The Logos Categorical Approach to Quantum Mechanics: I. Kochen-Specker Contextuality and Global Intensive Valuations

Abstract: In this paper we present a new categorical approach which attempts to provide an original understanding of QM. Our logos categorical approach attempts to consider the main features of the quantum formalism as the standpoint to develop a conceptual representation that explains what the theory is really talking about --rather than as problems that need to be bypassed in order to allow a restoration of a classical "common sense" understanding of what there is. In particular, we discuss a solution to Kochen-Specker contextuality through the generalization of the meaning of global valuation. This idea has been already addressed by the so called topos approach to QM --originally proposed by Isham, Butterfield and D\"oring-- in terms of sieve-valued valuations. The logos approach to QM presents a different solution in terms of the notion of intensive valuation. This new solution stresses an ontological (rather than epistemic) reading of the quantum formalism and the need to restore an objective (rather than classical) conceptual representation and understanding of quantum physical reality.