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Michael F. Otte
University of Bielefeld, Alemania Universidade Bandeirantes de São Paulo, Brasil
Tânia M. Mendonça
Universidade Bandeirantes de São Paulo, Brasil
Luiz de Barros
Universidade Bandeirantes de São Paulo, Brasil
Vol. 9 Núm. 3: Número monográfico en Generalización (Marzo, 2015), Artículos, Páginas 143-164
Recibido: Jun 24, 2017 Aceptado: Jun 24, 2017 Publicado: Mar 1, 2015


The problems of geometry and mechanics have driven forward the generalization of the concepts of number and function. This shows how application and generalization together prevent that mathematics becomes a mere formalism. Thoughts are signs and signs have meaning within a certain context. Meaning is a function of a term: This function produces a pattern. Algebra or modern axiomatic come to mind, as examples. However, strictly formalistic mathematics did not pay sufficient attention to the fact that modern axiomatic theories require a complementary element, in terms of intended applications or models, not to end up in a merely formal game.

La generalización es necesaria o incluso inevitable

Los problemas de geometría y mecánica han motivado la generalización de los conceptos de número y función. Esto muestra cómo la aplicación y la generalización previenen que las matemáticas sean un mero formalismo. Los pensamientos son signos y los signos tienen un significado dentro de un cierto contexto. El significado es una función de un término: esta función produce un patrón. El álgebra o la moderna axiomática vienen a la mente como ejemplos. Sin embargo, las matemáticas estrictamente formales no prestaron suficiente atención al hecho de que las teorías axiomáticas modernas requieren un elemento complementario, en términos de aplicaciones intencionadas o modelos, para no terminar en un juego meramente formal.



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