I show how Sir William Rowan 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 are 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 contemporary 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. Various 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 the potential energies of systems are grounded in facts about forces. Thus, if one can tolerate the view that forces are causes of motion, 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. (shrink)

The development and applicability of complex numbers is often cited in defence of the formalist philosophy of mathematics. This view is rejected through an examination of hamilton's development of the notion of complex numbers as ordered pairs of reals, And his later development of the quaternion theory, Which subsequently formed the basis of vector analysis. Formalism, By protecting informal assumptions from critical scrutiny, Constrained rather than encouraged the development of mathematics.

(1993). Thomas solly (1816–1875):an unknown pioneer of the mathematization of logic in england, 1839. History and Philosophy of Logic: Vol. 14, No. 2, pp. 133-169.