In Defense of the Trichotomy Thesis

According to a standard picture, for any two comparable objects and a basis for comparison, either one is greater than the other or they are equal with respect to the basis. This picture has been called the Trichotomy Thesis, and although it is intuitive and plausible, it has been called into question by such philosophers as Derek Parfit, James Griffin, Joseph Raz, and Ruth Chang. Chang’s discussion is particularly rich, for she proposes and provides a detailed account of a possible fourth relation that, she argues, provides a satisfying explanation of hard cases of comparison. In this paper, I will examine a version of the main argument against the Trichotomy Thesis and attempt to show that it is unsound