Bryson of Heraclea and Polyxenus have received little attention from scholars. Sources on these philosophers are few and difficult to interpret. However, they present interesting dialectical arguments that concern some of Plato’s and Aristotle’s most important theoretical elaborations: Bryson’s arguments on the issue of semantic ambiguity were explicitly discussed by Aristotle, and Polyxenus is credited with a particular version of the Third Man argument. My purpose in this paper is to reconstruct the historical background of these two philosophers and to (...) analyze the philosophical implications of the arguments that the ancient tradition ascribes to them. (shrink)

In this paper, I compare the Megarian thesis of Metaphysics IX 3 with other sources on the Megarians in order to clarify two questions: that of the unity and nature of the so-called Megarian school and that of Aristotle’s broader argument in IX 3. I first review the disputed issue of the status of the Megarian school and then examine two hypotheses regarding the identity behind Aristotle’s allusion in IX 3. Third, I explore the connection between Megarianism and Plato’s Euthydemus, (...) a task that helps us to contextualize Aristotle’s anti-Megarian polemic. Lastly, I build on the preceding argument in a re-examination of the Eleatic hypothesis with regard both to the Megarians as a whole and to the thesis that Aristotle transmits. (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)

Rationing is an unavoidable mechanism for reining in healthcare costs. It entails establishing cutoff points that distinguish between what is and is not offered or available to patients. When the resource to be distributed is defined by vague and indeterminate terms such as “beneficial,” “effective,” or even “futile,” the ability to draw meaningful boundary lines that are both ethically and medically sound is problematic. In this article, I draw a parallel between the challenges posed by this problem and the ancient (...) Greek philosophical conundrum known as the “sorites paradox.” I argue, like the paradox, that the dilemma is unsolvable by conventional means of logical analysis. However, I propose another approach that may offer a practical solution that could be applicable to real-life situations in which cutoffs must be decided (such as rationing). (shrink)

It is widely accepted that vagueness in law calls for a specific interpretation of the law—interpretation that changes the meaning of the law and makes it more precise. According to this view, vagueness causes gaps in the law, and the role of legal interpretation in the case of vagueness is to fill such gaps. I argue that this view is mistaken and defend the thesis that vagueness in law calls only for an application of the law to the case at (...) hand, leaving the meaning of the law intact. (shrink)

The only passage from Aristotle's works that seemsto discuss the paradox of the liar is within chapter 25 of Sophistici Elenchi (180a34–b7). This passage raises several questions: Is it really about the paradox of the liar? If it is, is it addressing a strong version of the paradox or some weak strain of it? If it is addressing a strong version of the paradox, what solution does it propose? The conciseness of the passage does not enable one to answer these (...) questions beyond doubt, and commentators have offered very different replies. However, a reasonable case can be made for claiming, first, that the passage in question is about the paradox of the liar, second, that it addresses a strong version of the paradox, and, third, that it attempts to solve it by assuming that someone uttering 'I am speaking falsely' (or whatever sentence-type the paradox turns on) is neither speaking truly nor speaking falsely absolutely. (shrink)

Refutaciones Sofísticas ha sido usualmente interpretado como un intento de clasificación de sofismas. Este acercamiento, sin embargo, corre el riesgo de oscurecer la dimensión de sus propias intenciones confrontativas. El presente trabajo se propone enfatizar la importancia de las Refutaciones Sofísticas como parte de un programa antierístico que tiene por objetivo prioritario la filosofía megárica, en las antípodas de Aristóteles en el terreno epistemológico. Bajo esta luz, la resolución de argumentos erísticos excede el estudio lógico así como también la denuncia (...) sobre sus efectos prácticos y se erige como parte de una discusión entre líneas de inspiración socrática sobre los alcances y fines de la dialéctica y la filosofía en general. (shrink)