| _version_ | 1866901352479719424 |
|---|---|
| author | SÉRGIO DE ANDRADE, PAULO |
| author_facet | SÉRGIO DE ANDRADE, PAULO |
| contents | This paper explores the intricate relationship between the structural properties of formal systems and the emergence of incompleteness, proposing a framework for understanding the "structural semantics of incompleteness." Drawing inspiration from Gödel's groundbreaking work, we move beyond the mere assertion of incompleteness to investigate how the internal architecture of a system—its syntax, axioms, rules of inference, and models—inherently constrains its expressive power and the totality of truths it can capture. We argue that incompleteness is not merely a limitation but an inherent semantic feature arising from the design principles and representational choices embedded within a system's structure. By analyzing various manifestations of incompleteness across mathematical logic, theoretical computer science, and linguistics, we develop a unified perspective. This structural semantic approach reveals that the boundaries of a system's completeness are largely determined by the specific ways in which meaning is constructed and interpreted within its formal edifice. We present a theoretical model that maps structural characteristics to semantic gaps, offering a deeper understanding of why and how certain truths remain inaccessible or undecidable within given frameworks. The implications of this framework extend to the design of artificial intelligence, the philosophy of mathematics, and the epistemology of knowledge representation. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17690046 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Structural Semantics of Incompleteness SÉRGIO DE ANDRADE, PAULO This paper explores the intricate relationship between the structural properties of formal systems and the emergence of incompleteness, proposing a framework for understanding the "structural semantics of incompleteness." Drawing inspiration from Gödel's groundbreaking work, we move beyond the mere assertion of incompleteness to investigate how the internal architecture of a system—its syntax, axioms, rules of inference, and models—inherently constrains its expressive power and the totality of truths it can capture. We argue that incompleteness is not merely a limitation but an inherent semantic feature arising from the design principles and representational choices embedded within a system's structure. By analyzing various manifestations of incompleteness across mathematical logic, theoretical computer science, and linguistics, we develop a unified perspective. This structural semantic approach reveals that the boundaries of a system's completeness are largely determined by the specific ways in which meaning is constructed and interpreted within its formal edifice. We present a theoretical model that maps structural characteristics to semantic gaps, offering a deeper understanding of why and how certain truths remain inaccessible or undecidable within given frameworks. The implications of this framework extend to the design of artificial intelligence, the philosophy of mathematics, and the epistemology of knowledge representation. |
| title | The Structural Semantics of Incompleteness |
| url | https://doi.org/10.5281/zenodo.17690046 |