What Cannot Be the Rationals, the Irrationals and Other Riddles

Abstract

This article aims to show that unless we consider Zeno’s paradoxes in the original metaphysical perspective in which they were generated, any attempt at understanding, let alone solving them, is destined to fail. This perspective, I argue, is the dichotomy of One and change. These latter were defined at the outset of Western philosophical thought by Parmenides as the two paths of the rational, i.e. accountable by a self-identical thought and thus real (One), and the non-identical change, irrational and unreal. In this perspective, the irrational, is by definition unnameable (alogos) and thus uncountable. I claim that we have inherited this dichotomic thought and if we become aware of this legacy, many deadlocked paradoxes or logical aporias in Western epistemology will acquire the status of logical necessities that follow directly from this dichotomy.