The Reflexive-Intentional Model of the Subject (RIMS) connects the subject's bipolar probabilistic behavior with its mental domain.  We demonstrate that the Matching law is a formal consequence of this tie.  RIMS allows us also to deduce theoretically the main patterns of animal behavior in the experiments with two alternatives where the Matching Law reveals itself.  This finding inclines us to put forth a hypothesis that this law reflects the process of self-programming of the subject with mental domain.  As a result, the subject acquires the ability to choose alternatives with fixed probabilities.  With this explanation, the relative frequencies of pressing a pedal or pecking at a key play the role of half-finished-products which after being downloaded into the self turn into the probabilities of choice.  The Matching Law can be regarded as an operational indication of the mental domain existence.