  In a previous preprint (quant-ph/0012122) we introduced a ``contextual
objectivity" formulation of quantum mechanics (QM). A central feature of this
approach is to define the quantum state in physical rather than in mathematical
terms, in such a way that it may be given an "objective reality". Here we use
some ideas about the system dimensionality, taken from quant-ph/0101012, to
propose a possible axiomatic approach to QM. In this approach the structure of
QM appears as a direct consequence of the non-commutative character of the
(classical geometrical) group of "knobs transformations", that relate between
themselves the different positions of the measurement apparatus.
