Representación y conocimiento en matemáticas: Una crítica al planteamiento de P. Kitcher
DOI:
https://doi.org/10.24310/Contrastescontrastes.v8i0.1837Keywords:
KITCHER, CONOCIMIENTO MATEMÁTICO, VERDAD MATEMÁTICA, MILLAbstract
RESUMEN
En este artículo se analizan críticamente algunos aspectos de la teoría de Kitcher sobre el conocimiento matemático. Se muestra que su definición de conocimiento carece de una caracterización convincente del concepto de verdad. Su teoría evolutiva del conocimiento matemático se centra en la idea kuhniana de que la historia de un campo científico determinado se puede entender como una secuencia de prácticas racionales; sin embargo, su caracterización de tales transiciones entre prácticas es bastante imprecisa. Por último, su construcción de la artimética como una teoría idealizada, siguiente algunas tesis de Mill conduce a un cierto tipo de apriorismo, lo cual contradice uno de los aspectos fundamentales de las tesis de Kitcher.
PALABRAS CLAVE
KITCHER, CONOCIMIENTO MATEMÁTICO, VERDAD MATEMÁTICA, MILL
ABSTRACT
Several aspects of the Kitcher´s theory about the nature of mathematical knowledge are critically analysed in this papel. It is showed that his definition of knowledge is lacked a convincent caracterization of truth. His evolutionary theory of mathematical knowledge is focussed on the Kuhnian insight that the history of a scientific fielg can be understood as a transitions is quite imprecise. Lastly, his construction of arithmetic as a idealized theory leads to a certain kind of apriorism, that contradicts one of the fundamental claims of Kitcher´s thesis.
KEY WORDS
KITCHER, MATHEMATICAL KNOWLEDGE, MATHEMATICAL TRUTH, MILL
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