Selection Postulates and Probability Rules in the Problem of Quantum Measurement

Various approaches to quantum measurement problem within the framework of usual unitary quantum dynamics are considered. It is argued that neither decoherence theory nor many-worlds interpretation of quantum mechanics do provide ultimate solution of the measurement problem: they cannot solve the problem of an alternative selection within the framework of unitary quantum dynamics. It is argued that the selection postulate in quantum theory is a very fundamental entity tightly connected with the nature of mathematics and with the nature of the mind, while the probability rules are more technical things admitting various approaches based on various sets of axioms.