The author discusses philosophical and methodological presuppositions of investigations in Cognitive Science. In this context a traditional philosophical and psychological idea of consciousness as the only certainty is critically analyzed, and the understanding of mental content in psychology and earlier cognitive science is studied. A special attention is given to a popular idea of situated, embodied and inacted Cognitive Science and to discussions about its philosophical interpretation. The idea of "the methodological solipsism as a strategy of Cognitive Science" by J. Fodor is criticized, as well as the interpretation of the situated Cognitive Science as going beyond the dichotomy of Realism-Idealism (A. Varela and others). The thesis about Activity Realism as an adequate interpretation of the idea of situated Cognition is argued. In this context the author analyzes the notion of "affordances" by J. Gibson, the idea of an interconnection between the Real World and an epistemic agent (the idea of "many worlds"), the role of actions and operations of a cognitive being in forming contacts with real objects. The problem of illusion and reality is analyzed, as well as relations between Naïve and Scientific Realism. A special attention is given to artificial objects as a special kind of existence.