The spectrum argument purports to show that the better-than relation is not transitive, and consequently that orthodox value theory is built on dubious foundations. The argument works by constructing a sequence of increasingly less painful but more drawn-out experiences, such that each experience in the spectrum is worse than the previous one, yet the final experience is better than the experience with which the spectrum began. Hence the betterness relation admits cycles, threatening either transitivity or asymmetry of the relation. This (...) paper examines recent attempts to block the spectrum argument, using the idea that it is a mistake to affirm that every experience in the spectrum is worse than its predecessor: an alternative hypothesis is that adjacent experiences may be incommensurable in value, or that due to vagueness in the underlying concepts, it is indeterminate which is better. While these attempts formally succeed as responses to the spectrum argument, they have additional, as yet unacknowledged costs that are significant. In order to effectively block the argument in its most typical form, in which the first element is radically inferior to the last, it is necessary to suppose that the incommensurability is particularly acute: what might be called radical incommensurability. We explain these costs, and draw some general lessons about the plausibility of the available options for those who wish to save orthodox axiology from the spectrum argument. (shrink)

In 1907 Borel published a remarkable essay on the paradox of the Heap (“Un paradoxe économique: le sophisme du tas de blé et les vérités statistiques”), in which Borel proposes what is likely the first statistical account of vagueness ever written, and where he discusses the practical implications of the sorites paradox, including in economics. Borel’s paper was integrated in his book Le Hasard, published 1914, but has gone mostly unnoticed since its publication. One of the originalities of Borel’s essay (...) is that it puts forward a model of vagueness as imprecision, making particular use of the Gaussian law of measurement errors to model categorization. The aim of our paper is to give a presentation of the historical context of Borel’s essay, to spell out the mathematical details of his model, and to provide a critical assessment of his theory. Three aspects of Borel’s account are particularly discussed: the first concerns the comparison between Borel’s statistical account and posterior degree-theoretic accounts of vagueness. The second concerns the anti-epistemicist flavor of Borel’s approach, whereby the idea of statistical fluctuation is used to undermine the notion of sharp boundary for vague predicates. The third concerns the problematic link between Borel’s model of vagueness as imprecision and the notion of semantic indeterminacy. An English translation of Borel’s original essay is appended to this paper (Erkenntnis, this issue). (shrink)

The standard argument for the claim that rational preferences are transitive is the pragmatic money-pump argument. However, a money-pump only exploits agents with cyclic strict preferences. In order to pump agents who violate transitivity but without a cycle of strict preferences, one needs to somehow induce such a cycle. Methods for inducing cycles of strict preferences from non-cyclic violations of transitivity have been proposed in the literature, based either on offering the agent small monetary transaction premiums or on multi-dimensional preferences. (...) This paper argues that previous proposals have been flawed and presents a new approach based on the dominance principle. (shrink)