Karl Popper, apart from being an epistemologist and methodologist of science, is a cosmologic methaphysicist. A basic idea of his cosmology is the idea of indeterminism, which he encounters to determinism of the logical empirism. Indeterminism is implicit in the theory of growth in the scientific knowledge, resting on the principle of falsification and, hence, allowing for a possibility of denial of the knowledge system in any moment of time. K.Popper builds his cosmological model by postulating emergentism and evolutionism, overcoming in this way the classical perception of the world as a causality-driven mechanism. The emergent cosmology with its indeterminism rests on the very productive hypothesis on the reality of the world of predispositions. By introducing the notion of predisposition, K.Popper could explain the world as a formation associated with the appearance of new qualities. The analysis covers cosmologic metaphysics of K.Popper, which postulates indeterminism in ontologically significant world of predispositions, the appearance of probability approach and the nature of the probability style of thinking in various domains of science, and ways the outlined probability (nonlinear, poly-variant) stereotype of thinking is applied to philosophy. The analysis is made with abundant references to K.Popper's works.