The development of logical-mathematical instruments and concepts of Kurt Gödel's First Incompleteness Theorem
The article seeks to elucidate the investigations and advances in Mathematics and Logicassociated with philosophical conceptions that culminated in Kurt Gödel's First Incompleteness Theorem. For this, we will make a historical and conceptual approach to Mathematics from the second half of the 1...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | Brasil |
| Institución: | Universidade Federal de Pernambuco (UFPE) |
| Repositorio: | Perspectiva Filosófica (Online) |
| Idioma: | portugués |
| OAI Identifier: | oai:oai.periodicos.ufpe.br:article/258607 |
| Acceso en línea: | https://periodicos.ufpe.br/revistas/perspectivafilosofica/article/view/258607 |
| Access Level: | acceso abierto |
| Palabra clave: | diagonalização finitismo geometrias não-euclidianas incompletude paradoxos Programa de Hilbert diagonalization finitism Hilbert's Program incompleteness non-euclidean geometries paradoxes |
| Sumario: | The article seeks to elucidate the investigations and advances in Mathematics and Logicassociated with philosophical conceptions that culminated in Kurt Gödel's First Incompleteness Theorem. For this, we will make a historical and conceptual approach to Mathematics from the second half of the 19th century to the first half of the 20th century, indicating elements and mathematical instruments developed to solve problems, as well as philosophical assumptions and commitments that accompany activities aimed at the formalization and foundation of contemporary mathematical logic that helped Gödel to elaborate his demonstration and clarify the limitations of formal systems with a minimum of Arithmetic. In this way, we will deal with how the problems from the establishment of non-Euclidean geometries and the Set Theory culminated in different lines of research focused on the foundations of Mathematics, as well as the discovery of paradoxes and the controversial notion of the Infinite demanded finitary and recursive methods, such as instruments created for mathematical demonstrations in this period helped in the emergence of metamathematics until Gödel's proof. At the end, we will make a general synthesis and reflection on this intellectual enterprise in the progress of mathematical investigation itself. |
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