Intuição e conceito: a transformação do pensamento matemático de Kant a Bolzano
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2014-05-30
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Universidade Federal de Goiás
Resumo
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.
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Citação
CLÍMACO, Humberto de Assis. Intuição e conceito: a transformação do pensamento matemático de Kant a Bolzano. 2014. 171 f. Tese (Doutorado em Educação) - Universidade Federal de Goiás, 2014.