Frege e as Leis da Aritmética: do ideal de fundamentação ao paradoxo
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Data
2015-07-08Autor
Coury, Aline Germano Fonseca
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Since the end of the nineteenth century and early twentieth century, some scholars
such as Frege, Russell, Dedekind, Wittgenstein, among others, started to seek the
foundations of the mathematics. Specifically, Frege developed studies in order to build
the arithmetic foundation based on classical logic, i. e., using logic, he intended to build
a system capable of formalizing mathematical definitions and proof methods. These
works resulted in the publication of The Foundations of the Arithmetic in 1884 and
subsequently in 1893 and 1902, The Basic Laws of Arithmetic. However, Frege’s
attempt to reduce arithmetic to logic was inadequate due to a paradox discovered by
Bertrand Russell in 1902. The aim of this research was to reconstruct mathematically
and logically the Russell paradox in its original formulation in the Frege’s The Basic
Laws of Arithmetic. This study had as primary bibliography Frege’s works and as
secondary bibliography, works of his commentators, as well as the correspondence
between Frege and Russell. This research provides a logical, philosophical and
mathematical formation for the educator who is in contact with this event that covers
both the areas that is disciplinary today. It is a fertile moment in the history of philosophy
of mathematics and logic, configured as a watershed for mathematical theories since it
enabled Gödel's incompleteness theorems and non-classical logics to be formulated,
and also has repercussions in contemporary philosophy and which is of unquestionable
value for the teacher formation.