Academic literature on the topic 'Transitivity/intransitivity'

This paper addresses some crucial categories in contemporary practices of memorialisation and public sculpture, including the polarities of “abstraction / figuration” and “transitivity / intransitivity” and the questions of anthropomorphism and embodiment. Referring to paradigmatic cases belonging to different media—sculpture, architecture, video installations—and comparing different memorialistic subjects (the Holocaust memorials, the Italian fascist sacraria, the monuments dedicated to the Vietnam war), the chapter investigates the dialectics of presence and absence in the relationship between the present material body of the monument and the absent bodies evoked by the process of memorialisation.

This chapter defends the Time-Relative Interest Account of the misfortune of death against the two ingenious objections that Tim Campbell advances in chapter 18 of this volume. Campbell argues that this account, when combined with two other highly plausible claims, generates intransitive judgments about which options we ought to choose in a series of choices among pairs of options. He then argues that even if we can accept the intransitivity, our judgments must violate the principle of Contraction Consistency. I argue that there are good explanations of why the violations of transitivity and Contraction Consistency are innocuous.

This chapter proposes a new solution to Derek Parfit’s Mere Addition Paradox. It argues that the paradox trades on an ambiguity about the context of choice. There is a sense in which all three intuitive judgments about Parfit’s case are true, namely as pairwise comparisons in a two-possible case, i.e. in a choice situation where the option set contains only these two outcomes. The air of paradox arises from the assumption that these pairwise judgments carry over to a three-possible case, in which all three outcomes are possible. But this, the chapter argues, is not the case. If sound, this argument shows how we can make sense of each of our pairwise intuitions in the Mere Addition Paradox, without incurring the cost of intransitivity within an option set. This solves the Mere Addition Paradox and blocks the argument toward the Repugnant Conclusion. Parfit’s case also holds a general lesson about the nature of value, but one that is less revisionary than some had thought. Correctly understood, Parfit’s Mere Addition Case challenges not the transitivity of the “better than”-relation, as Larry Temkin has argued, but instead a different, and less sacrosanct, idea, namely the so-called Independence of Irrelevant Alternatives principle. What Parfit’s puzzle teaches us is that betterness is sometimes context-dependent: the relative goodness of two outcomes can depend on whether or not a third outcome could have instead been chosen.