On the proof that every natural number has a successor in Die Grundlagen der Arithmetik, §§82-3
The aim of this paper is to present an alternative derivation within Frege's Arithmetic of theorem 149 in Grundgesetze der Arithmetik, which plays a central role in the proof of the theorem that states that every natural number has a successor. In Grundgesetze, the derivation of this theorem de...
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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/258425 |
| Acceso en línea: | https://periodicos.ufpe.br/revistas/perspectivafilosofica/article/view/258425 |
| Access Level: | acceso abierto |
| Palabra clave: | Gottlob Frege Die Grundlagen der Arithmetik Grundgestze der Arithmetik teorema 149 teorema IVa theorem 149 theorem IVa |
| Sumario: | The aim of this paper is to present an alternative derivation within Frege's Arithmetic of theorem 149 in Grundgesetze der Arithmetik, which plays a central role in the proof of the theorem that states that every natural number has a successor. In Grundgesetze, the derivation of this theorem depends on the theorem IVa, whose analogue in Frege's Arithmetic (IVa*) is independent of the axioms of the system. It is shown that the use of IVa in Grundgesetze is not essential and therefore that (IVa*) is not necessary for derivation of theorem 149 within Frege's Arithmetic. |
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