O projeto logicista de fundamentação da aritmética, de Gottlob Frege, e sua inconsistência interna

Abstract

In his work Begriffsschrift, Gottlob Frege builds, for the first time in history, a formal system (and the very notion of formal system) that will intend, some years later, to be able to give foundation to arithmetic. His system intended to be capable of formalizing all the arithmetic notions of his time, based solely and exclusively on basic laws of logic – an attempt that became historically known as logicism. As is known, however, this project – presented for the first time in his work The Foundations of Arithmetic – failed, as shown in a paradigmatic way by Russell's Paradox pointed out by Bertrand Russell in a letter to Frege in June 1902. Our aim here is to carry out a historical reconstruction of the Fregean project, in order to understand its motivations and also the reasons for its failure