ABSTRACT
Quite apart from Zeno's difficulties with infinity, and Hume's empiricist objections, the notion of denseness and continuity is incompatible with the notion of nextness, and hence, on one of its interpretations, of succession. If time is dense, there cannot be a next instant after this one; because for any instant after this one there is, by the definition of denseness, another instant between it and this one; so that it could not have been the next one. Arguments from quantum mechanics can be adduced for there being an ultimately granular structure of time and space, with quanta of duration and distance, as well as of action. Cine films are composed of large numbers of separate stills, but give the impression of continuous motion; and time too might be composed of discrete minimum moments, with non-infinitesimal changes occurring or not occurring from one to the next.
