Some ideas of V.I. Vernadsky, which today participate in the formation of the philosophical and scientific foundations of the new reality and, in particular, the new living science or the sphere approach, are considered. The lack of predictive potential in the linear schematization of the types of scientific rationality of Academician V.S. Stepin is shown. Another type of schematization (triangular balance) is proposed, in which it is possible to express the predictive potential. Four types of synthetic worldview are considered, which generally form a spherical approach, and examples of each of them are given. The principles of 'more than oneself' (synergy) and 'less than oneself' (symplergy) have been introduced for the process of cognition. The new spherical rationality is characterized by the symmetry of these principles, whereas in the previous rationality the principle of 'more than oneself' is forbidden. The features of the sphere approach are formulated in its comparison with the object, environmental and system approaches

synthesis, classics, non-classics, post-non-classics, system, environment, sphere, synergy, symplergy, V.I. Vernadsky