Topological Aspects of McLaughlin-Miller's Model of Motion

Abstract

McLaughlin and Miller (1992) provided a novel framework for resolving Zeno's paradox by employing Nelson-style nonstandard analysis. The following two principles play the key roles in their model of motion.The first is the ontological principle that every point in space-time is described as a vector of hyperreals. The second one is epistemological: one cannot distinguish two points in space-time that are infinitely close to each other. In this paper, we extract the topological essence from their argument. More precisely, we argue that the above principles correspond to introducing two topologies on the hyperreals, called Q-topology and μ-topology. We also consider Hellman-Shapiro's account of nonstandard analysis in the context of philosophy of continua.