  Familiar formulations of classical and quantum mechanics are shown to follow
from a general theory of mechanics based on pure states with an intrinsic
probability structure. This theory is developed to the stage where theorems
from quantum logic enable expression of the state geometry in Hilbert space.
Quantum and classical mechanics are then elaborated and applied to subsystems
and the measurement process. Consideration is also given to space-time geometry
and the constraints this places on the dynamics. Physics and Mathematics, it is
argued, are growing apart; the inadequate treatment of approximations in
general and localisation in quantum mechanics in particular are seen as
contributing factors. In the description of systems, the link between
localisation and lack of knowledge shows that quantum mechanics should reflect
the domain of applicability. Restricting the class of states provides a means
of achieving this goal. Localisation is then shown to have a mathematical
expression in terms of compactness, which in turn is applied to yield a
topological theory of bound and scattering states. Finally, the thesis
questions the validity of classical limits and quantisations in intertheoretic
reduction, and demonstrates that a widely accepted classical limit does not
constitute a proof of reduction. It proposes a procedure for determining
whether classical and quantum mechanics are weakly equivalent over a domain of
applicability, and concludes that, in this restricted sense, classical
mechanics reduces to quantum mechanics.
