  This paper deals with the foundations of quantum mechanics. We start by
outlining the characterisation, due to Birkhoff and Von Neumann, of the logical
structures of the theories of classical physics and quantum mechanics, as
boolean and modular lattices respectively. We then derive these descriptions
from what we claim are basic properties of any physical theory - i.e. the
notion that a quantity in such a theory may be analysed into parts and that the
results of this analysis may be treated in languages with an underlying boolean
structure. We shall see that in the course of constructing a model of a theory
with these properties different indistinguishable possibilities will arise for
how the elements of the model may be named, that is to say different
possibilities arise for how they can be associated with points from Set. Taking
a particular collection of possibilities gives the usual boolean lattice of the
propositions of classical physics. Taking all possibilities - in a sense, the
set of all things that may be described by physical theories - gives the
lattice of quantum mechanical propositions. This gives an interpretation of
quantum mechanics as the complete set of such possible descriptions, the
complete physical description of the world.
