Achilles, the Tortoise, and the Time Machine: A Carrollian dialogue

Drawing on near-contemporaneous works by Lewis Carroll and H. G. Wells, this paper uses an imaginary dialogue between Achilles and the Tortoise to explore the supertask possibilities offered by combining Zeno’s (and Carroll’s) original Eleatic race set-ups with unlimited Wellsian time travel. Besides offering new thoughts on how to address some perennial worries about time travel, e.g. by paying due attention to the distinction between counterfactual and causal dependence, this paper also offers a new form of Eleatic ‘paradox’ in which Achilles is condemned to run an unending (i.e. infinite time) race at constant finite velocity over a racetrack of finite length. This time round, the Tortoise shows Achilles just how Wellsian time machines can also be infinity machines, which allow unsuspected scope for ‘bifurcated’ supertasks and unending Eleatic races.