A acolhida do Teorema da Incompletude de Gödel pelos matemáticos
| Autor: | Rosemeire de Fatima Batistela, Maria Aparecida Viggiani Bicudo, Henrique Lazari |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Perspectivas da Educação Matemática. 13:1-20 |
| ISSN: | 2359-2842 1982-7652 |
| DOI: | 10.46312/pem.v13i31.6737 |
| Popis: | In this article, one presents how some of the most important mathematicians of the early twentieth century – those responsible for organizing mathematics into algebraic, topological and order structures, which one studied in undergraduate courses in mathematics – received the results established by Godel´s Incompleteness Theorem. One understands that the stance taken by Bourbaki group and revealed in his works thus claims how the mathematicians of that time welcomed the incompleteness theorem and handled with its consequences. The attitude assumed by the group was to continue doing Mathematics with the same ideal of complete formalization, although they faced with the proof of the existence of a non-empty set of true and undemonstrable propositions – via mathematical tools for producing this science – and of the incompleteness of any theory that contains Peano axioms. One also presents Wittgenstein's perspective on Godel's Incompleteness Theorem. Finally, one apprehends that this theorem is understood by the mathematical community as a messenger of incompleteness as a characteristic inherent to axiomatization, not as an impediment to the continuation of the activity with formal systems, but as an invigorating result for Mathematics. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|