The Threshold of Pursuit: Displaced Presence in Zeno's Achilles Paradox?

Abstract

This paper presents a novel interpretation of Zeno's Achilles paradox through direct textual analysis of Aristotle's Physics (239b14–18). We argue that the paradox's recursive logic reveals a structure of 'displaced presence' whereby sequential exclusivity prevents spatiotemporal co-occupation. Unlike interpretations that import modern mathematical concepts foreign to 5th century BCE thought, our reading requires only concepts demonstrably available to ancient Greeks: exclusive spatial occupation, temporal sequence, and observable pursuit dynamics. We make no claims about Zeno's intentions but analyse what the paradox's logic necessarily implies. A new line of evidence is introduced: Aristotle's own chain of definitions in Physics V.3 (226b34–227a17), distinguishing successive (ἐφεξῆς), contiguous (ἐχόμενον), and continuous (συνεχές) relations, formally describes the very structure the Achilles paradox exploits, a relation locked in succession that can never become contiguity. This approach opens philosophical inquiry rather than dissolving the paradox through anachronistic frameworks.