Axiomatic utility theory plays a foundational role in some accounts of normative principles. In this context, it is sometimes argued that transitivity of “better than” is a logical truth. Larry Temkin and Stuart Rachels use various examples to argue that “better than” is non–transitive, and that transitivity is not a logical truth. These examples typically involve some sort of “discontinuity.” In his discussion of one of these examples, John Broome suggests that we should reject the claim which involves “discontinuity.” We can, I suggest, make sense of the examples which Temkin uses while sacrificing neither transitivity nor “discontinuity.” This response to Temkin's examples involves developing and modifying James Griffin's account of “discontinuity.” If the account of “discontinuity” seems implausible, that is because of a failure to allow for vagueness. A similar argument can be made in the context of the well-known “repugnant conclusion.”
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