In this paper, I will show to what extent we can use our modern understanding of the Square of Opposition in order to make sense of Kant 's double standard solution to the cosmological antinomies. Notoriously, for Kant, both theses and antitheses of the mathematical antinomies are false, while both theses and antitheses of the dynamical antinomies are true. Kantian philosophers and interpreters have criticized Kant 's solution as artificial and prejudicial. In the paper, I do not dispute such claims, (...) but I show that our modern understanding of the Square of Opposition enables us to more naturally deliver the result Kant was aiming at. Accordingly, the paper does not pretend to be exegetically accurate. It is an attempt to revise the antinomies with the help of standard classical logic. And although such a revision entails some re-interpretation, in the end, it will actually help to unveil some of Kant 's thoughts. (shrink)

Based on an analysis of the category of “infinite judgments” in Kant, we will introduce the logical hexagon of predicate negation. This hexagon allows us to visualize in a single diagram the general structure of both Kant’s solution of the antinomies of pure reason and his argument in favor of Transcendental Idealism.

O presente artigo tem como objetivo mostrar que a teoria kantiana da possibilidade de juízos a priori, o conteúdo essencial da sua crítica da razão pura, foi elaborada no intuito de garantir a solubilidade dos problemas necessários da razão pura e que essa teoria pode ser interpretada como uma semântica transcendental (a priori). The problems of pure reason and the transcendental semanticsThis article aims at showing that Kant´s theory of possibility of a priori judgments, which is the essential content of (...) his critique of pure reason, was elaborated in order to guarantee the solubility of necessary problems of pure reason and that this theory can be interpreted as atranscendental semantics. (shrink)

: Neste artigo argumento contra a interpretação muito difundida segundo a qual o ano de 1769 representou um marco na formação da filosofia transcendental e a Dissertação de 1770 corresponde ao primeiro texto crítico. O objetivo deste artigo é investigar a origem das antinomias nas Reflexões da década de 1770. Não se trata de esboçá-las, pois sobre elas Kant é reticente nesse período. Elas são objeto da atenção dele somente às vésperas da redação da Crítica da razão pura. Eu me (...) ocupo apenas com alguns dos elementos que possibilitarão sua formulação e solução na Crítica da razão pura. (shrink)

In the section of the Antinomy of pure Reason Kant presents three notions of infinity. By investigating these concepts of infinity, this paper highlights important ‘building blocks’ of the structure of the mathematical antinomies, such as the ability of reason of producing ascending and descending series, as well as the notions of given and givable series. These structural features are discussed in order to clarify Ernst Zermelo’s reading of Kant’s antinomy, according to which the latter is deeply rooted in the (...) tendency of the mind of producing “creative progress” and “inclusive closure”. The aim of this paper is to explain in which sense and why Kant’s treatment of the antinomies attracts the attention of Zermelo in the early 1900s and which aspects of his second axiomatic system have been inspired by Kant’s philosophy. Thus, by reading Kant’s antinomy ‘through Zermelo’s eyes’—with emphasis on the concept of regressive series in indefinitum and on that of regressive series ad infinitum – this paper identifies the echoes of Kant’s work in the making of the ZFC set theory. (shrink)