The Problem of the Actual Infinity and the Path of the New European Classical Epistemology: from Genesis to the Modern Crisis

Introduction. The purpose of the paper is to show the prospects of the problem of actual infinity for understanding the ways of New European classical epistemology. The relevance of the work is due to the need to fill a gap in the history of New European epistemology, which today makes it difficult to understand the essence of its crisis. Such a lacuna was formed by the lack of grounds for the transition from the probabilistic concept of natural science, which takes into account apophaticism associated with the idea of actual infinity, to positive science, which presupposes a positive understanding of actual infinity.Methodology and sources. The author of the paper reconstructs and critically analyzes the attempts of the founders of New European science (Galileo and Descartes) to reform the ontological project of Nikolai Kuzansky due to the need for a positive understanding of the actual infinity. The author distinguishes between the reception of the problem of actual infinity in the New European philosophy and its objective state. Based on a comparative analysis, the author of the article establishes the identity of the logic of the development of the problem of actual infinity in the studies of Zeno of Elea and in New European epistemology, thereby testifying to its enduring significance.Results and discussion. The author shows that in the development of the problem of actual infinity, an objective regularity manifests itself, consisting in the fact that an unjustified assumption of the possibility of changing physical nature on the basis of the actual infinite really leads to a change in nature, but only the basis for this change is not actual, but potential infinity. This logic was reproduced in the history of New European epistemology. Thereby, mathematical natural science really turned out to be possible, but not on what its creators put in the basis (actual infinity), but on a derivative of it (potential infinity), and as a result it strengthens the position of supporters of non-classics.Conclusion. The problem of actual infinity makes it possible to understand the logic of the development of New European epistemology from its genesis to the modern crisis, and shows a deep interconnection between these two points.