Continuous Time and Instantaneous Speed in the Works of William Heytesbury and Richard Swineshead

Abstract

The term ‘instantaneous speed’ that appears explicitly in the works of famous Oxford fourteenth-century natural philosophers, William Heytesbury and Richard Swineshead (nicknamed The Calculator), seems odd in the context of the then accepted Aristotelian worldview for at least two reasons. First, Aristotle himself stated unambiguously that no motion can occur in an instant. Second, after fourteenth-century atomism was rejected, the majority of thinkers denied the existence of instants, understood as indivisibles. Nevertheless, both Oxford philosophers describe instantaneous speed, also in the context of the mean-speed theorem, in a way that allowed them to preserve the continuity of time. This description may seem similar to the one formulated by Newtonians in the seventeenth century, but is so only superficially, however, as their backgrounds and contexts were different.