Intuitionistic interpretation of quantum mechanics

Abstract

In the present paper, the decision problem of the Schr\"odinger equation (asking whether or not a given Hamiltonian operator has the nonempty solution set) is represented as a logical statement. As it is shown in the paper, the law of excluded middle would be applicable to the introduced statement if and only if quantum fundamentalism (asserting that everything in the universe is ultimately describable in quantum-mechanical terms) held. But, since the decision problem of the Schr\"odinger equation is in general undecidable, such a statement is allowed to be other than true or false, explicitly, it may fail to have truth values at all. This makes possible to abandon the law of excluded middle together with quantum fundamentalism in the proposed intuitionistic interpretation of quantum mechanics.