Como é possível o conhecimento matemático: uma análise a partir da epistemologia genética

• Autor(a) principal: Ferraz, Alexandre Augusto [UNESP]
• Data de Publicação: 2014
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://hdl.handle.net/11449/123130; http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/15-04-2015/000825010.pdf
• topic: Piaget, Jean, 1896-1980; Epistemologia genetica; Matemática - Filosofia; Matemática - Estudo e ensino; Educação - Filosofia

The aim of this work is to study, based on Genetic Epistemology, the correlation between the necessary structures of knowledge of the epistemic subject, the subject of knowledge, and logical-mathematical structures, and based on this correlation, to answer the following question: how is abstract mathematical knowledge possible? Given this context, in this work: (1) we introduce the usual definition of structures in Logic and Mathematics. (2) We explain the general notion of structure according to Piaget and the notion of necessary structures of knowledge, which are the epistemic-psychological structures. (3) We show examples of epistemic-psychological structures, specially the Practical Group of Displacements, the System of Transfiguration Schemas and the System of Transignation Schemas. (4) We explain the correlation between such epistemological-psychological structures and the logicalmathematical structures. Given such correlation, we elaborate some hypothesis to answer the following epistemological question: how can the subject understand the abstract logicalmathematical structures? We argue that the epistemic subject understands structures which are studied in Logic and Mathematics through a epistemological-psychological structure that we call the System of Operations over Signs, a system whose roots can be found in sensorymotor actions, and which gets its general form from Reflecting Abstractions and uninterrupted logical-mathematical experiences. According to our hypothesis, given its formal characteristics, this system allows the epistemic subject to represent logical-mathematical structures, therefore enabling his comprehension.