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V. I. Vernadsky left a unique legacy in the fields of philosophy and methodology of science. The logical structure of science, elaborated by him, is based on the principle of the objective truthfulness of scientific knowledge and its various manifestations in various parts of science, which are unequal in terms of truthfulness (authenticity). The first part is the one being quite authentic and constituting the frame of science, e.g. the core manifestation and content of scientific knowledge, whereas the second part 'clothes' the frame of science and constructs upon its. The notion of the frame of science, introduced by Vernadsky to signify the core structure of the scientific knowledge, seems to be a very accurate reflection of the knowledge system of logics, mathematics and scientific apparatus. Considering Vernadsky's theses on the issue, a series of arguments can be given in favor of treating mathematics, logics and scientific apparatus as the fundament of scientific knowledge. Yet, V. I. Vernadsky treats mathematics as a central component in the notion 'frame of science', introduced by him, as a genetic turn in its creation. Mathematics integrates 'frame of science' through logics, and this determines the exclusive role of mathematics in the science. The Vernadsky's treatment of mathematics is shown in great detail with reference to original works of him.
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