Abstract
Analysis of directly measurable subsystems of quantum systems (i.e., prepared and measured observable, parameters of symmetry transformations), based on the Einstein-Podolsky-Rosen definition of physical reality, shows that such subsystems cannot be deterministic. This effect is not specifically quantum: a physically different but mathematically similar situation arises in classical decision-making systems obeying classical logic. Direct consequences of this phenomenon are nonclassical behavior of probabilities and irreversibility of measurements (or decisions).
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