Los dos grandes problemas del enfoque supervaluacionista para la vaguedad son determinar cuáles son las precisificaciones admisibles y la vaguedad de orden superior ilimitado. Apelando al uso de los términos vagos por la comunidad lingüística competente puede dividirse de forma tajante la extension de un término precisando en qué casos se aplica definidamente, en cuáles se aplica indefinidamente y en cuales es indeterminado si se aplica. Esto produce dos órdenes de vaguedad, con lo que se bloquean los argumentos sorites. Finalmente (...) se indaga qué semántica resulta más adecuada para una vaguedad de segundo orden. La vaguedad se basa en una indeterminación determinada en la aplicación de ciertos términos por parte de los hablantes nativos. The two main problems for the supevaluationationist approach to vagueness are deciding which precifications are admissible and unlimited higher-order vagueness. Resorting to the use of vague terms by the competent linguistic community the extension of a term can be sharply divided, making precise in which cases it applies definitely, when it applies indefinitely and when it is undetermined whether it applies. This produces two orders of vagueness, and as a result sorties arguments are blocked. Finally, it is enquired what semantic fits better to second order vagueness. Vagueness is based on a determined indeteminacy concerning the application of certain terms by native speakers. (shrink)

We discuss the philosophical implications of formal results showing the con- sequences of adding the epsilon operator to intuitionistic predicate logic. These results are related to Diaconescu’s theorem, a result originating in topos theory that, translated to constructive set theory, says that the axiom of choice (an “existence principle”) implies the law of excluded middle (which purports to be a logical principle). As a logical choice principle, epsilon allows us to translate that result to a logical setting, where one can (...) get an analogue of Diaconescu’s result, but also can disentangle the roles of certain other assumptions that are hidden in mathematical presentations. It is our view that these results have not received the attention they deserve: logicians are unlikely to read a discussion because the results considered are “already well known,” while the results are simultaneously unknown to philosophers who do not specialize in what most philosophers will regard as esoteric logics. This is a problem, since these results have important implications for and promise signif i cant illumination of contem- porary debates in metaphysics. The point of this paper is to make the nature of the results clear in a way accessible to philosophers who do not specialize in logic, and in a way that makes clear their implications for contemporary philo- sophical discussions. To make the latter point, we will focus on Dummettian discussions of realism and anti-realism. Keywords: epsilon, axiom of choice, metaphysics, intuitionistic logic, Dummett, realism, antirealism. (shrink)