  Within the framework of quantum contextuality, we discuss the ideas of
extracontextuality and extravalence, that allow one to relate Kochen-Specker's
and Gleason's theorems. We emphasize that whereas Kochen-Specker's is
essentially a no-go theorem, Gleason's provides a mathematical justification of
Born's rule. Our extracontextual approach requires however a way to describe
the ``Heisenberg cut''. Following an article by John von Neumann on infinite
tensor products, this can be done by noticing that the usual formalism of
quantum mechanics, associated with unitary equivalence of representations,
stops working when countable infinities of particles (or degrees of freedom)
are encountered. This is because the dimension of the corresponding Hilbert
space becomes uncountably infinite, leading to the loss of unitary equivalence,
and to sectorisation. Such an intrinsically contextual approach provides a
unified mathematical model including both quantum and classical physics, that
appear as required incommensurable facets in the description of nature.
