This article is devoted to the philosophical foundations of anthropomorphism in the context of Human-Robot Interaction (HRI), a new interdisciplinary field of research. On the basis of modern scientific works, a positive concept of anthropomorphism as a cognitive mechanism ensuring human adaptation to a complex external environment is formulated. The theoretical principles of applied anthropomorphism (AA) are being developed to identify the conditions for activating anthropomorphic projections in a user during an HRI act. There are two key factors in the structure of AA: appearance and autonomous behaviour. Asymmetry principle is formulated: behavioral realism is more important than highly anthropomorphic appearance. The principle of coherence is formulated: the necessity of synchronisation of the appearance and the robot's behaviour, that is, the level of development of behavioral patterns of the robotic system determines the degree of its anthropomorphism. Various forms of anthropomorphism are distinguished. These differences can be described in terms of involvement in cognitive activity. Anthropomorphism as passive ascription and simple projection receives negative assessment in social robotics, while anthropomorphism, which is deduced from autonomous robots behaviour or initiated by them, is assessed positively. The epistemological foundations of the robotic revolution of the late 80s-early 90s of the XX century are analysed; the methodology of "behavior-based robotics" is examined thoroughly. The behavioral approach in robotics is based on the concept of weak artificial intelligence, within which computational operations and functions of a machine represent concatenation of processes and can lead to the illusion of intelligence in a robot, primarily due to projective intelligence from a human-observer side. These questions are analysed in the context of modern philosophical theories, such as second-order cybernetics, autopoiesis. Anthropomorphism as active ascription of cognitive or emotional states to the robot from the observer side in order to rationalise the behaviour of the object is correlated with D. Dennett's intentional stance. At the end of the article, the phenomenon of attribution of human characteristics to non-human entities in Eastern religious cults is studied. The question of the ontological status of gods and robots is raised.