Kant's Turn: Between Actual and Potential Infinity

Introduction. The purpose of the article is to show that Kant's turn is the answer to the problem of actual infinity, in the light of which it becomes clear how Immanuel Kant contributed to the turn of Western epistemology to non-classics. The relevance of the research is due to the need to make modern epistemology more “sighted” in relation to its own prospects and opportunities. Methodology and sources. The author of the article reconstructs and critically analyzes Kant's approach to neutralizing the problem of actual infinity on the basis of the involvement of both primary sources and historical-philosophical and historical-scientific works, modern research in the field of the theory of cognition. Results and discussion. Kant's separation of “in itself” and “for us” separates the finite and dependent world from the infinite and independent. The latter is emptied of its theological content (inherited from Nicholas of Cusa) and, instead of a central meaning, receives a peripheral one, is declared an unknowable thing in itself. And the former is endowed with some properties of the latter and is declared a self-sufficient education. So the transcendent becomes transcendental, and the problem of the connection between the finite and the infinite, discussed by Kant's predecessors (Galileo, Descartes, etc.), is neutralized and passes into the category of antinomies. But the discovery of the inconsistency of Kant's separation “in itself” and “for us” makes the problem of the ratio of the finite and the infinite relevant again. However, now the former becomes completely blind to the latter, so that everything that is beyond “for us” can be attributed to “in itself”. Thus, in place of the actual infinity as transcendent, a potential infinity arises that does not know the limits of its immanence. The author of the article shows that such substitution, while remaining unidentified, can disorient the modern theory of cognition even more. Conclusion. Revealing how Kant's reinterpretation of the relation of the finite and the infinite contributed to the substitution of the actual infinity by the potential infinity makes it clear that such a substitution does not neutralize the original problem of the actual infinity, but that such a substitution is itself a real problem, the sharpening of which promises great changes in the theory of knowledge.

Authors: Maria I. Philatova

Direction: Philosophy

Keywords: actual infinity, potential infinity, antinomies, Kant's turn, classical and non-classical epistemology, genesis of New European natural science

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