The article is devoted to the problem of communication between the earthly and unearthly mind. The authors contrasted Grice's theory of implicature with the Philosophy of the Cosmos. As a result, it has been found that the use of Grice's theory of implication at the scale of space exploration changes the meanings of the theory of implicature significantly. The opposition between Grice's theory of implicature and the Philosophy of the Cosmos updates the question "How acceptable are the similarities of the histories of cosmic civilizations at admissibility of similarity of the key phases of the physical, chemical, biological, and neurobiological evolution?" The study has shown that in the scope of space exploration, the meanings of the key term "the history of the cosmic civilization" are changing, in the question posed. They are formalized. The formalization of the term "history of the cosmic civilization" means the concentration of information in it, which is limited by the stages of neuroevolution and its external manifestations -"techne" (in the initial, antique senses). Based on the results obtained, the authors examined Grice's four maxims in space exploration and found their weak practical effect. It was proved that the basic Cooperative Principle, which was complemented by the Q and R Principles of Horn, effectively manifested itself in communication between space civilizations. The authors have concluded that 1) Grice's theory of implicature confirms the truth of the Philosophy of the Cosmos; 2) the main provisions of the theory of implicature are not refuted, however, they are specified.