Zeno’s Dichotomy and the Paradox of Logical Causality

Abstract

A number of versions of Zeno’s ‘Dichotomy’ is being discussed in literature. Some of them are versions of a paradox that can be called ‘the paradox of logical causality’. It can be traced back to Benardete; in recent decades it has been discussed by Priest, Yablo, Hawthorne, Uzquiano, Shackel, Caie, and others. Unlike the original ‘Dichotomy’, the paradox of logical causality is an open problem for it has no generally accepted solution. In the paper, I examine the solution to the paradox proposed by Hawthorne and argue that it has an essential flaw caused by Hawthorne’s rejection of what he calls ‘the Change Principle’. I also compare the paradox and Zeno’s ‘Dichotomy’ and specify features shared by them, and features distinguishing the paradox. Their shared features are using infinite open series and reasoning from logical premises to physical conclusions. What distinguishes the new paradox is presupposing motion, and applying Zeno’s series to phenomena of physical interaction.