The problem of the foundations of mathematics and the roots of logical anti-exceptionalism
The so-called foundational crisis started by the discovery of the set-theoretic paradoxes in naive set theory, as well as by the discovery of Gödel’s incom-pleteness theorems, was responsible for a series of reactions over the way we understand mathematical knowledge. Among the common views, the mos...
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2020 |
| País: | Brasil |
| Recursos: | Universidade Federal de Pernambuco (UFPE) |
| Repositório: | Perspectiva Filosófica (Online) |
| Idioma: | português |
| OAI Identifier: | oai:oai.periodicos.ufpe.br:article/248949 |
| Acesso em linha: | https://periodicos.ufpe.br/revistas/perspectivafilosofica/article/view/248949 |
| Access Level: | Acceso aberto |
| Palavra-chave: | logical anti-exceptionalism foundations of mathematics Lázslo Kálmar mathematical empiricism anti-excepcionalismo lógico fundamentos da matemática Lázslo Kalmár empirismo matemático |
| Resumo: | The so-called foundational crisis started by the discovery of the set-theoretic paradoxes in naive set theory, as well as by the discovery of Gödel’s incom-pleteness theorems, was responsible for a series of reactions over the way we understand mathematical knowledge. Among the common views, the most popular ones try to construct mathematical knowledge on a priori elements, such as the notion of proof, or even ideas of “primordial intuitions”, as de-fended by some intuitionists. The purpose of the present paper is to introdu-ce opposite views to the traditional aprioristic ones as a way to trace the his-torical roots of the so-called anti-exceptionalism about logic. In order to do so, the paper presents Lázslo Kalmár’s ideas over his mathematical empiricism as a way to contrast two types of anti-exceptionalism, namely pre- and post-Quine. The problem of mathematical foundations is explored as a demarcati-on criterion between these positions. |
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