Генезис науки XVII века: опыты по «приручению» бесконечности

Abstract

The author of the article considers the problem of actual infinity to be the meta-basis of the genesis of New European science. The author shows the advantages of this approach to identify the internal logic of the genesis of science of the XVII century, as well as to clarify the prospects of modern science, experiencing a crisis of its foundations. The author shows that Nikolai Kuzansky’s ontological project reveals the conditions necessary for the mathematization of nature for the transformation of the finite into the actually infinite, which overcomes the hopelessness of Zeno’s similar attempts. Zeno showed that there is no transition from the finite to the actually infinite. To transform the fi nite into the actually infi nite, the latter must already be given. This kind of presence is revealed by Kuzansky in the apophatic idea of the divine minimum coinciding with the maximum. But at the same time, Kuzansky speaks only about the imaginary, and not the real possibility of transforming nature on the basis of actual infinity. And in order to turn ‘scientific ignorance’ into ‘scientific knowledge’, it was necessary to present, outside the theological context, the possibility of transforming nature on the basis of actual infinity, discovered by Kuzansky. This task was set by the founders of the New European science. The author of the article analyzes and compares the attempts of Galileo and Descartes to ‘tame’ the actual infinity. The author shows that the difference in their positions on the question of the achievability of reliable knowledge, which laid important milestones in the history of the genesis of New European science (the transition from the scholastic tradition to probabilistic epistemology), is due to the awareness of the complexity of the problem of actual infinity. As a result, the author shows that neither the theoretical speculations of the founders of science, nor the attraction of modern additional resources unknown to antiquity or the Middle Ages (experiment, pinhole camera) were unable to change anything in the ratio of the finite and the infinite.