A Predicative Characterization of Quantum States and Matte Blanco's Bi-logic

We show a correspondence between a predicative characterization of quantum states, we have recently introduced, and bi-logic, a logical setting proposed by the Chilean psychoanalist I. Matte Blanco in order to describe the logic of the unconscious. The unconscious deals with “infinite” objects for which the “symmetric mode” is characterized, where negation and implication do not exist. In our model it is possible to define a class of first order domains, termed virtual singletons, that are uncountable, and that allow a generalization of the notion of duality, termed symmetry. Symmetry makes negation and logical consequence collapse, in favour of different links between judgements, that are due to quantum correlations.