Intransitivity without Zeno’s Paradox
نویسندگان
چکیده
Stuart Rachels and Larry Temkin have put forward a number of alleged counterexamples to the transitivity of the relation " all things considered better than ". 1 Several of these cases share a common structure. 2 A representative example by Rachels is as follows: Each outcome in [this] counterexample involves a single person's experience: A: 1 year of excruciating agony. B: 100 years of pain slightly (or somewhat) less intense than the pain in A. C: 10,000 years of pain slightly less intense than the pain in B. D: 1 million years of pain slightly less intense than the pain in C.. .. Y: 1 × 10 48 years of pain slightly less intense than the pain in X. Z: 1 × 10 50 years of pain slightly less intense than the mild pain in Y. […] Although A is worse than Z, the example creates a path from A to Z involving only changes for the worse. These changes are for the worse because increasing a pain's duration 100-fold offsets reducing its intensity slightly, or even somewhat. So the outcomes get worse until they are better, contradicting Tran-2 In particular, this is true of the first three examples in Rachels 1998, the first of which is quoted below, and of the main example in Temkin 1996, also quoted below. Examples of roughly this structure date back at least to Harrod 1936, p. 148. (Harrod does not, however, explicitly draw the conclusion that betterness is not transitive.) A seemingly different kind of example appears in Temkin 1987; 1997; Rachels 2001. Those cases will not be discussed here.
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