  I show how Hamilton's philosophical commitments led him to a causal
interpretation of classical mechanics. I argue that Hamilton's metaphysics of
causation was injected into his dynamics by way of a causal interpretation of
force. I then detail how forces remain indispensable to both Hamilton's
formulation of classical mechanics and what we now call Hamiltonian mechanics
(i.e., the modern formulation). On this point, my efforts primarily consist of
showing that the orthodox interpretation of potential energy is the
interpretation found in Hamilton's work. Hamilton called the potential energy
function the force-function because he believed that it represents forces at
work in the world. Multifarious non-historical arguments for this orthodox
interpretation of potential energy are provided, and matters are concluded by
showing that in classical Hamiltonian mechanics, facts about potential energies
of systems are grounded in facts about forces. Thus, if one can tolerate the
view that forces are causes of motions, then Hamilton provides one with a road
map for transporting causation into one of the most mathematically
sophisticated formulations of classical mechanics, viz., Hamiltonian mechanics.
