Uma aproximação das concepções de lógica de Kant e Frege

Abstract

In this master thesis, guided by the search of the relationship between mathematical logic and traditional logic, we address the characterizations of logic offered by Kant and Frege. First, we considered and specified several ways to understand the thesis according to which logic can be distinguished from other sciences through its abstraction of matter or knowledge content, and its attention to form. Two of these notions turned out to be indispensable to make explicit the relationships between the two conceptions of logic; namely, generality i.e. normative validity on all domains of the thought and formality i.e. complete abstraction of semantic content. Second, we pointed out the fundamental role of these notions in the Kantian characterization of logic. Kant, in consonance with his contemporaries, begins characterizing logic by its generality, but when he arrives at the fundamental thesis of his transcendental idealism, he innovates arguing also for its formality. Third, it becomes clear, at least with regard to the conception of logic, that Frege was under Kantian influence. In his first writings, Frege adopts the Kantian characterization, only later does he become aware that his technical innovations reject the formality of logic. However, the characterization by generality is a constant along the whole Fregean corpus, and it guarantees the link with all the precedent tradition. The main result of this master thesis is to point the common nucleus between the two conceptions of logic, and with it, the grounds for the divergence concerning the status of arithmetic. Only because logic meant the same for both, the miscarried logicist project could have proven that Kant was wrong concerning arithmetic.