Defending transitivity against zeno's paradox

Philosophy and Public Affairs

Volumn 31, Issue 3, 2003, Pages 272-279

  Binmore, Ken ^a   Voorhoeve, Alex ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

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[No Author keywords available]

Indexed keywords

EID: 22544476048     PISSN: 00483915     EISSN: 10884963     Source Type: Journal    
DOI: 10.1111/j.1088-4963.2003.00272.x     Document Type: Article

References (19)

1. See Larry Temkin, "A Continuum Argument for Intransitivity," Philosophy & Public Affairs 25 (1996): 175-210;
2. Stuart Rachels, A Theory of Beneficence (unpublished undergraduate thesis, University of Oxford, 1993)
3. "Counterexamples to the Transitivity of Better Than," Australasian lournal of Philosophy 76 (1998): 71-83
4. "A Set of Solutions to Parfit's Problems," Noûs 35 (2001): 214-38
5. and "Intransitivity," in volume II of The Encyclopedia of Ethics (2nd ed.), ed. Lawrence C. Becker and Charlotte Becker (London: Routledge, 2001), pp. 877-79.
6. Rachels, "Counterexamples," pp. 72-75 and pp. 78-79
7. and Ternkin, Continuum," 179.
8. Rachels, "Counterexamples," p. 73, mentions 100 times as long, while Temkin mentions twice as long. Nothing depends on this number.
9. Rachels, "A Set of Solutions to Parfit's Problems."
10. Temkin, "Continuum," pp. 209-10.
11. Note how our proposed utility function matches with Temkin, "Continuum," p. 192: "My model for this is something like the following. Torture's badness might range from 0 to 10, depending on its duration, with two years of torture being, say, a 7. A hangnail's badness might range from 0 to 1. Prolonging a hangnail increases the value of the decimal places representing its 'badness score', but the fundamental gap between 1 and 7 is never affected."
12. Temkin, "Continuum," pp. 191-92.
13. Rachels, "Counterexamples," pp. 75-78
14. "A Set of Solutions," pp. 215-16, and "Intransitivity. "
15. In "A Set of Solutions," Rachels calls this the "principle of duration."
16. In "A Set of Solutions," Rachels calls this the "principle of lexicality."
17. Rachels, "Counterexamples," p. 77.
18. The Independence of Irrelevant Alternatives was introduced by John Nash in "The Bargaining Problem," Econometrica 18 (1950): 155-62.
19. It differs from Kenneth Arrow's well-known condition of the same name that relates individual and social preferences.Amartya Sen, in "Internal Consistency of Choice," Econometricu 61 (1993): 495-521, expresses regret at the fact that Nash's and Arrow's conditions are often confused and renames Nash's condition "basic contraction consistency." If a choice function C specifies for any admissible nonempty set S of alternatives a nonempty subset C(S) called the choice set of S, then Sen formulates the condition as (x ∈ C(S) and x ∈ C(Q). For the condition to make sense, the alternatives must be formulated in a manner that makes it possible to eliminate alternatives from a feasible set without altering our relative valuation of the alternatives that remain. Sen describes cases where this property appears to be violated by a rational chooser, but all his examples involve cases where the removal of one of the unchosen options changes the (expected) worth of the remaining alternatives. This means that the removed options are not irrelevant to the remaining alternatives.