The work demonstrates that brain might reflect the external world causal relationships in the form of a logically consistent and prognostic model of reality, which shows up as consciousness. The paper analyses and solves the problem of statistical ambiguity and provides a formal model of causal relationships as probabilistic maximally specific rules. We suppose that brain makes all possible inferences from causal relationships. We prove that the suggested formal model has a property of an unambiguous inference: from consistent premises we infer a consistent conclusion. It enables a set of all inferences to form a consistent model of the perceived world. Causal relationships may create fixed points of cyclic inter-predictable properties. We consider the “natural” classification introduced by John St. Mill and demonstrate that a variety of fixed points of the objects’ attributes forms a “natural” classification of the external world. Then we consider notions of “natural” categories and causal models of categories, introduced by Eleanor Rosch and Bob Rehder and demonstrate that fixed points of causal relationships between objects attributes, which we perceive, formalize these notions. If the “natural” classification describes the objects of the external world, and “natural” concepts the perception of these objects, then the theory of integrated information, introduced by G. Tononi, describes the information processes of the brain for “natural” concepts formation that reflects the “natural” classification. We argue that integrated information provides high accuracy of the objects identification. A computer-based experiment is provided that illustrates fixed points formation for coded digits.