The article deals with the (flexible) rationality, combining rational and irrational moments of the scientific search of the cognizing subject. Linguo-cognitive model of the concept as the flexible regulative reveals the activity of the processes and the mentality of the epistemological-ontic subject, its leading constructive role in the formation of the language, and world pictures of conceptual post-non-classic type. Logic-mathematical languages reveal deep structures of the subject's rationality. The purpose of this paper is the analysis of the and logical-mathematical language. At the stage of the post-non-classic science, the issue of the in the science remains relevant. Moreover, possible correction of the scientific rationality, understood not as an abstract-logical but as a socio-cultural, developing, and structurally complex phenomenon. Scientists name its following main forms: anarchic (P. Feyerabend), moderate (V. A. Lektorsky), descriptive (I. T. Kasavin), paradoxical (V. N. Porus), open and closed (V. S. Shvirev), special (E. P. Nikitin), hyper-rationality (A. A. Novikov), communicative (George H. Mead & J. Habermas), value-rationality (V. G. Fedotova), etc.. But these forms of are not enough to show all its potential qualities and characteristics. Psychologists and philosophers were convinced that strictly theoretical thinking is not and cannot be the only form of the scientific thinking. It allows other rational forms: empirical thinking, common sense, and everyday awareness. Such is not a rigid procedure, it allows the inclusion of the subject in the process that enhances the possibilities of the subject cognition as a carrier of the rationality. The aspect of the analysis in the article is the one. In the science, the category of the cognitive rationality is introduced. It is absent in the modern science, but is demanded in the cognition of the nature of the cognizing subject. There are almost no works that address the rationality. This work examines this issue in the interdisciplinary aspect at the junction of the psychology, philosophy, linguistics, and non-classical mathematics. The object of the study is: as the capacity of the subject to the adequate and effective constructive scientific cognition. The subject of the study is logic-mathematical language of the rationality.