The Batesonian Completeness Conjecture: A Universal Framework for Mathematical Resolution via Recursive Type Arithmetic and Frame Ecology
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| Language: | English |
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2025
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| _version_ | 1866902334857019392 |
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| author | Kevin Fathi |
| author_facet | Kevin Fathi |
| contents | <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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15192061 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Batesonian Completeness Conjecture: A Universal Framework for Mathematical Resolution via Recursive Type Arithmetic and Frame Ecology Kevin Fathi Batesonian Logic Recursive Type Arithmetic (RTA) Bateson Game Mathematical Foundations Completeness Theorem Gödel's Incompleteness Formal Proof Systems Type Theory Ecological Logic Strategic Framing Logical Types Mathematical Logic Computational Complexity Recursive Coherence Entropy in Logic Undecidability Philosophy of Mathematics Mathematical Ecology Artificial Intelligence and Logic Foundations of Mathematics <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> |
| title | The Batesonian Completeness Conjecture: A Universal Framework for Mathematical Resolution via Recursive Type Arithmetic and Frame Ecology |
| topic | Batesonian Logic Recursive Type Arithmetic (RTA) Bateson Game Mathematical Foundations Completeness Theorem Gödel's Incompleteness Formal Proof Systems Type Theory Ecological Logic Strategic Framing Logical Types Mathematical Logic Computational Complexity Recursive Coherence Entropy in Logic Undecidability Philosophy of Mathematics Mathematical Ecology Artificial Intelligence and Logic Foundations of Mathematics |
| url | https://doi.org/10.5281/zenodo.15192061 |