The article aims to highlight that the conceptual apparatus of the contemporary science (not only the problem-solving techniques but also the type of the raised issues) testify the shift of the paradigm, namely, the passage from the Cosmos paradigm to the Chaos paradigm. The significance of the old paradigm, especially considering its astonishing longevity, is related not only with its explanatory potential but also with the innate strife of humans to dwell in the aesthetically and ethically attractive and unconditionally intelligible world. Reductionist methodology became established in the framework of the mechanistic worldview. In this case, simplicity is seen as the main measure of intelligibility; however, the important detail of the elasticity (or, in other words, vagueness) of the simplicity concept is insufficiently considered. The shift towards the new paradigm of chaos is presented as a well-grounded effort of liberation from the universe of anthropocentrism and apriority.