This chapter continues the exploration of transitivity. Chapter 6 showed that one important normative relation, “the not worse than” relation, may be nontransitive. It also developed and explored a model for understanding why that relation, and others, would be nontransitive. The chapter begins by discussing two other important normative relations that may be nontransitive, the “permissibility” relation and the “obligatoriness” relation. It then suggests that there is good reason to believe that if the “obligatoriness” relation is nontransitive, the “all-things-considered better than” relation will also be nontransitive. It next considers an important response to the claim that the “obligatoriness” relation is nontransitive. It directly takes up the question of whether the “all-things-considered better than” relation (in this book's wide reason-implying sense) could be nontransitive. It spells out the conditions under which the relation would or would not be transitive and reexamines some of the arguments of earlier chapters in this light. Finally, it notes some of the important theoretical commitments that accompany both the view that the “all-things-considered better than” relation (in the aforementioned wide reason-implying sense) is transitive and the contrary view that it may not be, pointing out that the former view will hold if a position called the Internal Aspects View is correct, while the latter view will hold if a position called the Essentially Comparative View is correct.
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