Gödel Mirror: A Formal System For Contradiction-Driven Recursion
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908548991025152 |
|---|---|
| author | Chan, Jhet |
| author_facet | Chan, Jhet |
| contents | We introduce the Gödel Mirror, a formal system defined in Lean 4 that treats contradiction as a control signal for recursive structural evolution.
Inspired by Gödelian self-reference, our system's operational semantics encode symbolic paradoxes as deterministic transitions. Unlike systems designed to guarantee normalization, the Gödel Mirror is a minimal and verifiable architecture that leverages a controlled, non-terminating loop as a productive feature.
Our Lean 4 mechanization proves that self-referential paradoxes are deterministically encapsulated and resolved into new structures without leading to logical explosion, yielding a paraconsistent inference loop: Paradox -> Encapsulate -> Reenter -> Node
We argue that this calculus opens a new class of symbolic systems in which contradiction is metabolized into structure, providing a formal basis for agents capable of resolving internal inconsistencies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16239 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gödel Mirror: A Formal System For Contradiction-Driven Recursion Chan, Jhet Logic in Computer Science Programming Languages 03B70, 68Q42 F.4.1; F.4.2; F.4.3; D.3.1 We introduce the Gödel Mirror, a formal system defined in Lean 4 that treats contradiction as a control signal for recursive structural evolution. Inspired by Gödelian self-reference, our system's operational semantics encode symbolic paradoxes as deterministic transitions. Unlike systems designed to guarantee normalization, the Gödel Mirror is a minimal and verifiable architecture that leverages a controlled, non-terminating loop as a productive feature. Our Lean 4 mechanization proves that self-referential paradoxes are deterministically encapsulated and resolved into new structures without leading to logical explosion, yielding a paraconsistent inference loop: Paradox -> Encapsulate -> Reenter -> Node We argue that this calculus opens a new class of symbolic systems in which contradiction is metabolized into structure, providing a formal basis for agents capable of resolving internal inconsistencies. |
| title | Gödel Mirror: A Formal System For Contradiction-Driven Recursion |
| topic | Logic in Computer Science Programming Languages 03B70, 68Q42 F.4.1; F.4.2; F.4.3; D.3.1 |
| url | https://arxiv.org/abs/2509.16239 |