Uma investigação sobre a ideia de número

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Universidade Federal de Goiás


In this assignment we aim to stimulate reflections about the millenary inquiry regarding what number really is. We aimed to show how historically controversial this question might be, which finds diversified comprehensions in the fields of philosophy, mathematics and the philosophy of mathematics. We came up with a historical pathway related to the construction of the idea of number, since the paleolithic period, reaching the end of the Nineteenth Century, when the mathematicians reevaluated the basics of mathematics and raised the ideas up to the level of the most rigorous languages involving logic. Frege (1884), in his book "The Fundamentals of Arithmetic", intended to explain and justify the real nature of the numbers idea, without appealing to geometry. Besides him, we have put a spotlight on the beautiful ideas as well as the important contributions of Bertrand Russell, Hilbert, Dedekind and Peano on the construction of the idea of number. The rational approach of the concepts and their validation through rational methods, without making use of sensorial experiments, are either philosophical and mathematics studies. In this assignment, we intended to bring some light to these ideas, acknowledging the relevance of a deeper and more structured comprehension of the idea of number.



Matemática, Número, Filosofia e lógica, Mathematics, Number, Philosophy and logic


SILVA, F. O. Uma investigação sobre a ideia de número. 2020. 71 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Catalão, 2020.