Sobre a distinção entre os usos imanente e transcedente do conceito de infinito na Crítica da razão pura

Abstract

Weve tried to extract from the Critique of Pure Reason an answer to the following question: which are the features of the transcendent and immanent uses of the concept of infinite? In order to examine the transcendent use of this concept, weve chosen the two antithesis of the first and second antinomy of pure reason, respectively. The first antithesis asserts that the universe is infinite in space and had no first instant in time. The second one establishes that the whole series of the division of the material substances is infinite. Weve concluded that both antitheses are false and transcendent because they implicitly assume the point of view of the transcendental realism, which leads them to comprehend the temporal-space universe and the totality of the material substancess parts as things existing in themselves and to assign to these auto-subsisting entities the property of being actually infinite. The immanent use of the concept of infinite is examined in two moments. Firstly, when we discuss the transformation of the constitutive ideas of the entire universe and of the complete series of the division of the material substances into regulative ideas. In this case, the idea of the infinity also changes: from a constitutive property of things existing in themselves to a regulative concept prescribed as a rule by reason. Secondly, when we analyze the Kantian theses concerning mathematics and the way these theses explain the legitimate and immanent use of the concept of infinite by Geometry, Algebra, Arithmetic and Calculus.