Recently, Stuart Rachels and Larry Temkin have o®ered a new argument against the transitivity of the relationship 'all things considered better than'. This argument invokes our intuitions about our preferences over di®erent bundles of pleasurable or painful experiences with di®erent durations, which, it is argued, will typically be intransitive. This paper defends the orthodox view that the relation 'all things considered better than' should be regarded as transitive against this argument, by

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... owing that it fails for the same reason that Achilles catches the tortoise in Zeno's paradox. Defending Transitivity Against Zeno's Paradox by Ken Binmore and Alex Voorhoeve Philosophers have recently been o®ered a new argument against the transitivity of the relationship 'all things considered better than ' (Rachels (1993; 1998; 2001a,b), Temkin (1996) ). This argument, in its various guises, invokes our intuitions about our preferences over di®erent bundles of pleasurable or painful experiences with di®erent durations, which, it is argued, will typically be intransitive. This paper defends the orthodox view that the relation 'all things considered better than' should be regarded as transitive against this argument, by showing that Rachels and Temkin are mistaken in supposing that a preference relation satisfying their assumptions must be intransitive. It makes clear where the argument goes wrong by showing that it is a version of Zeno's paradox of Achilles and the tortoise. The argument centres around two kinds of counterexamples to the transitivity of 'all things considered better than', one involving painful and the other involving pleasurable experiences of di®ering duration. Since Rachels and Temkin both o®er an example of painful experiences, we begin by discussing this case in section 1. Section 2 explains why the argument fails. Section 3 explains why the case of pleasure is of the same form, and can be solved in the same way. The ¯nal section contains some general remarks on counterexamples to the transitivity of 'all things considered better than'.