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Zholkov, S. Yu. Kant’s “Mathematical Antinomies” are not Antinomies

Published in journal "Philosophy and Culture", 2013-10 in rubric "Space and time", pages 1368-1378.

Resume: The article is devoted to the problems raise by Kat in his ‘mathematical antinomies’. Analysis is carried out in original formulation of Kant’s own terms and as a part of his own philosophical argumentation. The same problems are also viewed disregarding Kant’s philosophy. Validity and evidence which make it possible to structure analysis in a form of rigorous theory as it is seen by modern mathematics, allow to categorically state that Kant’s classification lacks grounds and his reasoning regarding ‘mathematical antinomies’ can’t be considered to be a proof. On the contrary both his theses and antitheses are irrefutable. The essence of problems is not in unavoidable contradictions of mind or process of cognition of transcendental world in the course of Kantian debates of mind with itself but in non-uniqueness of conceptual representations. As for the limited prescribed to a cognizing mind, they involve, in the first place, the laws that determine the architectonics of veritable theories.

Keywords: philosophy, “mathematical antinomies”, Kant, transcendental dialectics, antitetics, space, time, infinity, architectonics of theories, mind.

DOI: 10.7256/1999-2793.2013.10.7064

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