Por que a Lógica deveria se ocupar da rotação? Como o conteúdo realista de Principles of Mathematics continua a Dialética das Ciências da fase idealista de Russell - Amatucci, Marcos (2019)
Principles of Mathematics, 1903, is regarded as Russell's first realist book, which breaks with idealism and begins the logicist project of grounding mathematics by logic. The aim of this work is to demonstrate the thesis that Principles of Mathematics and Russell's disruption with British idealism are the direct result of solving the problems encountered throughout the Dialectic of Sciences program, beginning in 1895 and culminating in Principles. Following the neo-Hegelian doctrine, the problems of science are considered by Russell as antinomies, which must undergo a double treatment, the elimination of avoidable antinomies and the overcoming of the inevitable ones through a dialectical transition to a new science, science by science. Such problems found no solution within that doctrine, leading Russell to a gradual break with idealistic principles. Principles therefore continues the Dialectic of the Sciences, it is not a new beginning from a rupture. Thus the knowledge of the Dialectic program of the Sciences is fundamental to understand Russell's break with idealism, which was centred on Theory of Relationships. The study deals with the role of Rational Dynamics, present in Principles and little understood, as a metonymy of the general incomprehension of the character of continuity between the idealistic Dialectic of Science and the foundation of realistic mathematics. The paper concludes that Principles does not initiate the logistic project in isolation, but as a result of the resolution of the antinomies of the Dialectic of Sciences