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Abstract. Modern cosmology and physics has came to the limits of the "elemental" approach. As a result in the quantum mechanics, describing the deepest levels of reality, scientists can not find more "deep" structures. One of the prove of this is the statement of the absence of so-called "hidden variables" based on the violation of Bell's inequalities in experiments and investigation of pairing correlations integrated by the common past of elementary microscopic objects. We can see analogical situation in modern cosmology, when the most despite of the set of unsolved problem scientists-cosmologists follow Lambda-Cold Dark Matter. It means that the modern fundamental physics and cosmology touched to the ontological structures of the universe. Nobel laureate academician Ginzburg V.L. (1916-2009) in his Nobel lecture stressed "three" great "problems of modern physics. One of them is the problem of interpretation of nonrelativistic quantum mechanics and the opportunity to learn something new, even in the area of its application. Based on Ginzburg's approach we can give such formulation of problem of modern cosmology: the philosophical problem of modern cosmological theories is the problem of content (semantic, pragmatic) interpretation of the fundamental structural (syntactic) laws of the Book of Nature. This task of interpretation is, essentially, hermeneutical task and therefore traditional philosophical. Because modern science, especially modern cosmology is emerged as investigation of the structure of the macro-universe, as the study of syntax of Book of Nature, the interpretation of the Book of Nature is hermeneutics of the second Scripture. Thus, the search of ontological interpretation of modern cosmology is conducted in spiritual, social and cultural context of emergence of the modern science.