ABSTRACT
This chapter explains the question of how we should think of the 'small-scale' aspects of time's topology. For instants are extensionless parts of temporal intervals and if time were discrete any extended period of time would have a finite number of durationless parts of instants. One attractive feature of discrete time is that it admits of the development in theory at least of a particularly simple measure for the length of intervals. To have an adequate theory of mechanics one needs to do more than develop a system of difference equations which mirror the empirical predictions of the system of differential equations which constitute the core of Newtonian mechanics. In non-philosophical moments we are quite happy to assume unproblematically the existence both of intervals and of instants of time. First-order formulations of temporal theories involve quantification over instants. The conclusions that have been reached with regard to intervals of time have been limited and largely negative.
