Objetivo This project aims to transform our understanding of the logical paradoxes, their solution and significance for mathematics, philosophy and semantics. It seeks to show that some of the key inferences in the paradoxes should not uncritically be blocked, as is customary, but rather be tamed and put to valuable mathematical, philosophical and semantic use. By adopting a richer logical framework than usual, the paradoxes can be transformed from threats to valuable sources of insight. When discovered at the turn of the previous century, the paradoxes caused a foundational crisis in mathematics. Many logicians and philosophers now believe the crisis has been resolved. This project denies that an acceptable resolution has been found and aims to do better. A strong push remains towards paradox. This push arises from the widespread use of (and need for) higher-order logics (HOL), which allow quantification into the positions of predicates or plural noun phrases. Phase I seeks to reveal greater similarities between HOL and set theory than generally appreciated. Phase II explores four arguments that HOL collapses to first-order logic, i.e. that every higher-order entity defines a corresponding first-order entity. These arguments are generally ignored as they threaten to reintroduce the paradoxes. But we show that a properly circumscribed form of collapse is a valuable source of mathematical and semantic insight. Phase III examines controlled forms of collapse using notions of modality and groundedness. This enables us to motivate ZF set theory and valuable semantic theories, explain the nature of cognition about sets and properties, and show that mathematics cannot be fully extensionalized. Phase IV applies these insights to solve the paradoxes and criticize influential uses of HOL. Ámbito científico natural sciencesmathematicspure mathematicsdiscrete mathematicsmathematical logichumanitiesphilosophy, ethics and religionphilosophy Programa(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Tema(s) ERC-SG-ID1 - ERC Starting Grant Interdisciplinary Panel Convocatoria de propuestas ERC-2009-StG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-SG - ERC Starting Grant Institución de acogida UNIVERSITETET I OSLO Aportación de la UE € 507 769,33 Dirección PROBLEMVEIEN 5-7 0313 Oslo Noruega Ver en el mapa Región Norge Oslo og Viken Oslo Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Karen Haugland (Ms.) Investigador principal øystein Linnebo (Dr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (2) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo UNIVERSITETET I OSLO Noruega Aportación de la UE € 507 769,33 Dirección PROBLEMVEIEN 5-7 0313 Oslo Ver en el mapa Región Norge Oslo og Viken Oslo Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Karen Haugland (Ms.) Investigador principal øystein Linnebo (Dr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos BIRKBECK COLLEGE - UNIVERSITY OF LONDON La participación finalizó Reino Unido Aportación de la UE € 432 885,67 Dirección MALET STREET WC1E 7HX London Ver en el mapa Región London Inner London — West Camden and City of London Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Craig Bryce (Mr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos
