Актуальная бесконечность: псевдопроблема или метаоснование западноевропейской философии и науки?

Abstract

The author of the article reveals the theological context of the origin of the concept of actual infinity and clarifies the problem of actual infinity. The author shows that this problem is not a paradoxical category of thinking, but a problem of the unity of two realities (eternal, unchanging and infinite, and temporary, changeable and finite), which has been misunderstood. The author raises the question of the relevance of the problem of actual infinity brought by Christianity for modern secularized science and philosophy. The author shows that the problem of the unity of the two realities was declared much earlier than Christianity. This problem was already dealt with by the ancient Eleans. They initiated the one-sided view and incorrect understanding of this problem, which opened the main path of development of the entire Western European philosophy. With the advent of Christianity, all the dangers identified by the Eleans (and above all by Zeno) and then still unclear on this path received a new sharpness and now real force. The author of the article shows that the regularity of the relation of the finite, the actually infinite, and the potentially infinite, revealed by Zeno, was the basis for changing the classical rationality to the non-classical one. In turn, the fact of the collapse of the classics has become evidence of modernity that the problem of actual infinity is not a mental paradox, but contains the real possibility of changing the finite nature. But this change is not carried out in the direction suggested by the recognition of actual infinity itself, but in another direction, opposite to it, but closely connected with it. The disclosure of the essence of this connection will be the disclosure of the problem of actual infinity.