Infinity and continuity

Abstract

The prevalence of issues involving infinity and continuity Natural philosophy in the fourteenth century is, when compared to that of the preceding century, more extensive, less repetitious, and more varied in the problems it treats, the solutions it sets forth, and the approaches and methods it employs in reaching those solutions. However, if one examines in some depth not merely the expositions and questions dealing with the relevant works of Aristotle but also the numerous non-commentatorial works constituting this literature, one cannot but be impressed by the unusual amount of time and effort spent in dealing with problems involving in one manner or another the infinite and the continuous. Often these problems concern infinity or continuity from the outset; but equally often the problems are extended or developed by the fourteenth-century scholar to take into account some aspect of the infinite or the continuous in a manner that was not apparent in the problem as initially stated. A discussion of the way in which one should measure a quantity that varies in intensity throughout its subject might, for example, be carried so far as to accommodate ‘infinite values’. Alternatively, a discussion of angelic motion might involve one in a rather full investigation of the composition of all continuous quantities. Indeed, the prevalence of issues involving the infinite or the continuous in later medieval natural philosophy is such that an exhaustive history of these two notions in the later Middle Ages would constitute a very large part of the history of natural philosophy during this period.