Intuição e conceito: a transformação do pensamento matemático de Kant a Bolzano

• Autor(a) principal: Clímaco, Humberto de Assis
• Data de Publicação: 2014
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/4109
• topic: Kant; Bolzano; Intuição; Conceito; Kant; Bolzano; Intuition; Concept; EDUCACAO::ENSINO-APRENDIZAGEM

Taking part of the research line Grounds of the Educational Process of Post-graduate program in education of Universidade Federal de Goiás, this thesis reflects, in an original way, on the core issues the fundamentals of core issues of the today‘s mathematical education, opening new horizons for this area of knowledge. It discusses the transformation of the relationship between intuition and concept in the philosophy of mathematics occurred in the early nineteenth century, when the nature of mathematical knowledge has undergone such profound changes that mathematics came to be called Pure Mathematics, a subject that is relevant to understand the contradiction between simplicity and clarity sought by the creators of Pure Mathematics to make it a language, and the difficulty and lack of meaning with which it is often seen in schools. The way of conceiving knowledge was profoundly changed by this transformation, and in particular changed the meaning of intuition. Kant's work has been discussed in this thesis due to the constructive role that the philosopher attributed, in its critical period, to the intuition of the knower subject; with the work of Kant, a genetic issue, about the origins and the conditions in which knowledge occurs, was inaugurated in philosophy, whence derives the importance that gained in its system the subject's ability to perceive objects through the notions of space and time, as conditions for any knowledge. Kant concludes that what makes knowledge possible is the fact that for its development contributes the subject‘s intuition and constructive action, and that this is how he achieves the concept, general representation, based on intuition, particular representation. Bolzano sought to eliminate from the investigations on the theory of science the study of the conditions and origins of knowledge, which he considered as a social issue that should be written in an order that would allow it to be communicated. Therefore, Bolzano denied that space and time could support language and mathematics, and sought to found principles able to reorganize knowledge in a hierarchical structure in which more conceptual truths could not be substantiated by more intuitive ones. Although Bolzano has not investigated the learning process itself, the importance he gave to education was so great that in his most important work, the Doctrine of Science, Wissenschaftslehre, he defined science as determined organized knowledge so as to compose a textbook. The philosophical, scientific and cultural consequences of the Industrial Revolution that occurred in the early nineteenth century, were studied in this thesis because it was in the context of its emergence that emerged deep processes, on the one hand, to create a public knowledge through the reorganization of universities, the emergence of large Polytechnics who needed graduate engineers in large scale, proliferation of publications with educational concerns; and, on the other hand, a search for reorganizing knowledge created or arisen in previous centuries in a hierarchical manner according to principles, which led to a search for treating in a theoretical manner the knowledge hitherto seen as a set of isolated truths. The study of the authors treated in the thesis, especially Kant and Bolzano, were made based on their original works, and any recourse to commentators did not substitute a careful reading of their ones.