recursive<br>Type Arithmetic (RTA) and the Bateson Game (BG). This framework<br>encodes logic and arithmetic into a multi-layered ecology of strategic frames, recursive<br>coherence constraints, and entropy flow.<br>We define the space of ecologically coherent conjectures and prove that every such<br>conjecture has one of three fates: resolution (truth), collapse (falsity), or structured<br>undecidability via recursive double binds (n-binds). These outcomes are exhaustive<br>under the frame ecology. We demonstrate that this system respects classical logic<br>while resolving known paradoxes of undecidability through frame-level coherence.<br>The result is a generalized completeness theorem for RTA+BG, transcending G¨odel’s<br>limits in ZFC by modeling logical systems not as flat formal machines but as stratified<br>recursive ecologies. We conclude with implications for number theory, computational<br>complexity, set theory, and the foundations of physics.</p>