On the connection between the theorems of Gleason and of Kochen and Specker

We present an elementary proof of a reduced version of Gleason’s theorem and the Kochen–Specker theorem to provide a novel perspective on the relation between both theorems. The proof is based on a set of linear equations for the values of a function, m, on the unit sphere. In the case of Gleason’s theorem, the entire unit sphere needs to be considered, while a finite set of points suffices to prove the Kochen–Specker theorem.

The (virtual) conceptual necessity of quantum probabilities in cognitive psychology

We propose a way in which Pothos & Busemeyer (P&B) could strengthen their position. Taking a dynamic stance, we consider cognitive tests as functions that transfer a given input state into the state after testing. Under very general conditions, it can be shown that testable properties in cognition form an orthomodular lattice. Gleason's theorem then yields the conceptual necessity of quantum probabilities (QP).