PPP
"Plurals, Predicates, and Paradox: Towards a Type-Free Account"
| Coordinatore | UNIVERSITETET I OSLO
Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie. |
| Nazionalità Coordinatore | Norway [NO] |
| Totale costo | 940˙655 € |
| EC contributo | 940˙655 € |
| Programma | 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) |
| Code Call | ERC-2009-StG |
| Funding Scheme | ERC-SG |
| Anno di inizio | 2010 |
| Periodo (anno-mese-giorno) | 2010-01-01 - 2013-12-31 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
BIRKBECK COLLEGE - UNIVERSITY OF LONDON
Organization address
address: Malet Street contact info |
UK (LONDON) | beneficiary | 432˙885.66 |
| 2 |
UNIVERSITETET I OSLO
Organization address
address: Problemveien 5-7 contact info |
NO (OSLO) | hostInstitution | 507˙769.34 |
| 3 |
UNIVERSITETET I OSLO
Organization address
address: Problemveien 5-7 contact info |
NO (OSLO) | hostInstitution | 507˙769.34 |
Mappa
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Obiettivo del progetto (Objective)
'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.'