Hume's conception of causation and induction is discussed in the context where the causal evolution is represented by the motion of a free particle in space. The difference between classical and relativistic mechanics is shown to be significant for the discussion.

A mapping of a finite directed graph onto a curve in space-time is considered. The mapping induces the dynamics of a free particle moving along the curve. The distinction between the Lagrangian and the Hamiltonian formulation of particle mechanics is expressed in terms of the distinction between referring to a particle in space and time and referring to the points in space which the particle occupies, respectively. These elements are combined to yield an interpretation of Feynman's path integral formulation of (...) quantum mechanics. Describing a bound state of a system as a particle is discussed. (shrink)

The paper claims that analytic philosophy has failed within the philosophy of science due to the way the dynamic aspect of scientific theories is traditionally treated. On the formal side this failure manifests itself in the first-order logical and the model-theoretic analyses of scientific theories. An amendment of the treatment is sketched. It is based on using model generation, of the kind used in proving the Completeness Theorem for first-order logic, in such a way that some dynamic quantities in the (...) dynamic theory are formally represented as functions relating closed terms and sentences to their interpretations in a generated model. (shrink)

The mechanical aspect of momentum, basically its role as a tangent vector of the trajectory of the particle, is related to properties of the momentum found in the contexts of Hamilton's optico-mechanical analogy, de Broglie's matter waves, and quantum mechanics. These properties are treated in a systematic way by considering an approximation of the particle mechanical action of the particle by a step function. A special method of discretizing partial differential equations is shown to be required. Using this method, a (...) discrete dynamics is developed. It is shown that particle dynamics can be regarded as the limit case of the discrete dynamics as the step functions tend to the continuous ones. The equation of motion of a free particle in an arbitrary reference system is deduced in two ways: (i) in continuous dynamics by making use of the invariance of action within changes of reference systems, and (ii) by taking the mentioned limit in discrete dynamics of an equation which expresses that the mechanical and wave-theoretical aspects of the momentum are interrelated in specific way. (shrink)