Kant, infinity and his first antinomy
Lincoln, James William
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Kant's antinomies are exercises designed to illustrate the limits of human reasoning. He skillfully juxtaposes pairs of arguments and exposes the dangerous propensity for human reasoning to stretch beyond the conditioned and into the transcendental ideas of the unconditional. Kant believes this is a natural process and affirms the limits of pure reason in so much as they should prevent us from believing that we can truly know anything about the unconditional. His first antimony addresses the possibility of a beginning in time or no beginning in time. This thesis will focus on this first antinomy and critically assesses it in set theoretic terms. It is this author's belief that the mathematical nuances of infinite sets and the understanding of mathematical objects bear relevance to the proper interpretation of this antinomy. Ultimately, this composition will illustrate that Kant's argument in the first antinomy is flawed because it fails to account for infinite bounded sets and a conceptualization of the infinite as a mathematical object of reason.